PHOTOELECTRON SPECTROSCOPY INVESTIGATION OF BORON AND BORIDE CLUSTERS: THE FOUNDATION OF NEW BORON NANOSTRUCTURES By Weili Li B.S. University of Science and Technology of China, 2009 M.A. Brown University, 2011 A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the Department of Chemistry at Brown University Providence, Rhode Island May 2015 © Copyright 2015 by Weili Li This dissertation by Weili Li is accepted in the present form by the Department of Chemistry as satisfying the dissertation requirement for the degree of Doctor of Philosophy Date__________________ ____________________________________ Lai-Sheng Wang, Advisor Recommended to the Graduate Council Date__________________ ____________________________________ Peter M. Weber, Reader Date__________________ ____________________________________ Richard M. Stratt, Reader Approved by the Graduate Council Date__________________ __________________________________ Peter M. Weber, Dean of the Graduate School iii iii Curriculum Vitae Born, Hangzhou, Zhejiang, China Education Ph.D. Chemistry, Brown University, Providence, RI, USA, August 2014 M.A. Chemistry, Brown University, Providence, RI, USA, May 2011 B.S. Chemistry, University of Science and Technology of China, Hefei, China, July 2009 Honors and Awards Sigma Xi Award for Excellence in Graduate Research (2014) Chinese Government Award for Outstanding Self-Financed Students Abroad (2013) Brown University Chemistry Department Best Poster Award (2010) University Fellowship for First-year Students, Brown University (2009) Publication 1. Photoelectron Spectroscopic and Theoretical Studies of UOx− (x = 3 − 5) W. L. Li, G. J. Cao, G. V. Lopez, T. Jian, J. Su, L. S. Wang, and J. Li, in preparation. 2. A Joint High Resolution Photoelectron Spectroscopy and Theoretical Study on the Vibrational and Electronic Structure of Au2Al2− and Au2Al2 G. V. Lopez, Z. Yang, T. Jian, J. Czekner, W. L. Li, and L. S. Wang, in preparation. 3. The B35 Cluster with a Double-Hexagonal Vacancy: A New and More Flexible Structural Motif for Borophene W. L. Li, Q. Chen, W. J. Tian, H. Bai, Y. F. Zhao, H. S. Hu, J. Li, H. J. Zhai, S. D. Li, and L. S. Wang, J. Am. Chem. Soc. Doi: 10.1021/ja507235s. 4. On the Electronic Structure and Chemical Bonding of Titanium Tetraauride: TiAu4 and TiAu4− Y. Erdogdu, T. Jian, G. V. Lopez, W. L. Li, and L. S. Wang, Chem. Phys. Lett. 610- 611, 23-28 (2014) iv 5. A Photoelectron Spectroscopy and Ab Initio Study of the Structures and Chemical Bonding of the B25− Cluster Z. A. Piazza, I. A. Popov, W. L. Li, R. Pal, X. C. Zeng, A. I. Boldyrev, and L. S. Wang, J. Chem. Phys. 141, 034303, (2014) 6. The Electronic Structure and Chemical Bonding of A Highly Stable and Aromatic Auro-Aluminum Oxide Cluster G. V. Lopez, T. Jian, W. L. Li, and L. S. Wang, J. Phys. Chem. A, 118, 5204−5211, (2014). 7. Observation of an All-Boron Fullerene H. J. Zhai, Y. F. Zhao, W. L. Li, Q. Chen, H. Bai, H. S. Hu, Z. A. Piazza, W. J. Tian, H. G. Lu, Y. B. Wu, Y. W. Mu, G. F. W. Z. P. Liu, J. Li, S. D. Li and L. S. Wang, Nat. Chem. 6, 727-731 (2014). 8. B30−: A Quasiplanar Chiral Boron Cluster W. L. Li, Y. F. Zhao, H. S. Hu, J. Li and L. S. Wang, Angew. Chem. Int. Ed. 22, 5540-5545 (2014). (featured on the Frontispiece) 9. Understanding Boron through Size-Selected Clusters: Structure, Chemical Bonding, and Fluxionality P. Sergeeva, I. A. Popov, Z. A. Piazza, W. L. Li, C. Romanescu, L. S. Wang and A. I. Boldyrev, Acc. Chem. Res., 47, 1349-1358 (2014). 10. Strong Electron Correlation in UO2−: A Photoelectron Spectroscopy and Relativistic Quantum Chemistry Study W. L. Li, J. Su, T. Jian, G. V. Lopez, H. S. Hu, G. J. Cao, J. Li, and L. S. Wang, J. Chem. Phys., 140, 094306 (2014). 11. Hexagonal Bipyramidal [Ta2B6]−/0 Clusters: B6 Rings as Structural Motifs W. L. Li, L. Xie, T. Jian, C. Romanescu, X. Huang, and L. S. Wang, Angew. Chem. Int. Ed. 3, 1312-1316 (2014) v 12. Planar Hexagonal B36 as a Potential Basis for Extended Single-Atom Layer Boron Sheets Z. A. Piazza, H. S. Hu, W. L. Li, J. Li, and L. S. Wang, Nat. Commun. 5:3113 doi: 10.1038/ncomms4113 (2014). 13. Complexes between Planar Boron Clusters and Transition Metals: A Photoelectron Spectroscopy and Ab Initio Study of CoB12− and RhB12− I. A. Popov, W. L. Li, Z. A. Piazza, A. I. Boldyrev, and L. S. Wang, J. Phys. Chem. A, DOI: 10.1021/jp411867q. 14. Probing the Electronic Structures of Low Oxidation-State Uranium Fluoride Molecules UFx− (x = 2 − 4) W. L. Li, H. S. Hu, T. Jian, G. V. Lopez, J. Su, J. Li, and L. S. Wang, J. Chem. Phys. 139, 244303 (2013) 15. Pi and Sigma Double Conjugations in Boronyl Polyboroene Nanoribbons: Bn(BO)2− and Bn(BO)2 (n = 5 − 12) H. J. Zhai, Q. Chen, H. Bai, H.G. Lu, W. L. Li, S. D. Li, and L. S. Wang, J. Chem. Phys. 139, 174301 (2013). 16. Geometric and Electronic Factors in the Rational Design of Transition-Metal-Centered Boron Molecular Wheels Romanescu, T. R. Galeev, W. L. Li, A. I. Boldyrev, and L. S. Wang, J. Chem. Phys.138, 134315 (2013). 17. A Combined Photoelectron Spectroscopy and Ab initio Study of the Quasi-planar B24− Cluster I. A. Popov, Z. A. Piazza, W. L. Li, L. S. Wang, and A. I. Boldyrev, J. Chem. Phys. 139, 144307 (2013) 18. On the Way to the Highest Coordination Number in the Planar Metal-Centred Aromatic Ta©B10− Cluster: Evolution of the Structures of TaBn− (n = 3 – 8) vi W. L. Li, A. S. Ivanov, J. Federi, C. Romanescu, I. Černušák, A. I. Boldyrev, and L. S. Wang, J. Chem. Phys. 139, 104312 (2013) 19. A Photoelectron Spectroscopy and Density Functional Study of Di-Tantalum Boride Clusters: Ta2Bx− (x = 2 – 5) L. Xie, W. L. Li, C. Romanescu, X. Huang, and L. S. Wang, J. Chem. Phys. 138, 034308 (2013). 20. Transition-Metal-Centered Monocyclic Boron Wheel Clusters (M©Bn): A New Class of Aromatic Borometallic Compounds C. Romanescu, T. R. Galeev, W. L. Li, A. I. Boldyrev, and L. S. Wang, Acc. Chem. Res. 46, 350-358 (2013). 21. Photoelectron Spectroscopy and Ab Initio Study of Boron-Carbon Mixed Clusters – CB9− and C2B9− T. R. Galeev, W. L. Li, C. Romanescu, I. Černušák, L. S. Wang, and A. I. Boldyrev, J. Chem. Phys. 137, 234306 (2012). 22. Experimental and Computational Evidence of Octa- and Nona-Coordinated Planar Iron-Doped Boron Clusters: Fe©B8− and Fe©B9− C. Romanescu, T. R. Galeev, A. P. Sergeeva, W. L. Li, L. S. Wang, and A. I. Boldyrev, J. Organomet. Chem. 721-722, 148-154 (2012). 23. B22− and B23−: All-Boron Analogues of Anthracene and Phenanthrene A. P. Sergeeva, Z. A. Piazza, C. Romanescu, W. L. Li, A. I. Boldyrev, and L. S. Wang, J. Am. Chem. Soc. 134, 18065-18073 (2012). 24. Geometrical Requirements for Transition-Metal-Centered Aromatic Boron Wheels: the Case of VB10− W. L. Li, C. Romanescu, Z. A. Piazza, and L. S. Wang, Phys. Chem. Chem. Phys. 14, 13663-13669 (2012). 25. Elongation of Planar Boron Clusters by Hydrogenation: Boron Analogues of Polyenes vii W. L. Li, C. Romanescu, T. Jian, and L. S. Wang, J. Am. Chem. Soc. 134, 13228- 13231 (2012). 26. A Photoelectron Spectroscopy and Ab Initio Study of B21–: Negatively Charged Boron Clusters Continue to be Planar at 21 Z. A. Piazza, W. L. Li, C. Romanescu, A. P. Sergeeva, L.S. Wang, and A. I. Boldyrev, J. Chem. Phys. 136, 104310 (9) (2012). 27. Transition-Metal-Centered Nine-Membered Boron Rings: M©B9 and M©B9– (M = Rh, Ir) W. L. Li, C. Romanescu, T. R. Galeev, Z. A. Piazza, A. I. Boldyrev, and L. S. Wang, J. Am. Chem. Soc. 134, 165-168 (2012). 28. Observation of the Highest Coordination Number in Planar Species: Decacoordinated Ta©B10– and Nb©B10– Anions T. R. Galeev, C. Romanescu, W. L. Li, L.S. Wang, and A.I. Boldyrev, Angew. Chem. Int. Ed. 51, 2101-2105 (2012). 29. Observation of Metal-Centered Monocyclic Boron Rings as a New Class of Aromatic Compounds C. Romanescu, T. R. Galeev, W. L. Li, A. I. Boldyrev, and L.S. Wang, Angew. Chem. Int. Ed. 50, 9334-9337 (2011). 30. Aluminum Avoids the Central Position in AlB9− and AlB10−: Photoelectron Spectroscopy and Ab Initio Study W. L. Li, C. Romanescu, T.R. Galeev, L. S. Wang, and A. I. Boldyrev, J. Phys. Chem. A 115, 10391-10397 (2011). 31. Valence Isoelectronic Substitution in the B8– and B9– Molecular Wheels by an Al Dopant Atom: Umbrella-like Structures of AlB7– and AlB8– T.R. Galeev, C. Romanescu, W. L. Li, L.S. Wang, and A. I. Boldyrev, J. Chem. Phys. 135, 104301 (8) (2011). (featured on the cover) viii 32. Planarization of B7– and B12– Clusters by Isoelectronic Substitution: AlB6− and AlB11– C. Romanescu, A. P. Sergeeva, W. L. Li, A. I. Boldyrev, and L. S. Wang, J. Am. Chem. Soc. 133, 8646-8653 (2011). 33. Molecular Wheel to Monocyclic Ring Transition in Boron-Carbon Mixed Clusters C2B6– and C3B5– T. R. Galeev, A. S. Ivanov, C. Romanescu, W. L. Li, K. V. Bozhenko, L. S. Wang, and A. I. Boldyrev, Phys. Chem. Chem. Phys. 13, 8805-8810 (2011). Conferences Gordon Research Conferences on Clusters, Nanocrystals, and Nanostructures (2013) Poster: PES Studies of Strongly Correlated Electronic Systems: Uranium Oxides and Uranium Fluorides 68th OSU International Symposium on Molecular Spectroscopy (2013) Talk: UO2−: a Highly Correlated System Gordon Research Seminar on Atomic and Molecular Interactions (2012) Poster: Transition-Metal-Doped Planar Boron Clusters: A New Class of Highly Aromatic Compounds 67th OSU International Symposium on Molecular Spectroscopy (2012) Talk: Photoelectron Spectroscopy of Al-Doped Boron Clusters Gordon Research Conferences on Clusters, Nanocrystals, and Nanostructures (2011) Poster: Photoelectron Spectroscopy of Aluminum Boron Clusters ix To my family x Acknowledgments This dissertation would not have been possible without the support of many people. I am honored to show my sincere gratitude and appreciation to the following people. First of all, I would like to express my utmost appreciation to my advisor, Professor Lai-Sheng Wang, who guided me into the world of cluster chemistry and photoelectron spectroscopy. Together, we have made many fantastic discoveries over the past five years and received worldwide attention. His trust and encouragement have been vital for me to overcome the difficulties along this journey. Without him, all of this would not have been possible. Dr. Wang embodies the highest standard of excellence as a scientist, mentor, instructor, and role model. Our theoretical collaborators, Professors Alexander I. Boldyrev (Utah State University), Jun Li (Tsinghua University), Si-Dian Li (Shanxi University), Xin Huang (Fuzhou University) and Xiao Cheng Zeng (University of Nebraska-Lincoln) deserve significant credit for the success of this thesis. Most of the work presented in this thesis is the outcome of our joint effort. It has been such a pleasure and a unique opportunity to collaborate and learn from so many distinguished scholars. I would also like to express my gratitude to my thesis committee, Professor Peter M. Weber and Professor Richard M. Stratt for providing me with thought-provoking xi discussions, scientific insights, and encouragement throughout my graduate career. I gratefully acknowledge my co-workers, Dr. Constantin Romanescu, Dr. Gary V. Lopez, Tian Jian, and Zachary A. Piazza, who have contributed to the success of this thesis. I would also like to thank former and current Wang group members, Prof. Chuan-Gang Ning, Dr. Hong-Tao Liu, Dr. Zheng Yang, Dr. Iker León, Prof. Yusuf Erdogdu, Dr. Jing Chen, Dr. Phuong D. Dau, Dao-Ling Huang, Qian-Fan Zhang, Guo-Zhu Zhu, and Joseph Czekner for their scientific discussions and friendship. I am grateful to the faculty and stuff in the Chemistry Department at Brown University. In particular, I would like to acknowledge Al Tente, Kenneth Talbot, Randy Goulet, Margaret Doll, and Eric Friedfeld for their help. My research career would not have been as fun without the love and support of my family and friends. I am deeply grateful to my parents, brother, and sister-in-law, who always encourage me to make my own decisions, and are always there to support me. My special acknowledgement goes to my best friend since college, Xinxin Cheng. Together, we shared happiness, pain, challenges and success. Finally, I would like to thank my boyfriend, Yiming Chen, for his love and support, for sharing my wish to reach the goal of completing this task, and for celebrating good moments and enduring the bad. xii Table of Contents Acknowledgments......................................................................................................................... xii  Table of Contents ......................................................................................................................... xiv  List of Tables ................................................................................................................................ xx  List of Figures ............................................................................................................................. xxii  List of Abbreviations ................................................................................................................. xxix  Chapter 1  Introduction ............................................................................................................... 1  1.1  Gas Phase Clusters ................................................................................................ 2  1.2  Cluster Sources ...................................................................................................... 4  1.3  Spectroscopic Techniques for Cluster Structure Determination ........................... 6  1.3.1  Photoelectron Spectroscopy (PES) ............................................................... 7  1.3.2  Zero-eV Electron Kinetic Energy (ZEKE) Spectroscopy .......................... 16  1.3.3  Velocity Map Imaging (VMI) PES ............................................................ 17  1.3.4  Resonant Two-Photon Ionization Spectroscopy ........................................ 18  1.3.5  Time-Resolved Photoelectron Spectroscopy (TRPES) .............................. 18  1.3.6  Ion Mobility Spectrometry (IMS) .............................................................. 19  1.3.7  Gas-Phase Electron Diffraction (GED) ...................................................... 20  1.3.8  Infrared Multi-Photon Dissociation Spectroscopy ..................................... 23  1.3.9  Magnetic Deflection Experiment ............................................................... 23  1.3.10  Collision Induced Dissociation (CID) ........................................................ 25  1.3.11  Chemisorption Experiments ....................................................................... 26  1.4  Our Approach: Joint PES and Quantum Chemistry Study ................................. 26  1.5  Motivation and Objectives .................................................................................. 27  Chapter 2  Experimental Setup ................................................................................................. 31  xiii 2.1  Laser Vaporization Cluster Source ..................................................................... 32  2.2  Time-of-Flight Mass Spectrometer ..................................................................... 34  2.3  Mass Selection and Momentum Deceleration ..................................................... 36  2.4  Magnetic-Bottle Time-of-Flight Photoelectron Analyzer ................................... 38  2.5  Performance of the Photoelectron Spectrometer ................................................. 40  2.5.1  CAMAC Interface ...................................................................................... 40  2.5.2  National Instruments PXI Platform ............................................................ 44  2.6  Mass and Energy Calibration .............................................................................. 44  2.7  Temperature Effect and Control .......................................................................... 48  2.8  Theoretical Calculations ...................................................................................... 50  2.8.1  Global Minimum Structure Search............................................................. 50  2.8.2  Vertical and Adiabatic Detachment Energy Calculations .......................... 52  2.8.3  Chemical Bonding Analyses ...................................................................... 52  Chapter 3  A World of Flat Boron Clusters .............................................................................. 54  3.1  Experimental Results........................................................................................... 59  3.2  Theoretical Results .............................................................................................. 63  3.3  Comparison between Experimental and Theoretical Results .............................. 72  3.4  Chemical Bonding Analyses ............................................................................... 83  3.5  Conclusions ......................................................................................................... 94  Chapter 4  On the Way to Borophenes ..................................................................................... 96  4.1  Planar Hexagonal B36 as a Potential Basis for Extended Single-atom Layer Boron Sheets ............................................................................................................ 97  4.1.1  Experimental Results .................................................................................. 97  4.1.2  Theoretical Results ................................................................................... 101  4.1.3  Comparison between Experimental and Theoretical Results ................... 102  4.1.4  The Electronic Structure and Stability of the Hexagonal B36 .................. 105  xiv 4.1.5  The Relationship of the Hexagonal B36 and 2D Boron Sheets................. 108  4.2  B30−: Quasiplanar Chiral Boron Cluster ............................................................ 111  4.2.1  Experimental Results ................................................................................ 112  4.2.2  Theoretical Results ................................................................................... 115  4.2.3  Comparison between Experimental and Theoretical Results ................... 116  4.2.4  Chemical Bonding Analyses and Stability of Enantiomers ..................... 119  4.2.5  Conclusions .............................................................................................. 121  4.3  The B35 Cluster with a Double-Hexagonal Vacancy (DHV): A New and More Flexible Structural Motif for Borophene ............................................................... 121  4.3.1  Experimental Results ................................................................................ 122  4.3.2  Theoretical Results ................................................................................... 123  4.3.3  Comparison between Experimental and Theoretical Results ................... 125  4.3.4  Chemical Bonding Analyses and Stability of B35− ................................... 126  4.3.5  Conclusions .............................................................................................. 132  4.4  Structural Evolution of Anion Boron Clusters .................................................. 133  Chapter 5  An All-Boron Fullerene ........................................................................................ 135  5.1  Experimental Results......................................................................................... 136  5.2  Theoretical Results ............................................................................................ 138  5.3  Comparison between Experimental and Theoretical Results ............................ 141  5.4  The Electronic Structure and Stability of B40–/0 ................................................ 141  5.5  Discussion ......................................................................................................... 145  Chapter 6  Transition Metal Centered Boron Monocyclic Molecular Wheels ....................... 147  6.1  The Design Principle for Metal Centered Boron Wheel Clusters (M©Bnk−) .... 149  6.2  Case Studies of M©B8− Molecular Wheels: Co©B8− and Fe©B8− ................... 151  6.2.1  Experimental Results ................................................................................ 152  6.2.2  Theoretical Results ................................................................................... 153  6.2.3  Comparison between Experimental and Theoretical Results ................... 157  6.2.4  Discussion ................................................................................................ 159  xv 6.3  Case Studies of M©B9− Molecular Wheels: Fe©B9− and Ru©B9− ................... 160  6.3.1  Experimental Results ................................................................................ 161  6.3.2  Theoretical Results ................................................................................... 162  6.3.3  Comparison between Experimental and Theoretical Results ................... 163  6.3.4  Discussion ................................................................................................ 167  6.4  Case Studies of M©B9 Molecular Wheels: Rh©B9 and Ir©B9 ......................... 169  6.4.1  Experimental Results ................................................................................ 169  6.4.2  Theoretical Results ................................................................................... 171  6.4.3  Comparison between Experimental and Theoretical Results ................... 172  6.4.4  Discussion ................................................................................................ 174  6.5  Case Studies of M©B92− Molecular Wheels: V©B92−, NbB92−, TaB92− ........... 176  6.5.1  Experimental Results ................................................................................ 176  6.5.2  Theoretical Results ................................................................................... 178  6.5.3  Discussion and Interpretation of the Photoelectron Spectra .................... 180  6.6  Observation of the Highest Coordination Number in Planar Species: Nb©B10− and Ta©B10− ........................................................................................................... 187  6.6.1  Experimental Results ................................................................................ 188  6.6.2  Theoretical Results and Comparison with Experimental Results ............ 190  6.6.3  Discussion ................................................................................................ 195  6.7  Geometrical Requirements for Transition-Metal-Centered Aromatic Boron Wheels: the Case of VB10− ..................................................................................... 196  6.7.1  Experimental Results ................................................................................ 197  6.7.2  Theoretical Results and Comparison with Experimental Results ............ 199  6.7.3  Discussion ................................................................................................ 205  6.8  On the Way to the Highest Coordination Number in the Planar Metal-Centered Aromatic Ta©B10− Cluster: Evolution of the Structures of TaBn−(n = 3 – 8) ....... 205  6.8.1  Introduction .............................................................................................. 205  6.8.2  Experimental Results ................................................................................ 206  6.8.3  Theoretical Results ................................................................................... 209  6.8.4  Comparison between Experimental and Theoretical Results ................... 214  xvi 6.8.5  Structural Evolution and Chemical Bonding in TaBn– ............................. 218  6.8.6  Conclusions .............................................................................................. 224  6.9  Geometric Requirements ................................................................................... 225  6.10  Conclusions and Perspectives ........................................................................... 228  Chapter 7  Boron Clusters as the Foundation of New Boron Nanostructures ........................ 230  7.1  Elongation of Planar Boron Clusters by Hydrogenation: Boron Analogues of Polyenes ................................................................................................................. 232  7.1.1  Introduction .............................................................................................. 232  7.1.2  Experimental Results ................................................................................ 233  7.1.3  Theoretical Results and Comparison with Experimental Results ............ 236  7.1.4  Chemical Bonding Analyses and Discussion ........................................... 239  7.2  π and σ Double Conjugations in Boronyl Polyboroene Nanoribbons: Bn(BO)2− and Bn (BO)2 (n = 5 − 12) ...................................................................... 243  7.2.1  Introduction .............................................................................................. 243  7.2.2  Experimental Results ................................................................................ 244  7.2.3  Theoretical Results ................................................................................... 246  7.2.4  Comparison between Experimental and Theoretical Results ................... 248  7.2.5  Discussion ................................................................................................ 249  7.2.6  Conclusions .............................................................................................. 253  7.3  Structural Revaluation of Di-Tantalum Boride Clusters: Ta2Bx− (x = 2 – 5) .... 254  7.3.1  Introduction .............................................................................................. 254  7.3.2  Experimental Results ................................................................................ 255  7.3.3  Theoretical Results ................................................................................... 264  7.3.4  Comparison between Experimental and Theoretical Results ................... 268  7.3.5  Structural Evolution ................................................................................. 273  7.3.6  Conclusions .............................................................................................. 274  7.4  Hexagonal Bipyramidal Ta2B6−/0 Clusters: B6 Rings as Structural Motifs ....... 275  7.4.1  Introduction .............................................................................................. 275  7.4.2  Experimental Results ................................................................................ 275  7.4.3  Theoretical Results and Comparison with Experimental Results ............ 276  xvii 7.4.4  Chemical Bonding Analyses .................................................................... 280  7.4.5  Conclusions .............................................................................................. 282  7.5  Complexes between Planar Boron Clusters and Transition Metals: the case of CoB12– and RhB12– ................................................................................................. 283  7.5.1  Introduction .............................................................................................. 283  7.5.2  Experimental Results ................................................................................ 284  7.5.3  Theoretical Results ................................................................................... 286  7.5.4  Comparison between Experimental and Theoretical Results ................... 289  7.5.5  Chemical Bonding Analyses .................................................................... 290  7.5.6  Conclusions .............................................................................................. 293  Chapter 8  Gaseous Uranium Compounds ............................................................................. 294  8.1  Strong Electron Correlation in UO2 − ................................................................ 295  8.1.1  Introduction .............................................................................................. 295  8.1.2  Experimental Results ................................................................................ 297  8.1.3  Theoretical Results and Comparison with Experiment ............................ 300  8.1.4  Extensive two-electron Transitions and Strong Electron Correlation Effects ....................................................................................................... 309  8.1.5  Conclusions .............................................................................................. 316  8.2  Probing the Electronic Structures of low Oxidation-State Uranium Fluoride Molecules UFx− (x = 2 − 4). ................................................................................... 317  8.2.1  Introduction .............................................................................................. 317  8.2.2  Experimental Results ................................................................................ 318  8.2.3  Theoretical Results ................................................................................... 325  8.2.4  Discussion ................................................................................................ 326  8.2.5  Conclusion ................................................................................................ 333  Chapter 9  Concluding Remarks and Perspective .................................................................. 334  References ................................................................................................................................... 339  xviii List of Tables 3.1 Comparison of the experimental VDEs with the calculated values for B21–.. .................... 74  3.2 Comparison of the experimental VDEs with the calculated values for B22− and B23−. ..... .78  3.3 Comparison of the experimental VDEs with the calculated values for B24−.. .................... 80  3.4 Open-shell T1 diagnostic values for B24−. .......................................................................... 82  4.1 Comparison of the experimental VDEs with the calculated values for B36−. ................... 105  4.2 Comparison of the experimental VDEs with the calculated values for B30−. ................... 118  4.3 Comparison of the experimental VDEs with the calculated values for B35−. ................... 126  6.1 Observed VDEs for CoB8– compared with theoretical values. ........................................ 158  6.2 Observed VDEs for FeB8– compared with theoretical values. ......................................... 159  6.3 Observed VDEs for RuB9– compared with theoretical values. ........................................ 167  6.4 Observed VDEs for FeB9– compared with theoretical values. ......................................... 167  6.5 Comparison of the experimental VDEs with the calculated values of M©B9−. ............... 175  6.6 Observed VDEs of VB9−, NbB9− and TaB9− compared with the calculated values for the lowest energy isomer in each case.............................................................................. 186  6.7 Observed VDEs for TaB10− and NbB10− compared with theoretical values.. ................... 193  6.8 Observed VDEs of VB10– and comparion with theoretical values.. ................................. 204  6.9 Experimental VDEs compared with calculated VDEs for the global minimum structure and low-lying isomers of TaB3−, TaB4− and TaB5−. .......................................... 212  6.10 Experimental VDEs compared with calculated VDEs for the global minimum structure and low-lying isomers of TaB6−, TaB7− and TaB8−.. ......................................... 213  7.1 Observed ADEs, VDEs and vibrational frequencies for the ground state photodetachment transitions of D2Bn– (n = 7 – 12), compared with calculations. ........... 239  xix 7.2 Experimental ground sate ADEs and VDEs from the photoelectron spectra of BxO2– (x = 7  14), compared to theoretical calculations. .......................................................... 246  7.3 Experimental VDEs for Ta2Bx− (x = 2 − 3) compared to the calculated VDEs from the anion ground-state. ........................................................................................................... 262  7.4 Experimental VDEs for Ta2Bx− (x = 4 − 5) compared to the calculated VDEs from the anion ground state. ........................................................................................................... 263  7.5 Relative energies of the low-lying states of the Ta2Bx−/0 (x = 2 − 5) clusters at the BP86 level (within 0.10 eV), and comparisons with those from the CCSD(T) single- point calculations .............................................................................................................. 268  7.6 Observed VDEs for Ta2B6− compared with theoretical values. ...................................... 280  7.7 Observed VDEs of CoB12− and RhB12− compared with the calculated values................. 288  8.1 Observed VDEs of UO2− and comparison with theoretical calculations at different levels of theory with inclusion of spin-orbit coupling. .................................................... 311  8.2 All the observed features from the photoelectron spectra and their comparison with the CASSCF/CASPT2/SO calculation results of UO2−. .................................................. 312  8.3 The ground state and the lowest excited states of UO2−................................................... 314  8.4 The calculated vertical excitation energies of UO2 at the SR CASPT2 level. ................. 315  8.5 Observed VDEs and the first ADE for UFx− (x = 2 − 4) and the U-F stretching frequencies of the neutral ground state............................................................................. 331  8.6 Molecular symmetries, electron configurations, geometries and energies of UFx and UFx− (x = 1 – 6)................................................................................................................. 331  8.7 The calculated Mulliken charges and bond orders of UFx− (x = 1 − 6) based on different bonding index schemes. ..................................................................................... 332  xx List of Figures 1.1 A schematic view of photodetachment.. ............................................................................ 11  1.2 A schematic view of single electron picture of photodetachment process......................... 12  2.1 A schematic view of the PES apparatus equipped with a laser vaporization cluster source.................................................................................................................................. 32  2.2 A schematic view of the laser vaporization cluster source. ............................................... 34  2.3 A time-of-flight mass spectrum of Bn− clusters using a hot pressed 11B target. ................. 36  2.4 A schematic view of the mass gate and momentum decelerator. ....................................... 38  2.5 The time sequence in one experimental cycle for generating clusters and taking photoelectron spectrum from a cluster anion. .................................................................... 43  2.6 Photoelectron spectra of Bi− at three photon energies for energy calibration. ................... 47  3.1 The structures of Bn− (n = 3 − 20)....................................................................................... 58  3.2 Experimentally measured ADEs of Bn− (n = 3 − 20).......................................................... 58  3.3 PES spectrum of (a) B21–, (b) B22−, (c) B23− and (d) B24− at 193 nm. ................................. 62  3.4 The low-lying isomers of B21–. ........................................................................................... 65  3.5 The low-lying isomers of B22−............................................................................................ 67  3.6 The low-lying isomers of B23−. .......................................................................................... 68  3.7 The low-lying isomers of B24–. ........................................................................................... 71  3.8 Comparison of the experimental and simulated PES spectrum of B24−. ............................ 82  3.9 AdNDP analyses for isomer I of B21−. ............................................................................... 84  3.10 AdNDP analyses for isomer II of B21−. .............................................................................. 85  3.11 Elucidation of the analogy between the π bonding in the flattened B222− and anthracene. .......................................................................................................................... 87  3.12 Elucidation of the analogy between the π bonding in B23− and phenanthrene. .................. 90  xxi 3.13 AdNDP analyses of the neutral B24 (a) and the dianion B242− (a and b) at the geometry of B24−. ................................................................................................................................ 93  4.1 Photoelectron spectrum of B36– and comparison with simulation. ................................... 100  4.2 The global minimum and low-lying isomers of B36− and B36. ......................................... 102  4.3 Chemical bonding analyses for the hexagonal D6h structure of B36. ................................ 108  4.4 Relationship between B36 and borophene. ....................................................................... 110  4.5 Photoelectron spectrum of B30− at 193 nm (a) and simulated spectrum of isomer I/II (b) and isomer III (c)........................................................................................................ 113  4.6 The global minimum and low-lying isomers of B30−. ...................................................... 114  4.7 The global minimum and low-lying isomers for B30. ...................................................... 114  4.8 AdNDP chemical bonding analyses of the closed-shell B30 (C1, 1A). ............................. 120  4.9 Potential energy curve showing the transition state between the two enantiomers of B30− via a bending mode. .................................................................................................. 120  4.10 Experimental photoelectron spectrum of B35– at 193 nm (a), in comparison with simulated spectrum (b). .................................................................................................... 124  4.11 The optimized global-minimum structures of B35– (Cs, 1A) and neutral B35 (Cs, 2A) at the PBE0/6-311+G* level............................................................................................. 124  4.12 Comparison of the canonical π CMOs of (a) B35– (Cs, 1A) and (b) C22H12 (C2v, 1A1). ... 130  4.13 Results of AdNDP analyses for (a) B35– (Cs, 1A), (b) C22H12 (C2v, 1A1). ........................ 131  4.14 Schematic drawings of borophenes constructed from two different arrangements of the planar hexagonal B35 motif.. ....................................................................................... 132 4.15 The structures of the main contributors to the photoelectron spectra of boron clusters (Bn−, n = 3 − 24, 30, 35, 36).   xxii 5.1 Experimental photoelectron spectrum of B40– at (a) 266 nm, (b) 193 nm, in comparison with simulated spectrum based on the (c) quasi-planar structure 1 (Cs, 2A'), and (d) cage-like fullerene structure 2 (D2d, 2B2). ................................................... 137  5.2 Top and side views of the global minimum and low-lying isomers of B40– and B40 at PBE0/6-311+G* level. ..................................................................................................... 139  5.3 Configurational energy spectra at PBE0/6-311+G* level. a, B40–. b, B40. ....................... 140  5.4 Chemical bonding analyses for the D2d B40 fullerene. ..................................................... 142  5.5 Comparison of the AdNDP bonding patterns of (a) Cs B402– and (b) C2v C27H13+. .......... 145  6.1 Photoelectron spectra of CoB8− at (a) 193 nm and (b) 266 nm. ....................................... 153  6.2 Photoelectron spectra of FeB8− at (a) 193 nm and (b) 266 nm. ........................................ 153  6.3 (a) Optimized structures and (b) CMOs of Co©B8− and Co©B8. ................................... 155  6.4 (a) Optimized structures for Fe©B82/−/0, (b) CMOs of Fe©B8−........................................ 156  6.5 AdNDP analyses for Co©B8−. .......................................................................................... 160  6.6 Photoelectron spectra of RuB9− at (a) 193 nm and (b) 266 nm. ....................................... 162  6.7 Photoelectron spectra of FeB9− at (a) 193 nm and (b) 266 nm. ........................................ 162  6.8 (a) Optimized structures, and (b) MOs for Ru©B9− and Ru©B9. .................................. 165  6.9 (a) Optimized structures, and (b) MOs for Fe©B9− and Fe©B9. ...................................... 166  6.10 AdNDP analyses for Ru©B9−. .......................................................................................... 169  6.11 Photoelectron spectra of RhB9− and IrB9− at 355, 266, and 193 nm.. .............................. 171  6.12 Optimized geometries of (a) Rh©B9−, (b) Ir©B9−, (c) Rh©B9, (d) Ir©B9 and valence CMOs of (e) Rh©B9 and (f) Ir©B9.. ................................................................................ 172  6.13 Photoelectron spectra of VB9− at (a) 193 nm and (b) 266 nm, NbB9− at (c) 193 nm and (d) 266 nm, and Ta B9− at (e) 193 nm and (f) 266 nm. .............................................. 178  6.14 Global minimum structures of VB9−, NbB9−, and TaB9−. ................................................ 179  xxiii 6.15 Optimized structures of neutral VB9, NbB9, and TaB9 and the doubly charged VB92−, NbB92−, and TaB92− clusters. ............................................................................................ 180  6.16 Valence CMO plots of V©B92− (D9h, 1A1'). ..................................................................... 184  6.17 Valence CMO plots of (a) V©B9−, (b) Nb©B9− and (c) Ta©B9−. .................................... 185  6.18 Photoelectron spectra of TaB10− at (a) TaB10− 193 nm, (b) 266 nm, NbB10− at (c) TaB10− 193 nm, (d) 266 nm. ............................................................................................. 189  6.19 Structures of the two lowest energy isomers of a) TaB10− and b) NbB10−. ...................... 192  6.20 (a) CMOs and (b) chemical bonding pattern of Ta©B10−. ............................................... 194  6.21 Photoelectron spectra of VB10– at (a) 355 nm, (b) 266 nm, and (c) 193 nm. ................... 198  6.22 The low-lying structures of VB10–. ................................................................................... 202  6.23 Comparison of the detailed structures of (a) the global minimum isomer I (1A C2) and (b) the low-lying isomer II (3A2, C2v) with that of their optimized neutral (2A1, C2v) (c).. ................................................................................................................................. 202  6.24 Simulated spectra of (a) isomer I and (b) isomer II, compared with (c) experimental spectrum at 193 nm. ......................................................................................................... 203  6.25 Photoelectron spectra of TaBn− (n = 3 – 8) at 193 nm. .................................................... 208  6.26 The global minimum structures and low-lying isomers of (a) TaB3−, (b) TaB4−, (c) TaB5−, and (d) TaB6−. ...................................................................................................... 211  6.27 The global minimum structures of (a) TaB7−, (b) TaB8−, (c) TaB9−, and (d) TaB10−.. ..... 211  6.28 Results of AdNDP analyses for the global minimum structures of TaB3− (I.1), TaB4− (II.1), and TaB5− (III.1)..................................................................................................... 222  6.29 Results of AdNDP analyses for the global minimum structures of TaB6− (IV.1) and TaB7− (V.1). ...................................................................................................................... 223  6.30 Results of AdNDP analyses for the C8v and Cs TaB8−...................................................... 224  xxiv 6.31 Comparison of the photoelectron spectrum of VB10– with those of NbB10– and TaB10– at 193 nm. ......................................................................................................................... 227  6.32 The relative energies of MB10− (M = V, Nb, Ta) between the wheel-type structures and the boat-like structures............................................................................................... 228  7.1 Photoelectron spectra of D2Bn– (n = 7 – 12). (A) D2B7– at 266 nm. (B) D2B8– at 355 nm. (C) D2B9– at 355 nm. (D) D2B10– at 266 nm. (E) D2B11– at 266 nm. (F) D2B12– at 355 nm. ............................................................................................................................. 234  7.2 Photoelectron spectra of D2Bn– (n = 7 – 12) at 193 nm compared with simulated spectra for the optimized global minimum ladder structures. .......................................... 235  7.3 Optimized global minimum structures for H2Bn– (n = 7 – 12). ........................................ 238  7.4 Chemical bonding analyses using the AdNDP method. (A) H2B7–. (B) H2B8. (C) H2B9–. (D) H2B102–. (E) H2B11–. (F) H2B12. ...................................................................... 241  7.5 Comparison of the π CMOs of the boron cluster dihydrides with those of conjugated alkenes. (A) The π orbitals of H2B7–, H2B8, H2B9–, and butadiene (C4H6). (B) The π orbitals of H2B102–, H2B11–, H2B12, and 1,3,5-hexatriene (C6H8). .................................... 242  7.6 Photoelectron spectra of BxO2– (x = 7  14) at 193 nm.. .................................................. 245  7.7 Optimized double-chain nanoribbon global-minimum structures for Bn(BO)2– (n = 4  12). ................................................................................................................................ 247  7.8 The experimental EAs of Bn(BO)2 (n = 4  12; solid dots) as a function of n, compared to theoretical values at the single-point CCSD(T) level (empty dots). ........... 248  7.9 Comparison of the delocalized  CMOs of C2H4 (a) and B4(BO)2 (b), C4H6 (c) and B8(BO)2 (d), and C6H8 (e) and B12(BO)2 (f). .................................................................... 250  7.10 AdNDP analyses for closed-shell Bn(BO)2, Bn(BO)2–, and Bn(BO)22– (n = 4  12).. ...... 252  7.11 AdNDP analyses for the boronyl polyboroenes, B16(BO)2 and B20(BO)2. ...................... 253  7.12 Photoelectron spectra of Ta2B2− at (a) 355 nm, (b) 266 nm, (c) 193 nm. ........................ 258  xxv 7.13 Photoelectron spectra of Ta2B3− at (a) 355 nm, (b) 266 nm, (c) 193 nm. ........................ 259  7.14 Photoelectron spectra of Ta2B4− at (a) 355 nm, (b) 266 nm, (c) 193 nm. ........................ 260  7.15 Photoelectron spectra of Ta2B5− at (a) 355 nm, (b) 266 nm, (c) 193 nm. ........................ 261  7.16 Low-lying isomers for (a) Ta2B2−, (b) Ta2B2, (c) Ta2B3−, (d) Ta2B3, (e) Ta2B4−, (f) Ta2B4, (g) Ta2B5−, and (h) Ta2B5 at the BP86 level of theory.. ........................................ 267  7.17 Comparison of the experimental spectra of Ta2Bx− (x = 2 − 5) with the simulated spectra from the lowest energy structures.. ...................................................................... 272  7.18 The highest occupied orbitals and the Mülliken spin density for (a) Ta2B2−, (b) Ta2B3− (C2v, 3B2), (c) Ta2B4− (C2v, 2A1), and (d) Ta2B5− (C2v, 1A1). ................................. 273  7.19 Structure evolution of Ta2Bx− (x = 2 − 5). ........................................................................ 274  7.20 Photoelectron spectra of Ta2B6− at (a) 532 nm, (b) 355 nm, (c) 266 nm and (d) 193 nm. ................................................................................................................................. 277  7.21 Optimized structures of Ta2B6− and Ta2B6 at the BP86/Ta/ Stuttgart+2f1g/B/aug-cc- pVTZ level of theory.. ...................................................................................................... 278  7.22 Valence conical orbitals of Ta2B6− at the BP86/Ta/Stuttgart+2f1g /B/aug-cc-pVTZ level of theory. .................................................................................................................. 281  7.23 Chemical bonding analyses of Ta2B6 using the AdNDP method. .................................... 282  7.24 Photoelectron spectra of CoB12− (a,b) and RhB12− (c,d) at 193 nm and 266 nm. The 266 nm spectra offer better spectral resolution than the 193 nm spectra. ........................ 286  7.25 Two views of the global minimum structures of (a) RhB12− and (b) CoB12−. .................. 287  7.26 Rotational barriers of the inner boron triangle with respect to the outer ring for B12 and MB12−.. ....................................................................................................................... 288  7.27 AdNDP analyses for RhB12−. ........................................................................................... 292  8.1 Photoelectron spectra of UO2− at (a) 532 nm, (b) 355 nm, (c) 266 nm and (d) 193 nm. . 299  8.2 Optimized structures of UO2− and UO2. ........................................................................... 302  xxvi 8.3 Qualitative scalar-relativistic valence MO energy-level scheme for UO2− ...................... 302  8.4 Contour plots of the valence MOs of UO2− at the DFT/PBE level (iso = 0.038 a.u.) with a (2u)2(1u)1 electron configuration........................................................................ 303  8.5 Photoelectron spectra of UF2− at (a) 532 nm, (b) 355 nm, (c) 266 nm, and (d) 193 nm. . 322  8.6 Photoelectron spectra of UF3− at (a) 532 nm, (b) 355 nm, (c) 266 nm, and (d) 193 nm. . 323  8.7 Photoelectron spectra of UF4− at (a) 532 nm, (b) 355 nm, (c) 266 nm, and (d) 193 nm. . 324  8.8 Contours of the scalar-relativistic valence CMOs of (a) UF2− (C2v), (b) UF3− (C3v), (c) UF4− (D2d). ........................................................................................................................ 330  9.1 The structures of the main contributors to the photoelectron spectra of boron clusters (Bn−, n = 3 − 24, 30, 35, 36, 40). ...................................................................................... 335  9.2 The structures of the main contributors to the photoelectron spectra of M©Bn− (n = 8, 9, 10). ................................................................................................................................ 337  xxvii List of Abbreviations Abbreviation Full Name Page PES Photoelectron Spectroscopy 7 XPS X-ray photoelectron spectroscopy 7 UPS Ultraviolet Photoelectron Spectroscopy 7 EA Electron Affinity 8 TOF Time-of-Flight 8 MO Molecular Orbital 10 HF-SCF Hatree-Fock Self-Consistent Field 10 HOMO Highest Occupied Molecular Orbital 12 VDE Vertical detachment energy 13 ADE Adiabatic detachment energy 13 ZEKE Zero Electron Kinetic Energy 16 VMI Velocity Map Imaging 17 CCD Charge-coupled device 17 MCP Microchannel Plate 17 TRPES Time-resolved Photoelectron Spectroscopy 18 IMS Ion Mobility Spectrometry 19 TOF-MS Time-of-Flight Mass Spectrometer 20 GED Gas-phase electron diffraction 20 RTPD Resonant two-color photodissociation spectroscopy 23 CID Collision Induced Dissociation 25 GEGA Gradient Embedded Genetic Algorithm 26 CK Coalescence Kick 26 CW Cartesian Walking 26 AdNDP Adaptive Natural Density Partitioning 27 FWHM Full With at Half Maximum 46 xxviii DFT Density Functional Theory 51 TDDFT Time-Dependent Density Functional Theory 52 CMO Canonical Molecular Orbital 52 ON Occupation Number 53 nc-2e n-center two-electron 53 NBO Natural Bond Orbital 53 DHV Double-Hexagonal Vacancy 98 LUMO Lowest Unoccupied Molecular Orbital 99 GGA Generalized Gradient Approximation 107 WFT Wave Function Theory 296 SOC Spin-Orbital Coupling 296 SR Scalar Relativistic 300 xxix Abstract of “PHOTOELECTRON SPECTROSCOPY INVESTIGATION OF BORON AND BORIDE CLUSTERS: THE FOUNDATION OF NEW BORON NANOSTRUCTURES”, by Weili Li, Ph.D., Brown University, August 2014. Chemistry is the science of molecules and materials, as well as their compositions, structures, properties and transformations. The search for new materials with tailored properties is a central theme in chemistry. Atomic clusters, with structures and properties intermediate between individual atoms and bulk solids, have provided fertile ground for the understanding of chemical bonding and for the rational design of novel nano-systems. Photoelectron spectroscopy is the most powerful experimental technique to probe the structures and chemical bonding of size-selected clusters. This dissertation mainly focuses on the studies of boron related clusters using combined photoelectron spectroscopy and quantum chemistry calculations. A world of flat boron (Bn−, n ≤ 20) was previously discovered by the Wang group and its collaborators. The research presented in this thesis shows that the flat boron world expands to n = 24 and continues at the sizes of n = 30, 35, 36 and 40. The B30−, B35−, B36− and B40− clusters feature isolated or adjacent hexagonal vacancies in the all-triangular lattices, providing experimental evidence for the viability of the infinitely large boronsheets, for which we coined the word “borophene”. The first experimental observation of an all-boron fullerene is detailed in this thesis at B40−, which is called borospherene. xxx To search for new boron-based motifs or building blocks for new materials, we proposed an electronic design principle for transition metal centered monocyclic molecular wheels (M©Bnq−). Eight-, nine- and ten-membered molecular wheels are discovered on the basis of the design principle. We have also reported boron-based molecular wires, bipyramid as well as half-sandwiched clusters. These clusters serve as potential ligands or building blocks for nanomaterials. Finally, the photoelectron spectra of uranium oxides and fluorides are presented. Uranium exhibits a strong correlation effect between its 7s2 electrons. These actinide compounds are important as benchmarks for calibrating various relativistic quantum chemistry methods, especially those developed for systems with strong electron correlations. xxxi Chapter 1 Introduction Chemistry is a branch of physical science that studies molecules and materials, as well as their compositions, structures, properties and transformations. The smallest indivisible unit of a chemical substance is the atom, which bonds to each other through various interactions to form molecules and complex materials. The search for new materials with tailored properties has been a central theme for chemists and material scientists in an effort to solve the energy crisis and other environmental problems. Nanotechnology opens a world with new forms of nanomaterials that exhibit novel mechanical, thermal, electronic, optical, and catalytic properties. The properties of these nano-sized materials are different from the macroscopic systems and are size-dependent and structure-specific. For instance, chemically inert gold exhibits surprisingly high catalytic activity for oxidation and hydrogenation when the size is reduced to less than 10 nm.1 New gold nanoparticles are continuing to be found with extraordinary catalytic activities in the size range from a single atom to 2 nm in size.2 Many of the chemical and physical properties of nanomaterials have been attributed to their large surface-area-to-volume ratios, which provide plentiful active spots for chemical reactions and therefore largely enhance the efficiency. The exact catalytic mechanisms over gold nanoparticles, however, are still not well understood.3 There has been increasing interest towards a molecular-level understanding of the properties of 1 nanomaterials. Of particular interest is why and how the size and shape affect the properties, or more importantly whether it is possible to we design novel materials with desired properties. One of the most valuable approaches is to build proper chemical models that can be controlled in size and varied in composition. Clusters with sizes ranging from two to several thousand atoms provide the flexibility to build such chemical models to elucidate the chemical interactions among atoms, molecules, and surfaces. This size range covers the molecular-like species, nanoparticles, and bulk-like species. The insights obtained could eventually lead to a comprehension of the behavior of nanoparticles, bulk surfaces and could potentially be used to rationally design new materials. 1.1 Gas‐Phase Clusters In chemistry, atomic clusters are defined as finite aggregates of atoms. The earliest reference to a cluster may date back to the 17th century when Robert Boyle spoke about “minute masses or clusters” in his book “The Sceptical Chymist: or Chymico-Physical Doubts & Paradoxes”. The word “cluster” was later coined by F. A. Cotton to describe inorganic compounds with metal-metal bonds.4 Cluster chemistry is flourishing with various types of bare atomic clusters made from any metal or non-metal elements in either pure or mixed forms. This thesis concerns the investigation of bare gas phase atomic clusters between 2 and 100 atoms. 2 Atomic clusters are a new state of matter, distinct from gases, liquids, and solids. They have structures and properties intermediate between that of individual atoms and bulk solids. The study of atomic clusters is an interdisciplinary field that has a profound impact in catalysis, surface science, condensed matter physics, and materials science. One important discovery in cluster science was the observation of a third form of carbon (C60) in a laser vaporization cluster source.5 The C60 cluster is a covalently bonded cluster of sixty carbon atoms, each occupying the sixty vertices of a soccer ball. It was named Buckminsterfullerene (Buckyball) after Buckminster Fuller, the architect who designed the geodesic dome.5 After diamond and graphite, this C60 cluster represents a new form of carbon. The purification and separation of C60 in large quantities in the solid-state phase appeared five years after the gas-phase observation,6 providing a bridge between cluster chemistry and solid-state chemistry.7 The discovery of the C60 buckyball and larger carbon cages, collectively called fullerenes, has led to a new field of chemistry and material science. It also paved the way to the emergency of nanoscience. After the discovery of C60, extensive research efforts have been devoted to cluster chemistry. Over the past three decades, researchers have found that small clusters provide significant insight into the intermolecular interactions and chemical dynamics. Of great interest is the investigation of the precise behavior of a given property, such as cluster geometry and electronic structures. Another interest is to systematically study the evolution 3 of a given property by varying the number of atoms one by one. The advances of quantum chemistry and computer technology have made it possible to understand these properties from a quantitative point of view. New techniques, both experimental and theoretical, are continuously being developed in cluster chemistry for various research purposes. Studies on cluster have several advantages. First, clusters are finite in size, allowing their detailed structures and atomic connectivity to be obtained. Second, non-stoichiometric clusters can be readily prepared, making it possible for the discovery of new structural motifs and chemical bonding. Third, the compositions and size of clusters can be controlled and tuned, allowing systematic studies of structure evolution. The size-dependent investigations create a bridge between isolated systems and bulk materials. Fourth, clusters can provide quantitative data to verify and benchmark theoretical methods. 1.2 Cluster Sources Various techniques have been developed to produce clusters, including laser vaporization, electrospray ionization, magnetron sputtering, and electrical arc discharge and so on. Each technique has its own advantages and disadvantages. Some of the features from these cluster sources are described below. Laser Vaporization Cluster Source: Laser vaporization, or laser ablation, is the process of removing materials from a solid surface using a high-power laser beam. It was originally applied to produce clusters in a molecular beam by the Smalley group at Rice 4 University5,8,9 and now has become one of the most popular techniques in the study of clusters and the synthesis of thin films. The hot plasma produced by the intense laser is usually quenched by a high-pressure inert gas to assist the formation of clusters. The laser vaporization cluster source can produce almost any kinds of clusters from metal or non- metal elements, with the cluster size from one to several hundred atoms. Details of the laser vaporization cluster source used for this thesis will be described in Chapter 2. Electrospray Ionization Cluster Source: Electrospray Ionization is a powerful technique to produce multiply charged molecules and cluster ions in the gas phase with a wide mass range,10 ranging from small inorganic and organic molecules to large scale of peptides and proteins. Electrospray Ionization can produce sufficient anions for spectroscopic experiments. Charged species present in the solution phase can often be directly isolated from the solution phase environment to the gas phase. This soft ionization method is sufficient to form multiple charges on the analyte, cluster of analytes, and solvent molecules. Magnetron Sputtering Cluster Source: Sputtering, or ion bombardment, is a process whereby atoms and ions are ejected from solid materials. A magnetron gun is usually employed to produce a high energy Ar+ plasma (Kr+ or Xe+ could also be used), which is focused onto the target made of desired elements and substrate.11 Secondary electrons are trapped by a magnetic field near the target, which then undergo more ionizing 5 collisions with neutral gases near the target. This enhances the ionization of the plasma near the target and leads to high sputtering rate. The Ar+ ions accelerate towards a target with sufficient force to ‘knock out’ atoms or ions. The magnetron-sputtering source produces high intensity of small clusters, yet the intensities for larger clusters (more than 10 atoms) drop dramatically. Electrical Arc Discharge Cluster Source: The electrical arc discharge is similar to laser vaporization, but the atoms are ionized by a pulsed electric arc.12 The most common arc discharge configuration consists of a vacuum chamber and two electrodes, which contains the desired elements. A carrier-gas pulse (usually He) produced by pulsed valves flows over the electrodes at the moment of the arc. The metal vapor and the helium mix during the discharge process, and the resulting plasma undergo a supersonic expansion to produce a cluster beam. It is an economic cluster source with high beam intensity and therefore is widely used for thin film deposition. However, the application of the source is limited to conducting materials. 1.3 Spectroscopic Techniques for Cluster Structure Determination Although the cluster geometric properties are of extreme interest, there is no spectroscopic method for direct structural determination for clusters in such small size. Various spectroscopic techniques have been developed to elucidate the electronic structures of size-selected clusters in the past several decades. Combined with quantum chemistry, the 6 spectroscopic fingerprint could be used to identify the cluster structures and other properties.13 Here a brief summary of several popular spectroscopic techniques for size- selected clusters, including their principle and application is provided. The advantages of the photoelectron spectroscopy for negatively charged species will be emphasized. 1.3.1 Photoelectron Spectroscopy (PES) PES is a powerful technique to elucidate the electronic structures of molecules, ions and clusters. PES has two major branches, depending on the photon energy: X-ray photoelectron spectroscopy (XPS) and ultraviolet photoelectron spectroscopy (UPS). The origin of XPS can be traced back to the 1960’s when the Siegbahn group at University of Uppsala measured the core electron binding energies of the ThB.14,15 XPS utilizes soft X- rays with photon energies of 200-2000 eV to examine the core-level electrons. It has been widely used in condensed matter studies. In the 1970’s, the Turner group at Oxford University developed a new technique, UPS, to study molecules in the gas phase.15,16 Due to the lower photon energy, UPS can only ionize the valence electrons rather than the core electrons. However, the photoelectrons emitted from the objects carry smaller kinetic energies, allowing better spectral resolution comparing to XPS. In the following decades, PES has been extensively improved and advanced for numerous applications in chemistry and physics. 7 The first implantation of PES to negatively charged species was in 1967, which directly measured the electron affinity (EA) of helium.17 PES became a popular approach for cluster anion studies in the early 1980’s, pioneered by the groups of Lineberger,18 Smalley,19 and Meiwes-Broer20. The groups of Bowen,21 Newmark,22,23 Zewail,24 Kaya,25 Wang,26-28 Haberland and Issendorff,29-31 and Ganteför32,33 have made extensive contributions to the PES studies of cluster anions. Additionally, the groups of Jarrold34, Zheng35 and Tang36 have also contributed to the anion cluster PES studies. PES of size- selected anions is currently the most powerful technique to elucidate the electronic structures of a wide range of clusters, providing insight into their physical and chemical properties. In PES experiments, a size-selected anion cluster is photodetached by a laser beam with certain photon energy (hν) and yields photoelectrons carrying different kinetic energies ( ). The photoelectrons are separated and analyzed based on their kinetic energies in an energy analyzer. The number of electrons and their time-of-flight (TOF) are recorded for an Intensity- photoelectron spectrum. With the development of efficient electron analyzers and laser techniques, PES has evolved into a highly versatile technique capable of addressing fundamental problems in spectroscopy as well as in chemical dynamics. The most popular one is the magnetic-bottle time-of-flight PES, which uses an inhomogeneous magnetic field to guide electrons to the detector for kinetic energy analysis. The magnetic- 8 bottle PES has extremely high electron collection efficiency (~100%)5,8,9,37 and decent energy resolution (ΔEk/Ek, ~ 2 – 5%), i.e. 20-50 meV for electrons with 1 eV kinetic energy. As the main experimental technique for this thesis, a detailed magnetic-bottle PES apparatus will be discussed in Chapter two. The obtained Intensity- PES spectrum can be interpreted by two approaches: 1) the quantum chemistry description. Figure 1.1 shows a schematic view of photodetachment transition, which occurs from the ground state of an anion (M−) to the ground state (M) and excited states (M*) of the corresponding neutral species, as shown in the Eq. 1. ∗ → Eq. 1 The energy difference between the initial and final states is denoted as the electron binding energy ( ) of the anion, i.e. ∗ Eq. 2 According to energy conservation or Einstein’s photoelectric equations, equals to , i.e. Eq. 3 thus, ∗ Eq.4 PES features represent the energy differences between the neutral ground (excited) states and the anion ground state. In other words, PES directly gives the electronic energy levels 9 of the neutral clusters. 2) Molecular Orbitals (MOs) description. From the MO point of view, PES can be understood as ejecting electrons from occupied orbitals (Figure 1.2). In the Hartree-Fock delf-vonsistent field approximate (HF-SCF), electrons are treated individually in the potential field produced by the fixed nuclei and averaged interactions of the other electrons. Koopmans’ theorem states that if orbital relaxation is neglected, the experimental vertical ionization energy ( ) of an orbital is approximately equal to the negative of the eigenvalue (ɛ ) of that orbital, i.e. ɛ Eq. 5 Koopmans’ theorem provides the bridge between PES and the MO theory. The ionization energy is the energy difference between the photon and the emitted electron according to energy conservation, i.e. Eq. 6 In the anion species, the binding energy ( ) denotes the “ionized energy”, i.e. ɛ Eq. 7 Eq. 8 Thus PES is able to provide measurement of the EAs (Figure 1.2) and the Intensity- PES spectrum represents a picture of the occupied MOs of the anion cluster. The Koopmans’ theorem is only an approximate model and can be used to qualitatively interpret PES spectra. 10 High-level theoretical calculations are usually incorporated to achieve quantitative understanding of the PES spectra. Figure 1.1 A schematic view of photodetachment. Photodetachment transition occurs from the ground state of an anion (M−) to the ground state (M) and excited states (M*) of the corresponding neutral species. 11 Figure 1.2 A schematic view of single electron picture of photodetachment process. HOMO stands for highest occupied molecular orbital. 12 Vertical detachment energy (VDE): Due to the possible structural relaxation of the cluster upon electron detachment, transitions might exist between the anion vibrational ground state to the neutral vibrational excited states (0−n transition). The Franck-Cordon principle states that the most probable vibronic transitions happen when the initial state and finial state have the same geometrical structures, which correspond to vertical detachments.15 On the basis of the Franck-Cordon principle, VDE represents the most intense feature in the vibrational profile. For small clusters or simple systems, PES bands are well separated and each band represents a single detachment transition. In some cases, the experimental features are the results of more than one detachment transitions and the VDE is only a reference for the sake of discussion. Commonly, the peak marked as X represents the transition between the ground electronic states of the anion and the neutral species, while the higher binding energy peaks (A, B, ...) denote transitions to electronic excited states of the neutral cluster. Adiabatic detachment energy (ADE): The ADE is the minimum amount of energy required to remove an electron from the anion, i.e. the energy difference between the vibrational ground state of the anion and the neutral (0−0 transition). The ADE could be measured accurately for vibrationally resolved spectra. If no vibrational transtions are resolved, the ADE value could only be estimated, usually by drawing a straight line along the leading edge of the band and then adding the experimental resolution to the intersection 13 with the binding energy axis. The ADE also represents the EA of the corresponding neutral cluster. Spectral band intensity: The spectral intensity corresponds the number of electron counts within certain kinetic energy window. The absolute intensity is a reflection of the detachment cross-section of the MOs, and is dependent on the photon energy. Relative intensities among the features is a direct indication of the cross-section of the anion MOs. The s-atomic orbital (AO) based MOs usually have larger cross section than those of f–AO based MOs.38-40 Extra features: PES spectrum could be interpreated using exact quantum descriptions or Koopmans’ theorem. However, in some cases, the experimental spectrum will show extra features that could not be explained. The possible causes for these extra features are: 1) anion vibrational excited states. When the cluster is hot, the vibrational excited states of the anion might be populated and therefore produce features with lower binding energies. These features are called “hot band”. They are usually weak and can be minimized by lowering the cluster temperature. 2) low-lying isomers. The high cluster temperature may also cause the population of low-lying isomers, especially for those having close energies to the global minimum structure. The low-lying isomers usually generate a series of features labeled with X', A' and so on. The intensity depends on the relative energy of the low-lying isomers to the global minima. Similar to the hot bands, the intensity of low- 14 lying isomer peaks can be tuned via experimental conditions. 3) iso-mass species. The clusters are size-selected according to their masses. If two species have the same mass, both of them will be observed in the PES spectrum. The iso-mass species could be due to isotopical conincidence or oxygen/hydrogen contamination, which can be avoided using isotopically enriched materials or carefully preparing the targets under water/O2 free conditions. 4) multielectron processes. If the extra features cannot be explained by the above reasons, they might come from multielectron process. As discussed before, PES mainly involves one-electron processes where each spectral band corresponds to one- electron detachment from one MO. However, a second electron may be excited to a higher energy orbital as the first electron is detached. This is called a shake-up transition. Shake-up transitions, due to electron correlations, are usually very weak. The shake-up processes could be calculated using multi-reference quantum mechanical methods. 5) other possiblities. There are other possible reasons for extra features in PES, e.g. spin-orbit splitting (for heavy elements), resonant transitions or autodetachment and so on. They will be discussed case-by-case in the following chapters. Magnetic-bottle PES has large collection efficiency but limited resolution, especially for the vibrational and rotational progressions. Field-free analyzers can potentially achieve much better resolution; however at low collection efficiency. Short flight tubes (< 1 m) are commonly used as a compensation for collection efficiency. As a result, photoelectron 15 electrons must have low kinetic energies to reach high resolution. The development of tunable laser made it possible to detach electrons with extremely low kinetic energies and eventually, produces extremely high resolution PES spectra. 1.3.2 Zero‐eV Electron Kinetic Energy (ZEKE) Spectroscopy ZEKE spectroscopy is a high-resolution approach, which collects only the resonance ionization photoelectrons that have zero eV kinetic energy. The Schlag group first invented this technique for neutral molecules.41,42 The Neumark group has applied this technique to negative cluster ions and has obtained interesting vibrationally resolved spectra for several small semiconductor clusters.43 The Yang44 and Heaven45 groups have applied this technique to study neutral and cationic clusters. However, the application of ZEKE to anions is limited due to the Wigner threshold law,46 . ∝ Eq. 9 where is the detachment cross section, is the difference between the photon energy and the threshold, and l is the angular momentum of the emitted electron. For s outgoing wave (from a p electron), l = 0, the cross section increases as the photon energy near the threshold; for p outgoing wave (from an s electron), l = 1, the cross section remain near zero for a range of ~ meV electrons. Thus for s outgoing wave electron threshold detachment, the cross section increases as the square root of photon energy. But for any 16 electron with angular momentum larger than 0, the cross section is so small that such threshold detachment is difficult to be observed experimently. 1.3.3 Velocity Map Imaging (VMI) PES VMI PES uses a charge-coupled device (CCD) camera to capture the detached electrons, different from the microchannel plate (MCP) for the magnetic-bottle PES. VMI PES records the velocity as well as the angular distributions of photoelectrons. The imaging technique was originally developed to record the distributions of photodissociation products.47 It was soon applied to detect photoelectrons48,49 and has become a powerful alternative PES technique over the past decade.50-55 First developed by Eppink and Parker56, the velocity-map imaging is capable of high-resolution photoelectron spectra for low kinetic energy electrons.50,57-59 Pioneered by the Boardas,60,61 Sanov55,62 groups, more groups have applied this technique to anion clusters.50,59,63 The sensitivity of the imaging method to slow-electrons has allowed high resolution photoelectron spectra to be obtained for near zero-eV kinetic energy electrons, which is known as slow electron velocity-map imaging (SEVI) by the Neumark group.59 The Wang group has improved the spectral resolution to 3 cm-1 for anionic clusters.50 More recently, rotational resolution has been reported for slow electron imaging of small neutral molecules.64 The advantage of VMI not only lies at its high detection efficiency and high resolution, but also at its ability to provide photoelectron angular information in the meantime. 17 1.3.4 Resonant Two‐Photon Ionization Spectroscopy In resonant two-photon ionization spectroscopy, neutral clusters in the electronic ground state are excited using laser beams with tunable photon energies.13,65,66 A second laser with fixed photon energy, usually operating in the ultraviolet region, ionizes the excited clusters. The intensity of the ions is recorded as a function of the photon energy of the tunable laser. The spectra exhibit peaks at photon energies corresponding to resonant absorptions of the neutral cluster. Only dipole allowed transitions can be observed. This is a high-resolution technique, but limited to very small clusters, such as dimers, and trimers, etc. 1.3.5 Time‐Resolved Photoelectron Spectroscopy (TRPES) TRPES is a spectroscopic technique to probe the dynamic processes in materials or chemical compounds. It was first applied to study semiconductor surfaces in the mid 1980’s and indeed, is still a powerful tool in the investigation of metal and semiconductor surfaces. The past two decades have witnessed an explosion in the use of ultrafast lasers to follow chemical dynamics in the femtosecond time scale,67,68 which has led to breakthroughs in our understanding of fundamental chemical processes. TRPES experiments have been performed on mass-selected negative cluster ions by the Neumark group69 and recently by the Eberhardt group.70 While the more complex sources and lower number densities in negative ion experiments present challenges in comparison to neutral experiments, detachment energies are generally significantly lower than ionization energies in neutral 18 species. So it is easier to generate probe laser pulses with sufficient energy to eject an electron. In addition, studies of clusters are straightforward in negative ion experiments because the ions can be mass-selected prior to their interaction with the laser pulses; analogous neutral studies require collecting photoions in coincidence with photoelectrons so that the identity of the ionized species can be ascertained. The advantages of TRPES includes 1) one can indeed monitor evolution of the excited state dynamics along the entire reaction coordinate, and 2) the probe laser does not have to be tuned, since the PES spectrum at each delay provides the full mapping of the evolving wave packet onto those electronic states accessible by photodetachment (or photoionization, in the case of neutrals). 1.3.6 Ion Mobility Spectrometry (IMS) IMS is a gas-phase electrophoretic technique that allows gas phase species to be distinguished on the basis of their sizes and shapes. The application of IMS to structural studies of small clusters has been recognized since 1970s.71,72 It has been proved that IMS can be used to study the structural characteristics of a wide range of chemical species, from atomic clusters to biomolecules. The ion mobility method as such has been developed long ago by Mason and McDaniel73 and the combination of this technique with modern mass spectrometry has been pioneered by the Bowers’ group.74 In recent years, Jarrold and coworkers have developed high-resolution drift cells. They applied this technique to a large 19 variety of different ionic systems such as fullerenes and fullerene derivatives, biopolymers, silicon clusters and a variety of metal clusters.75,76 More recently, Clemmer and co-workers have used an ion trap to accumulate and concentrate the ions before injection into a drift cell. This is followed by a time-of-flight mass spectrometer (TOF-MS).77 This setup has been optimized for rapid data acquisition, i.e., TOF mass spectral and drift time distributions are recorded simultaneously. It allows rapid screening of (for example) peptide libraries, the unfolding reactions and the analysis of the size parameters of the various amino acids in peptides. The Kappes group developed an ion mobility technique to study the structures of clusters and discovered planar gold clusters anions recently.78 Unlike PES, the ion mobility method is sensitive to the collision cross section of a cluster and is therefore effectively for smaller metal clusters. 1.3.7 Gas‐Phase Electron Diffraction (GED) The first GED investigation of a molecular structure, that of CCl4, was reported by Mark and Wierl in 1930,79 only three years after the discovery of electron diffraction for a crystal of nickel by Davisson and Germer,80 and for a thin film of celluloid by Thomson and Reid.81 The GED was refined to elucidate the precise arrangement of atoms in molecules beginning with Linus Pauling at Caltech.82 Until the early 1970s, electron diffraction patterns were recorded exclusively with photographic film. The replacement of these film- based detectors with an electronic detector by Fink and Bonham was a major advance in 20 GED.83 The introduction of 2D area detectors, CCD with fiber optic coupling and image intensification, represents the current state-of-the-art in digital diffraction imaging. Rood and Milledge84, Bartell and Dibble,85 Ewbank86 have applied this technique to investigate decomposition, phase changes and photofragmentation. Mourou and Williamson pioneered to use a modified streak camera to generate 100-ps electron pulses to record diffraction images from thin aluminum films in transmission mode; they subsequently produced 20-ps electron pulses to study the phase transformation in these films before and after irradiation with a laser.87 Elsayed-Ali and co-workers succeeded in using 200-ps electron pulses to investigate surface melting with reflection high-energy electron diffraction.88 The GED technique was also applied to clusters for direct structural determination.89 However, GED on mass-selected atomic clusters has presented an exceedingly difficult challenge. Cluster sources contribute to this difficulty since they produce beams with broad cluster size distributions. An adequate cluster flux for diffraction measurements requires the full source output beam; the uncertainties in cluster size and internal energy prevent an unambiguous interpretation of electron diffraction patterns. To achieve this goal, Parks and coworker developed an advanced technique that relies upon an RF Paul trap to take advantage of the current cluster source technologies, yet avoid the shortcomings of beam measurements.90,91 The RF Paul trap enables one to accumulate size selected cluster ions, collisionally relax their vibrational energy distribution, and store the cluster ions for an 21 adequate time to allow electron-diffraction measurements. The first experiment by the Park group92 was a case on C60+, followed by a structural determination of a series of size- selected CsCl cluster cations.93 In Parks’s setup, the RF trap, Faraday cup, and MCP/phosphor screen detector are mounted to maintain cylindrical symmetry around the electron beam axis. A CCD camera external to the ultrahigh vacuum chamber images the diffraction pattern, which is in the form of Debye-Scherrer rings similar to powder diffraction as a result of the orientational and spatial disorder of the trapped cluster ions. The RF trap operates at 600 kHz with an end-cap electrode spacing of 1 cm. The diffraction electron beam of 0.5 mm diameter traverses the trap through 2-mm apertures in the grounded end-cap electrodes. Diffraction data are obtained at an electron-beam energy of 40 keV and a beam current of several hundred nA. The diffraction volume and the 2-mm end- cap aperture allow detection of scattered electrons with a maximum scattering angle of 68.1°. Ions are loaded into the trap and then vibrationally and translationally relaxed by exposure to a helium background gas at a low pressure and a known temperature (90-300K). After mass isolation of clusters by resonance ejection of all other ions, the cluster ions were positioned at the trap operating point during diffraction exposures. The mass spectrum after the diffraction exposure is determined by resonantly ejecting the ions into a channeltron detector. 22 1.3.8 Infrared Multi‐Photon Dissociation Spectroscopy Infrared photodissociation spectroscopy13,65 is usually performed on cluster- molecules complexes and probes chemisorption interactions of clusters. In such experiment, a powerful infrared laser excites the characteristic vibrations of the molecules adsorbed on the surfaces of the clusters, causing the complexes to dissociate. The resulting photodissociation spectrum reveals whether or not the adsorbed molecules have undergone a chemical reaction after sticking to the surface of the cluster. It is anticipated that these experiments will contribute to our understanding of particle size effects and their influence on reaction mechanisms and pathways in heterogeneous catalysis systems. A caveat in photodissociation spectroscopy is that photoabsorption is only detected when the absorbed energy results in dissociation. Thus, single photon photodissociation spectra are a convolution of the absorption and dissociation events for each given cluster. These two events can be separated by using two different color photons to perform resonant two-color photodissociation spectroscopy (RTPD). In RTPD, clusters are irradiated with the first photon, followed by the second photon. The first photon performs the spectroscopy and the second higher energy photons add additional energy so that the clusters can dissociate. 1.3.9 Magnetic Deflection Experiment It is well known that most transition metal atoms are magnetic, however, only the late 3d transition metals Fe, Co and Ni are known to be ferromagnetic in the bulk. Therefore, 23 fascinating size-dependent magnetism is expected to exist in small transition metal clusters. The magnetism of bulk transition metals is known to be due to itinerant d electrons on the metallic side in contrast to the magnetism of atoms and insulators that is due to electrons localized in atomic-like orbitals. Thus, the study on this problem will also help to answer fundamental questions of electron delocalization as a function of cluster size. The dependence of the magnetic properties on the cluster size can be determined in a Stern-Gerlach experiment in which the free magnetic clusters interact with an applied inhomogeneous magnetic field and are deflected from the original beam trajectory. The deflection experiments are normally analyzed assuming that the free ferromagnetic clusters are single-domain particles following super paramagnetic behavior. In this case the N atomic moments of a particle with N atoms are coupled by the exchange interaction, giving rise to a large total magnetic moment that is essentially free of the cluster’s lattice. This orientation freedom allows the magnetic moment to align with an external magnetic field. For an ensemble of particles in thermodynamic equilibrium in an external field B, the magnetization (that is the average projection of the magnetic moment of the particles along the field direction) reduces, in the low-field limit ( ≪ ) and for large particles.94 Cox and coworkers95 conducted the first measurement of the magnetic properties of isolated iron clusters ranging from 2 to 17 atoms as well as the magnetic behavior of the monoxides and dioxides of smaller Fe clusters. Later, de Heer and co-workers96 did 24 extensive experiment on the magnetic moments of Fe, Co and Ni clusters with sizes ranging from about 20 to 700 atoms. Bloomfield and co-workers97-99 measured the magnetic moments of size-selected Co clusters and Ni clusters with up to 200 atoms. Most recently, the de Heer group developed a ultra-low temperature cluster source for high precision magnetic deflection experiments.100 1.3.10 Collision Induced Dissociation (CID) In a CID experiment,13,65 the molecular ions are usually accelerated to high kinetic energy and then allowed to collide with neutral molecules. During the collision process, some of the kinetic energy is converted into internal energy, which causes bond breakage and the fragmentation of molecular ions into smaller fragments. CID experiments can yield quantitative thermodynamic stabilities of clusters. Usually, a positively charged cluster beam with a well-defined and variable kinetic energy (0-1000 eV) is injected into a radio frequency octopole ion beam guide. The octopole directs the beam through a gas cell that contains a neutral collision gas (Xe, for example). The octopole minimizes losses due to scattering of both reactant and product ions. Thus, the ions are collected with high efficiency and injected into a quadrupole mass filter for product mass analysis. The mass intensity is converted into reaction cross sections from the laboratory to center-of-mass frame. This kind has work mainly been carried out by Armentrout group.101 25 1.3.11 Chemisorption Experiments Chemisorption has been used extensively to probe the geometric structures of clusters by Riley’s group.37 This technique uses the adsorption of weakly bound non- invasive molecules to probe the morphology of a cluster’s surface. Since most of the atoms of a cluster are on the cluster surface, the accessible surface sites contain information about the cluster structure. The measured size-dependent information of the number and strength of the surface’s binding site can then be used to select structures consistent with the adsorbate binding patterns. Using this method, cluster structures for a number of species such as Co, Fe, Ni, and so on have been investigated. 1.4 Our Approach: Joint PES and Quantum Chemistry Study Our approach is summarized by four steps: 1) Photoelectron Spectroscopy. PES is used to probe the electronic structure of clusters. The experiment is carried out by generating the clusters using laser vaporization and analyzing them in a TOF-MS. The cluster of interest is mass-selected and photodetached by a laser beam. The photoelectrons are analyzed in a magnetic-bottle photoelectron analyzer.26,37 2) Theoretical global minimum search. The potential energy surface of the cluster is explored to locate the most viable chemical structures and low-lying isomers. This task is usually performed using various algorithms such as the Gradient Embedded Genetic Algorithm (GEGA),102 Coalescence Kick (CK),103 Basin Hopping method,104,105 Cartesian Walking (CW) 26 method,106 and so on. 3) Comparison of the experimental and theoretical vertical detachment energies. Assignment of the global minimum structure is based on comparison of the measured VDEs from the photoelectron spectra with theoretically calculated VDEs corresponding to the lowest energy isomer(s). 4) Chemical bonding analysis. We rationalize the structure of the global minimum through chemical bonding analyses, including the use of the Adaptive Natural Density Partitioning (AdNDP) algorithm and MO theory.107 These analyses explain what governs the geometric and electronic structures and stability of the cluster at hand. 1.5 Motivation and Objectives In this dissertation, I present the investigations of a series of bare boron clusters106,108-112, doped boron clusters113-121 and uranium compounds38,39 using joint PES and quantum chemistry calculations. The motivation of the bare boron cluster project is to explore the flat world of boron clusters and to search for novel boron nanostructures. Elemental boron in the bulk is characterized by a large variety of allotropes comprised of three-dimensional (3D) B12- icosahedral cages.122-127 However, boron tends to form 2D structures as gas-phase clusters.103,104,128-139 Joint PES and ab initio studies over the past two decades by the Wang group have shown that anionic boron clusters are planar or quasi-planar at least for up to 20 atoms.103,104,128-138 What is the largest planar anionic boron cluster? On the other hand, 27 inspired by the carbon based nano-structures,140 extensive theoretical efforts have been devoted to search for boron nanostructures, such as boron fullerenes,141-145 two-dimensional sheets,146-154 nanotubes,155-157 nanoribbons,158 and core-shell stuffed boron fullerenes.159-162 An interesting question is: are they viable? With these two questions, we systematically investigated the boron clusters in the range of 21 to 100 atoms. Chapter 3 presents the Bn− (n = 21 – 24) clusters, which are found to possess 2D structures. The boron clusters exhibit congested spectroscopic features as well as complicated potential energy surfaces. As with the previously reported anionic boron cluster,103,104,128-138 Bn− (n = 21 – 24) clusters are all planar and are all-boron hydrocarbon analogues. A significant part of this thesis involves the discovery of boron clusters with single hexagonal vacancy, B36− and B30−, and boron clusters with double hexagonal vacancies, B35− and B40− (Chapters 4 and 5). The observation of hexagonal holes in the all-triangular lattices in this size regime provides strong evidence of the viability of two dimensional boronsheets (which we named “borophene”).142,145,147-149,151-153,163 Another significant part of this thesis is the discovery of the first all-boron fullerene. After the discovery of the C60 fullerene,5 there were immediate speculations about the existence of a B60 fullerene. However, mass spectra showed no special abundance of the B60 cluster.164 Our PES and ab initio studies have shown that the first all-boron fullerene is B40−. This 28 finding marks the onset of all-boron fullerenes, suggesting that a new class of related borospherene may exist. In the project of doped boron clusters (Chapters 6 and 7), we set out to search for highly stable clusters with novel structures and chemical bonding, which may be used as building blocks or could be synthesized in the condensed phase. A series of transition-metal centered boron molecular wheels have been discovered, each featuring a transition metal center and a monocyclic boron ring (Dnh-M©Bnk−).113-121 Their stabilities are understood by the doubly aromatic electronic structures. We have also observed the “boat”-like (VB10−), half-sandwiches (C3v-M©B12−, M = Rh, Ir), and bipyramidal (D6h-Ta2B6−/0) clusters, as well as molecular wires (H2Bn−, Bn(BO)2−). Because of the d electron lone pairs on the metal atom, appropriate ligands might be conceived to coordinate to these clusters, providing chemical protection and therefore allowing synthesis of this new class of novel boron based complexes. In the last chapter, I present the study of four uranium molecules: UO2−, UFx− (x = 2 – 4). The motivation of the actinide project is to investigate the electronic structures of actinide compounds for comprehensive understanding of the 5f electron behavior and to provide prototypes to calibrate and benchmark relativistic quantum chemistry methods. Strong electron-electron correlations are observed between the 7s electrons, resulting in numerous unexpected electronic transitions for both UO2− and UF2−. The UF3− and UF4− 29 anions do not have the 7s2 configuration and thus no correlation induced extra features are observed. These experimental observations provide new data for the calibration of theoretical methods for actinide systems. 30 Chapter 2 Experimental Setup The experiments in the current thesis are carried out using a magnetic-bottle time-of- flight photoelectron spectroscopy apparatus equipped with a laser vaporization cluster source. Briefly, the clusters are produced by laser vaporizing of a disk target. They are entrained by a carrier gas and undergo a supersonic expansion to form a collimated and vibrationally cold cluster beam. The anionic clusters are extracted and subsequently analyzed using a modified Wiley-McLaren TOF mass spectrometer. The cluster of interest is mass-selected and decelerated before being photodetached by a probe laser beam. The emitted photoelectrons are collected at nearly 100% efficiency by the magnetic-bottle and analyzed in a 3.5 m long electron flight tube.37 A schematic diagram of the experimental apparatus is shown in Figure 2.1. The main parts will be described in detail in the following sections. 31 Figure 2.1 A schematic view of the PES apparatus equipped with a laser vaporization cluster source. 2.1 Laser Vaporization Cluster Source The cluster source used in our apparatus involves the laser vaporization technique, which was invented and developed mainly by Smalley’s group.5,8,9 It consists of a disk target, a set of target control motors, a vaporization laser, and two modified Jordan Valves (R. M. Jordan Co., CA), as seen in the Laser Vaporization Cluster Source part of Figure 2.1 and Figure 2.2. 32 The target is made by cold or hot pressing the desired elemental powders into a disk shape of 13 mm diameter and 0.2 − 2 mm thickness. Metal powders, such as Bi, Au, Pb, or Ag, are sometimes used as target binders and in the meantime, provide the atomic anion calibrants for the PES apparatus. The target is glued to a target holder that connects to an up-down movement motor and a rotation motor to ensure evenly vaporization of the whole target surface. The vaporization laser runs at 10 − 20 mJ/pulse, 10 Hz repetition rate and 10 nanosecond pulse width, from the second harmonic (532 nm, green light) of a Nd:YAG laser. As shown in Figure 2.2 , the laser beam is focused down to a 1 mm diameter spot onto the target surface to produce hot plasma of atoms, ions and radicals at about 10 K temperature. Two pulsed Jordan Valves, symmetrically mounted, are used to deliver a short and intense helium carrier gas pulse at 10 atm backing pressure. The helium gas mixes with and cools the nascent plasma in the large ‘waiting room’ to produce clusters, including both neutral and charged clusters. The formation of cluster in this step is primarily due to three body processes: when two atoms collide, they form a temporarily bound dimer; if it lives long enough to collide with a He atom, it can be stabilized by collisional deactivation; once the dimers are formed, the process repeats for trimers and larger clusters. The cluster/helium mixture undergoes a supersonic expansion to the vacuum chamber through the 3mm orifice and is skimmed to form a well-collimated cluster beam into the ion extraction chamber. The supersonic expansion further cools down the formed clusters. 33 Figure 2.2 A schematic view of the laser vaporization cluster source. 2.2 Time‐of‐Flight Mass Spectrometer The clusters generated from the laser vaporization cluster source are mixtures of positively, negatively charged species as well as neutral species. In the current work, only negative charged clusters are extracted perpendicularly from the molecular beam by a high voltage pulse (Repeller, 1.0 kV to 3.0 kV) and subjected to a TOF mass analysis. Our mass spectrometer is a modified Wiley-McLaren type for large volume ion extraction and simultaneous high mass resolution.165,166 The major modification is an addition of a short (~ 0.5 inch) free-flight zone in between the two acceleration stages of the original Wiley- McLaren design. This modification allows us to achieve a mass resolution (M/ΔM) of more than 300. The resolution deteriorates slightly at higher masses, mainly limited by the fringe field effect due to the ion steering optics to compensate for the transverse velocity of the clusters. 34 The mass spectrometer is able to detect clusters with molecular mass from several amu to tens of thousands amu. For the smaller mass range (<1000 amu), low repeller voltage (0.8 kV to 1.2 kV) is needed. To obtain well-resolved mass spectrum for larger clusters, several experimental conditions need to be tuned. First, the repeller stack needs to be rotated to the right position that is favorable for heavier clusters. Secondly, the voltage on the repeller stack has to be increased to accelerate heavier clusters to a reasonable speed to obtain a compact mass packet. Finally the voltages on the first ion deflector and the focusing Einzel lens have to be tuned accordingly to achieve the best mass resolution. The Einzel lens consists of three isolated copper cylinders. The two end cylinders are grounded while the middle one is biased at -400 V typically (for 1000 V extraction voltage). A set of stainless steel electrostatic deflectors is located behind the Einzel lens and can be used to adjust the cluster beam horizontally and vertically. This fine tuning of the ion beam is critical to align the ion beams and laser beam in the detachment zone. The TOF mass spectra of the cluster ions are measured with a set of two micro-channel plates and a pre- amplifier. Figure 2.3 shows a typical mass spectrum of Bn− clusters (n > 7) with 1 kV extraction voltage. 35 Figure 2.3 A time-of-flight mass spectrum of Bn− clusters using a hot pressed 11B target. 2.3 Mass Selection and Momentum Deceleration In the PES experiment, only clusters of interest are selected to enter the photoelectron detachment zone. The cluster anions are selected by a mass gate and decelerated by a momentum decelerator. A schematic view of the mass gate and momentum decelerator is shown in Figure 2.4. A three-grid mass gate is used for mass selection. The first and third grids are grounded, and the middle grid is at a negative high voltage (-1 kV to -3 kV). Once the desired clusters arrive at the first grid, the high voltage is pulsed to ground for a short period of time (~ 80 ns to 800 ns depending on the cluster size). After the selected cluster anions pass, the high voltage is engaged again to block the anions with other 36 masses. A fast transistor switch is used to deliver sharp and variable width pulses for the mass gate. After passing through the mass gate, the selected cluster anion packet enters a momentum deceleration167 zone as shown in Figure 2.4. Once the cluster anion packet passes the third grid of the mass gate, a positive square high-voltage pulse is applied to this grid for the momentum deceleration. The high voltage is pulsed to ground before the ion packet leaves the deceleration stack, which consists of 10 guarded rings to ensure a uniform deceleration electrical field. Both the pulse amplitude and the pulse width can be varied to achieve the best deceleration effect. During the momentum deceleration, all ions experience the same decelerating force within the same period of time, thus will be decelerated by the same amount of linear momentum. The initial ion energy spread is decreased after the deceleration. The deceleration step is critical for electron energy resolution as it allows us to decelerate a given cluster ion packet down to such a low kinetic energies that minimizes the Doppler-broadening. For large clusters that the mass peaks could not be separated to the base line, the PES spectra are insured to be from pure clusters by applying narrow mass gate timing. By applying a mass gate voltage in a narrow period of time, only the middle part of the mass packet was selected to enter the deceleration zone. On the other hand, to make sure the PES 37 spectra are from a pure cluster, one has to take PES spectra from the front part of a mass peak and rear part of the same peak, and see if any difference is found in the spectra. Figure 2.4 A schematic view of the mass gate and momentum decelerator. 2.4 Magnetic‐Bottle Time‐of‐Flight Photoelectron Analyzer Photoelectron spectroscopy measures the kinetic energy distribution of photon- emitted electrons of an underlying system (atoms, molecules, clusters, and surfaces, etc.) at fixed photon energies. From energy conservation, the spectrum represents the binding energy distribution of the electrons in the system. The magnetic-bottle type TOF 38 photoelectron spectrometer first described by Kruit and Read is ideal for the study of clusters due to its high collecting efficiency (2 solid angle).168 In this work, the apparatus is a modified version of the magnetic-bottle TOF with a 4 solid angle.26,37,169 As shown in the right part of Figure 2.1, the magnetic field is generated by a permanent magnet tip with a V shape head of 75 degree and magnetic flux intensity of about 5000 Gauss at the tip surface machined from a magnetic rod with 3/4 inch in both diameter and length. The distance between the magnet and the detachment laser beam can be varied for different photon energies (532, 355, 266, 193 nm). A short distance is used for 532, 355 and 266 nm experiments to achieve optimal PES resolution. The distance is increased for photon energies higher than 193 nm to minimize background electrons emitted from the magnet tip by scattered photons. To reduce the background electron emission, the surface of the magnet tip is coated with graphite (Aquadag E layer). This coating has two purposes: 1) to reduce the noise, because the working function of graphite is higher than the materials of the magnet; 2) to achieve a relatively uniform electric field around the detachment zone. From our experience, the photoelectron resolution is very sensitive to the variation of work functions in the detachment chamber. The magnetic-bottle TOF tube is 3.5 m long; a weak and uniform magnetic field along the tube is generated by a solenoid on the outside wall of the flight tube. 39 We use two detachment lasers, a Nd:YAG laser (1064 nm, 532 nm, 355 nm, 266 nm), and an excimer laser 193 nm). The TOF spectra of the electrons are measured with a set three micro-channel plates (the Z stack from Jordon company), and then the TOF spectra are recorded with a 200MHz transient digitizer. 2.5 Performance of the Photoelectron Spectrometer 2.5.1 CAMAC Interface The experiment is controlled with a computer through a CAMAC interface. The computer originates a sequence of commands to generate timing pulses and delays through the CAMAC interface to initiate the experiment and acquire the data. The CAMAC interface (Transiac Model 6002) is a combined CAMAC crate controller and dataway display module. This module receives data, commands from the computer, executes the proper CAMAC commands and then sends data back to the computer. The transient recorder (LeCroy model TR 8828D) receives data from the MCPs (ion signals or electron signals). The analog signal is sampled on the positive edge of the clock, converted to a digital number and stored in the transient memories (LeCroy model MM 8150 memory). This sequence continues until a stop-trigger is detected after which the selected number of post-trigger samples is transferred to the computer memory. There are two other CAMAC based modules for the experimental control. One module is a 12 bit digital-to-analog (DAC) converter (Kinetic System Model 3112 DAC) with 8 channels. This module enables the 40 digital signals read from the computer to be converted to analog signals, which is used to control the deflector voltage. The other is a 15 channel motor controller (Bi-RA 3101) to position the target through two stepping motors. The 8-channel timing pulse generator (Kinetic System Model 3655) is a CAMAC module with a 16-bit counter and eight 16-bit set point registers that are compared with the counter. The comparisons can be used to either stop or clear the counter. The module provides its own crystal clock, and the input frequency to the counter is software-controlled to be any number from 1 Hz to 1 MHz. In our experimental mode, the input to the counter is from an external source. Two of the comparisons can set and clear the dataway inhibit. The outputs of these pulse generators are only 200 ns wide and unable to drive normal BNC cables. Besides, they cannot be disabled and enabled separately. Therefore, a CAMAC module (Gate 16) was built as the output stages of the pulses. It can gate all 16 pulses individually and gives 15 microsecond wide pulses, each of which can drive two 50 ohm terminators. Each gate can be enabled and disabled independently. The time resolution of these pulses is about 1 microsecond. For the finer time delay, we use another time delay generator (LeCroy Model 4222), which has four channels with wide dynamic range (170 ns - 16.7 ms) and high time resolution (1 ns steps). This module is started by trigger inputs providing the precise trigger signals for the mass gate, momentum 41 decelerator, detachment laser, and most importantly for the stop signal for the digitizer in the mass mode. The timing sequence in one experimental cycle is described as follows (Figure 2.5). The experiment starts by triggering the Jordan valve, which takes ~430 µsec to respond and to deliver the carrier gas to the waiting room. The vaporization laser is fired at the leading edge of the carrier gas flow or at the peak of the carrier gas pulse. The typical delay time (F1) for the vaporization laser is from 390 to 500 µsec relative to the Jordon valve trigger signal. The focused laser beam generates a plume of plasma. The plasma is cooled by the carrier gas and clustering starts. The resident time of clusters inside the nozzle is about 10~100 µsec. The resulting clusters entrained in the carrier gas expand into the source chamber to form a supersonic jet. A skimmer is mounted in about 13” downstream from the nozzle and collimates the cluster beam. Once the collimated cluster beam reaches the center of the extraction zone in the A-chamber, they are accelerated perpendicularly for the TOF mass analysis. The time delay between the trigger for the extraction voltage and the vaporization laser is scanable. We refer it in the program as parameter F3. F3 usually is in the range from 220 to 400 µsec. The flight length for the mass analysis is 1.4 m, the TOF for Bi− is typically around 53 µs at 1 kV extraction voltage. The mass gate time (F6) is roughly ~88.8% of the total TOF of each ion. The delay time (F7) between the mass gate pulse and the deceleration pulse is in the range from 0.4 µsec to 2.5 µsec in this experimental work, for 42 instance, F7 is about 0.7 µsec for Bi− and Au−. The time delay between the deceleration pulse and the detachment laser (F8) is usually around 8 to 20 µsec. Figure 2.5 The time sequence in one experimental cycle for generating clusters and taking photoelectron spectrum from a cluster anion. 43 2.5.2 National Instruments PXI Platform The experimental control interface was later upgraded to the new National Instrument PXI platform and controlled by a Labview based program. The new control system includes a NI PXI-1042 8-slot chassis equipped with a controller (PXI-8108) and five modules. A PXI-7340 module is used as a motion controller for the target movement. All the 10 Hz pulse triggers for cluster generation and TOF mass spectrometer, namely the Jordan Valves, vaporization laser and its Q-switch, and the Repeller, are generated by a PXI-6552 100 MHz digital waveform generator. The 20 Hz pulse triggers for the photoelectron detachment part, such as the triggers for mass gate, momentum decelerator and the detachment laser and its Q-switch, are generated using a MH DG-101 (Mink Hollow Systems, Inc.) four channel digital delay generator. The ion and electron signals from the multichannel plates are digitized by a PXI-5154 module to the controller. 2.6 Mass and Energy Calibration Mass measurement depends on the proper calibration of the instrumental time scale. The time of flight is related to the kinetic energy of the clusters supplied by the extraction stack and the mass of the clusters in the following relationship: Eq. 10 which can be simplified as √ Eq. 11 44 By fitting the time of flight and the square root of the mass, a set of parameters a and b could be obtained for further mass calibration. The a and b parameters largely depends on the voltage and direction of the repeller stack. Similarly, accurate energy measurements depend on the proper calibration of the instrumental energy scale. The kinetic energy of an electron is related to its time of flight in the following relationship Eq. 12 where a, b and c are parameters related to individual experimental conditions of the whole system. They present combined experimental conditions to the PES spectra. There are a number of reasons that cause the change of these parameters: 1) different electron trajectories induced by a slight non-uniformity of the electric field or magnetic field in the photoelectron detachment zone may cause a change of parameter a; 2) slight unequal vacuum in the detachment chamber or in the 3.5 meter magnetic-bottle TOF tube may induce a change of parameter b; 3) slight changes of the detachment laser position and bandwidth may induce a change of parameter c. The known PES spectra of Bi−, Pb−, Ag− and Au− atomic anions are used for spectrometer calibration to convert TOF to binding energy spectra for different photon energies. The energy levels corresponding to peaks in the PES spectra of these atomic anions are known and are used to obtain the calibration parameters, a, b, c for each experiment. 45 Figure 2.6 shows the Bi− spectra at three photon energies: 3.496, 4.661 and 6.424 eV. In the 193 nm spectrum (6.424 eV), we observe transitions from the ground state of Bi− (3P2, 6s26p4) to the ground state (4S1/2, 6s26p3) and four excited states (2D3/2, 5/2, 2P1/2, 3/2, 6s26p3) of Bi. The 355 nm (3.496 eV) spectrum represents the best resolution of our PES spectrometer with very large momentum deceleration. The full with at half maximum (FWHM) for the 4S1/2, 2D3/2, and 2D5/2 states are 55, 24, and 16 meV, respectively, indicating the dependence of the energy resolution on the electron kinetic energies. This dependence is also shown clearly from the increasing peak widths for the 266 nm and 193 nm spectra. The bandwidth of the excimer laser (~ 50 meV) also contributes to the broadening of the 193 nm spectrum. From Figure 2.6, it can be seen that noise begins to show up at the high binding energy side of the 266 and 193 nm spectra above ~ 3.5 eV. The 193 nm spectrum shows that the noise becomes significant above 4 eV and thus often low photon flux is used to reduce the noise problem. 46 Figure 2.6 Photoelectron spectra of Bi− at three photon energies for energy calibration. 47 2.7 Temperature Effect and Control Besides the Doppler broadening that could be eliminated with the previous mentioned momentum decelerator, the quality of PES spectrum is also determined by a number of factors. The first is the intrinsic nature of the electronic structure of the cluster, i.e., if it intrinsically has large density of states or multiple vibrational modes active upon electron detachment. Those clusters usually have low structural symmetries or floppy structures. The second factor is the instrumental resolution, which in our case can be improved using the optimal magnet position and the length of electron TOF tube. The best resolution can be achieved is ~ 25 meV for photoelectrons with 1 eV kinetic energy. The third factor, cluster temperatures, is critical to the PES spectrum but cannot be easily measured or controlled. The hot clusters have significant population of electronic excited states or in some cases, low-lying isomers, either of which will generate a new set of detachment bands. As shown previously, the temperature of cluster anions is critical in determining the quality of PES spectra.170,171 Cold clusters yield much better resolved spectra by eliminating vibrational hot bands or low-lying isomers. 10,12 In the current setup, the clusters are generated using laser vaporization of a solid target, which results in hot plasma at about 10000 K in temperature. Collision with He carrier gas releases the heat of the hot ions and initiates the nucleate of clusters. Supersonic expansion through a small orifice to vacuum further cools down the temperature of clusters 48 and enhances the population of larger clusters, which produces significant low temperature cluster compared with other techniques. The temperature of clusters generated using laser vaporization technique depend on a number of parameters, such as source geometry, types of pulsed valves, vaporization laser power, types of carrier gases, carrier gas temperatures and pressures, etc. To achieve lower temperature, several strategies have been used in the experiment: 1) Control the residence time of clusters in the nozzle.171 The residual time is tuned by the time delay between the Jordan valve trigger and the vaporization laser trigger (F1). To obtain cold cluster, the optimal F1 time is between 445 ms to 460 ms for boron clusters. The application of large waiting room nozzle is found to significantly lower the cluster temperature by allowing the nascent clusters to stay inside the nozzle longer and sufficiently colliding with carrier gas. 2) Extraction time. The time delay between the extraction voltage and the vaporization laser triggers (F3) determines the part of molecular beam to be extracted. As shown in Figure 2.2, the early part of molecular beam contains small and warm clusters due to less residual time in the nozzle; the later part contains large and cold clusters. Typically, F3 falls between 300 ms to 360 ms for boron cluster. 3) Ar seeded carrier gas. The initiation of clustering is by the collision with the carrier gas. Larger carrier gas can take away more thermal energy compared to the small carrier gas and therefore 49 produces colder clusters. Previous experiments on Au cluster have shown that the 5% Ar seeded He carrier gas produce coldest clusters.172-174 2.8 Theoretical Calculations The chemical and physical properties of clusters are dependent on their geometrical structures. However, there is no experimental method for direct structural determination. PES probes the electronic structures of clusters, which, in combined with theoretical calculations, is the most powerful technique to eclucidate the structures of clusters. Our first goal is to obtain cluster structures by comparing experimental data with calculations. Then we analyze the cluster structure to understand the stability, chemical bonding and other properties. Theoretical approaches include three steps: 1) Theoretical global minimum search. 2) Comparison of the experimental and theoretical vertical detachment energies. 3) Chemical bonding analyses. They will be described in detail in the following sections. 2.8.1 Global Minimum Structure Search The potential energy surface of the cluster is explored to locate the most viable chemical structures and low-lying isomers. This task is performed using various programs such as the 1) Simulated Annealing.175 The Simulated Annealing is based on a procedure simulating the process of self-organizing of clusters when we heat them to a high temperature and then gradually cool them down. In this case, atoms will be assembled into 50 the most stable structure. 2) Basin Hopping method.104,105,176 The Basin Hoping method can be considered as a modification of Simulated Annealing. In Basin Hopping algorithm, the local minimum structure in the basin is used as the initial structures to calculate the probability of acceptance of the transformed structure. 3) Gradient Embedded Genetic Algorithm (GEGA).102 The Genetic Algorithm generates new structures via mating of two “parent” structures, which are already optimized as local minimum structures. This can also prevent the search to be entrapped in some local minima. 4) Coalescence Kick (CK) method.103 The CK method subjects large populations of randomly generated structures to a coalescence procedure, in which all atoms are pushed gradually to the center of mass to avoid generation of fragmented structures, and then optimizes them to the nearest local minima. 5) Cartesian Walking (CW) method.106 The CW method uses a constrained random walking procedure on a grid of Cartesian points, placing one atom down at each step to generate trial structures that are then optimized. Walks were constrained by allowing a maximum distance per step and by rejecting all moves which placed an atom within the minimum distance or less than any previously placed atoms. 6) TGMin.177 TGmin is a constrained Basin-Hopping code, which applies controlled perturbation to the initial structure and pre-optimizes the geometry. TGmin is usually used for large clusters. The initial structures generated by those algorithms are first optimized using density functional theory (DFT) methods and small basis set. The lowest isomers are then 51 reoptimized as higher level of theory using larger basis set. Single-point energy calculations for the lowest energy isomers of will further be performed using the restricted (unrestricted) coupled cluster method with single, double, and noniterative triple excitations [R(U)CCSD(T)].178-181 2.8.2 Vertical and Adiabatic Detachment Energy Calculations Assignment of the global minimum structure is based on comparison of the measured VDEs and ADEs from the photoelectron spectra with theoretically calculated VDEs corresponding to the lowest energy isomer(s). The first VDE is calculated as the energy difference between the anion and the neutral, where the neutral single point calculation is performed at the anionic geometry, as measured in the photoelectron spectroscopy experiment. The ADE, which also represents the EA of the corresponding neutral species, is the energy difference of the anion and the neutral at their own optimized geometries. Higher VDEs are calculated by adding vertical excitation energies of the neutral cluster obtained by time-dependent DFT (TDDFT) method182,183, Green Function method184- 187 or coupled cluster method178-181. 2.8.3 Chemical Bonding Analyses We rationalize the structure of the global minimum through chemical bonding analyses, including the use of the AdNDP algorithm and canonical molecular orbitals (CMOs).107 These analyses explain what governs the geometric and electronic structure and 52 stability of the cluster. The AdNDP method has been successfully used to produce chemical bonding pictures of not only small boron clusters, but of boron and carbon 2D materials.188- 190 It analyzes the first-order density matrix in order to obtain its local block eigenfunctions with optimal convergence properties for an electron density description. The obtained local blocks correspond to the sets of n-atoms (n ranging from one to the total number of atoms in the molecule) that are tested for the presence of n-electron objects [n-center two-electron (nc-2e) bonds], including core electrons and lone pairs as a special case of n = 1 associated with this particular set of n-atoms. AdNDP initially searches for core electron pairs and lone pairs (1c-2e), then 2c-2e, 3c-2e... and finally up to nc-2e bonds. At every step, the density matrix is depleted of the density corresponding to the appropriate bonding elements. The user-directed form of the AdNDP analyses can be applied to specified molecular fragments and is analogous to the directed search option of the standard natural bond orbital (NBO) code.191,192 AdNDP accepts only those bonding elements whose occupation numbers (ONs) exceed specified threshold values which are usually chosen to be close to 2.00 |e|. The AdNDP method recovers both Lewis bonding elements (1c-2e and 2c-2e objects, corresponding to the core electrons and lone pairs, and 2c-2e bonds) and delocalized bonding elements, which are associated with the concepts of aromaticity and antiaromaticity. From this point of view, AdNDP achieves a seamless description of systems featuring both localized and delocalized bonding without invoking the concept of resonance. 53 Chapter 3 A World of Flat Boron Clusters Boron compounds have been used in daily life since the beginning of written history. The most important boron compound found in nature is the borax, which has been used to prepare hard glasses and glazes.4,193 Nowadays, boron compounds have a vast range of applications from superhard materials, semiconductors to biological compounds with antiseptic, antiviral, antitumor and antifungal properties. Elemental boron was recognized in 1808 by Sir Humphry Davy, Joseph Louis Gay- Lussac and Louis Jacques Thénard, but pure boron was not obtained until 1892.2 Similar to its neighbor carbon, boron can form strong covalent bonds with almost all the elements in the Periodic Table. With one less electron than the number of valence orbitals, boron is electron deficient and thus exhibits interesting chemical bonding. A few milestones in the history of boron chemistry should be pointed out: 1) Three-center-two-electron (3c-2e) bond. Diborane (B2H6) was first synthesized in the 19th century and was identified by Alfred Stock. It does not have enough electrons to form an ethane-like structure according to the octet rule. The structure of B2H6 with bridging H-atoms was gradually discovered by Walter Dilthey,194 W.C. Price,195,196 Hugh Longuet-Higgins, M. Roberts,197,198 and others. This structure was later supported by infrared spectroscopy data199 and low-temperature X-ray diffraction200. The concept of 3c-2e bond over the B-H-B bridge in diborane was developed 54 during these studies and was put forward by William Lipscomb in an effort to understand the quantum mechanical details of the interaction in diborane. William Lipscomb was awarded the Nobel Prize in 1976 for his contribution in boron chemistry. 2) Hydroboration. Boranes are so chemically reactive that they can react rapidly with hydrocarbons to produce organoborane compounds, which are important synthetic intermediates. With proper oxidation agents, organoborane compounds could be used to produce useful compounds, such as alcohols, amines, alkyl halides. This two-step reaction is called hydroboration– oxidation reaction. It was first reported in the late 1950s by Herbert Brown,201 who won the Nobel Prize in Chemistry in 1979. Bulk boron flourishes with a number of polymorphs consisting of B12-icosahedral building blocks.122 Though only four pure elemental phases have been synthesized,123-127 new forms of boron are continuing to be discovered.122 There were early speculations if small boron clusters might also have cage structures. However, early theoretical calculations suggested that the cage structures are not stable as isolated units in the gas phase. Instead, planar or quasi-planar structures are more favored.202-213 Joint experimental and computational investigations over the past two decades by Wang group and collaborators have demonstrated that negatively charged boron clusters (Bn−) possess planar or quasi-planar (2D) pancake structures at least up to n = 20 (Figure 3.1).103,104,128-138 Their ADEs are shown in Figure 3.2, which display an even-odd pattern and increase as the 55 number of boron atom. One of the key structural features that have emerged from joint experimental and computational investigations is that each planar boron cluster contains an outer boron ring and one or more inner atom(s). Chemical bonding analyses of the boron clusters have shown the periphery is bonded via classical 2c-2e B-B bonds while the inner B atoms bond to the outer ring via delocalized σ and π bonding,103,104,128-138 giving rise to concepts of σ- and π-aromaticity, σ- and π-antiaromaticity, or conflicting aromaticity- antiaromaticity.103,104,107,128-138,214 The following species, B82− and B9−,132,134 B10, B11− and B12,133 and the B13+ cation214-217 each have three occupied  CMOs and have been considered all-boron analogues of benzene, all with six delocalized electrons satisfying the 4N+2 Hückel rule for  aromaticity. The B13− and B14 clusters each with 8  electrons are considered to be  antiaromatic according to the 4N Hückel rule, conforming to their elongated shapes.133 The B162− and B17− clusters, each with 10 delocalized  electrons, have been shown to be analogous to naphthalene.103,138 The B19− cluster has been found to possess a highly circular spider-web-like structure with a 13-atom outer ring and an internal B-centered pentagonal unit.104 It is doubly  aromatic, consisting unprecedentedly of two concentric  systems, analogous to coronene. The unique structure and bonding of B19− has inspired the proposal of a molecular Wankel motor, because the barrier of the in-plane internal rotation of the inner pentagonal system against the thirteen-atom peripheral ring is found to be quite low.218 Similar fluxional behavior has also been found subsequently in the 56 planar B13+ cluster for its internal B3 triangle.219 It is even suggested recently that circularly polarized light can be used to achieve a desirable uni-directional rotation, rendering a photo- driven molecular Wankel motor.220 On the other hand, the positively charged boron clusters are found to be planar up to 16 atoms.139 Direct experimental studies of neutral boron clusters have been challenging and the 2D-to-3D transition has not been experimentally confirmed yet. Even though the neutral B20 was found computationally to have a 3D double ring global minimum structure on its potential energy surface,135,221 recent infrared experiment failed to detect this structure.222 Similarly, the proposed 3D structure for B14 (Ref. 141) runs counter to the recent infrared experiment that neutral B11, B16, and B17 are planar.222 Whether the anionic boron clusters will adopt 3D structures remains an open question. Another interesting question is: which will be the smallest 3D anionic boron clusters? In this chapter, joint PES and ab initio investigations of boron clusters in the size range of 21 to 24 atoms are reported. All these four clusters display relatively congested and broad spectral features compared to the smallest clusters. Global minimum structure searches have found quasiplanar structures featuring 7 (for B21–) or 8 interior (for B22– to B24–) atoms as their global minimum structures, which are confirmed by comparing their simulated spectra to the experimental data. Chemical bonding analyses show that the Bn– (n = 21 – 24) clusters are all boron analogues of hydrocarbons. 57 Figure 3.1 The structures of Bn− (n = 3 − 20). Figure 3.2 Experimentally measured ADEs of Bn− (n = 3 − 20). The uncertainty is given in parentheses. 58 3.1 Experimental Results The photoelectron spectra of Bn– (n = 21 – 24) at 193 nm are shown in Figure 3.3. The VDEs of major detachment features are summarized in Table 3.1, Table 3.2, and Table 3.3, respectively, where they are compared with the theoretical results (vide infra). B21−: The 193 nm spectrum of B21− (Figure 3.3a) shows a broad detachment band at around 4.6 eV, followed by an almost continuous spectral region spanning the binding energy range from 5 to beyond 6 eV with discernible fine features. The intense and broad 4.6 eV band seems to consist of more than one detachment channels. We assign the leading edge of the peak to the X band and a shoulder on the higher energy side to the A band. The VDE for the band X is measure at 4.58 ± 0.04 eV. The ground state ADE was estimated to be 4.38 ± 0.05 eV for B21−, which represents the EA of neutral B21. For the A band, we estimated a VDE of 4.79 ± 0.06 eV. On the high binding energy side, we tentatively assign three more electronic bands (B, C, and D) with VDEs of 5.17 ± 0.04, 5.43 ± 0.05, and 5.72 ± 0.05 eV, respectively. Finally, we note the presence of a weak tail on the low binding energy side below 4.3 eV. This tail was present in all of our experiments using different boron isotopes and targets. We conclude that this feature could be due to either hot band transitions and/or higher energy isomers in the cluster beam because its contribution diminishes when colder expansion conditions were used.170,171 59 B22−: The PES spectrum of B22– (Figure 3.3b) is quite congested with photodetachment features spanning the binding energy range from 3.3 eV to beyond 6 eV. The ground-state band X has a VDE of 3.48 ± 0.05 eV and an ADE of 3.34 ± 0.06 eV. The next resolved electronic bands are labeled as X′ (~ 3.6 eV), A (3.87 ± 0.04 eV), and B (4.10 ± 0.05 eV). As will be shown below, the X′ band comes from low-lying isomers of B22–. Following a small energy gap, the spectrum displays a broader feature that is assigned to two closely spaced detachment channels, C (4.48 ± 0.05 eV) and D (4.64 ± 0.04 eV). At the high binding energy side, we observed a few more bands and tentatively assigned them as E (5.01 ± 0.05 eV), F (5.51 ± 0.05 eV), and G (.89 ± 0.04 eV). The congested spectrum suggested that there might be contributions from close-lying isomers of B22–. B23−: In comparison to B22–, B23– has a higher binding energy and a relatively simpler spectrum (Figure 3.3c). The first photodetachment band, X, is well resolved and seems to contain fine features due to either possible vibrational structures or overlapping detachment channels. The X band yields a VDE of 4.46 ± 0.03 eV and an ADE of 4.32 ± 0.06 eV. The next two features, A (4.95 ± 0.04 eV) and B (5.22 ± 0.05 eV), are broad and not well resolved, indicating a possible overlap of additional detachment bands. At the high binding energy side of the spectrum, we observed a strong and well-defined resolved band C with a VDE of 5.56 ± 0.03 eV, followed by a well-resolved band D with a VDE of 6.06 ± 0.03 eV. 60 B24−: The PES spectrum of B24− is shown in Figure 3.3d at 193 nm. The first detachment channel of B24− is defined by feature X with a VDE of 3.75 ± 0.07 eV and an ADE of 3.55 ± 0.07 eV. The broad width of the X band and relatively large difference between the ADE and VDE suggests significant geometry changes from the anion ground state to that of the neutral upon electron detachment. Following an energy gap of ∼1 eV, a set of intense and congested features are observed. Features A, B, and C are observed with VDEs of 4.61 ± 0.08, 4.79 ±0.08, and 5.12 ± 0.08 eV, respectively. One more intense feature D is observed at 5.62 ± 0.06 eV, followed by a weaker feature E at 5.96 ± 0.05 eV. All these spectral bands are relatively broad, suggesting that they may contain more than one detachment channel. 61 Figure 3.3 PES spectra of (a) B21–, (b) B22−, (c) B23− and (d) B24− at 193 nm. 62 3.2 Theoretical Results Searches for the global minimum and low lying isomers of Bn– (n = 21 – 24) were done using the CK and CW method at the DFT level of theory using small basis set (3- 21G)223. The lowest-lying isomers were further reoptimized using larger basis set, and frequencies were calculated to make sure the structures were true minima. Single point calculation at CCSD(T) (for B21−, B22− and B24−) were performed for the several lowest- lying isomers for more accurate relative energies. B21−: Both CK and CW methods identified the same set of ten low-lying isomers, as shown in Figure 3.4. The global minimum isomer I has Cs symmetry and 14 peripheral atoms. One B-B bond connects two symmetric pentagon holes inside the ring. The isomer II was found to be the global minima at PBE0224-226 and MP2227,228 levels but as the second isomers according to CCSD(T) calculation. The relative energy to isomer I is only 1.9 kcal/mol at CCSD(T) level of theory. The geometric optimization MP2 level shows that isomer II distorts to a quasi-planar C1 structure. Also presented in Figure 3.4 are results of the relative energies of the single-point energy calculations for the five lowest energy isomers at the CCSD(T) level along with their relative energies at the MP2/6-311+G*229-231 level, and the relative energies of the ten lowest lying isomers at the B3LYP/6-311+G* and PBE0/6-311+G* levels. It should be pointed out that the MP2/6-311+G* results differ significantly from the most accurate CCSD(T)/6-311+G* data, which are seen to agree 63 much more closely with the DFT results, as also observed previously for smaller boron clusters.103,104,138 The two low-lying isomers (I and II) of B21− are very similar to the two corresponding low-lying isomers of B19−.104 The global minimum of B19− is a perfect planar and doubly π aromatic system with a central B atom surrounded by a five-membered ring and a 13-atom outer ring. The global minimum of B21− (Figure 3.4) can be viewed as adding a B atom to one apex of the five-membered ring in the interior and one B atom to the outer ring of the global minimum of B19−. The isomer II of B21− can be viewed similarly as adding one B atom to the interior and one B atom to the outer ring of the second lowest- lying planar structure of B19−.104 It should be emphasized that the global minimum searches of B21− using the CK and CW methods were performed more extensively and were done totally independently without any references to the structures of B19−. It is also interesting to note that the second isomer of B19− was found to be 3.73 kcal/mol higher in energy than the global minimum at the CCSD(T) level and was much less populated in the cluster beam under similar experimental conditions. In the current work, we find that isomer II of B21− is only 1.9 kcal/mol higher in energy than the global minimum isomer I at the CCSD(T) level and is expected to be much more populated experimentally. The CCSD(T) energetics are consistent with the fact that the PES spectrum of B21− appears more congested (Figure 3.3a) in comparison with the spectrum of B19−, which displayed more prominent spectral 64 features.104 These observations suggest the validity of the CCSD(T) energetics for these complicated clusters and lend further credence to the identified global minima and low- lying isomers for both clusters. Figure 3.4 The low-lying isomers of B21–. Relative energies are given at the CCSD(T)/6- 311+G*//B3LYP/6-311+G* level (I-V), at the B3LYP/6-311+G* level (in parenthesis), at the PBE0/6-311+G* level (in curly brackets), and at MP2/6-311+G* level (in square brackets for I-V). All values are corrected for ZPEs. B22−: The global minimum and low-lying isomers of B22− are presented in Figure 3.5. The 3D tubular isomer I (Ci, 2Au) is lowest in energy according to each level of theory. Our frequency calculation revealed that this structure has one imaginary frequency (–90 cm–1 at 65 PBE0/6-311+G* level), although when this mode was followed and the structure reoptimized, the similar Ci structure was returned. The next lowest in energy is the quasi- planar isomer II (C2, 2B), only 0.78 kcal/mol higher at the CCSD(T) level (Figure 3.5). Isomers I and II can be considered degenerate within the accuracy of our calculations. The quasi-planar isomer II comprises a 14-atom peripheral ring with 8 interior atoms and can be described as a buckled triangular lattice (the maximum out-of-plane distortion is 0.93 Å. The next lowest in energy are isomers III and IV, which are 1.79 and 2.44 kcal/mol higher in energy, respectively, according to the CCSD(T)/6-311+G* level of theory. These two isomers are also quasi-planar, each with 14 peripheral atoms and 8 inner atoms, except they each contain a hole in the lattice. Structures I–IV are all low enough in energy to warrant comparison with the experimental spectrum. We encountered high norm values in the CCSD(T) calculations of the B22– isomers (Norm values indicate multiconfigurational contributions to the CCSD(T) wave functions). A norm value of larger than 1.5 is considered high in CCSD(T) calculations. Isomers I–IV of B22– all have norm values near or above 1.5 and could not converge any of the CASSCF single-point calculations of the isomers. This suggests the multiconfigurational nature of B22– and therefore the relative energies obtained using CCSD(T) level of theory are questionable. The best we could do in this case was to compute the VDEs for all the low- lying isomers to see which structure agrees with the PES spectrum of B22–. As will be 66 discussed below, the quasi-planar (C2, 2B) isomer appears to be a major contributor to the PES spectrum with structures III and IV being minor contributors. Figure 3.5 The low-lying isomers of B22−. Relative energies are given in kcal/mol at the CCSD(T)/6- 311+G*//PBE0/6-311+G*, PBE0/6-311+G* (in parenthesis), and B3LYP/6-311+G* (in square brackets) levels of theory. The PBE0/6-311+G* and B3LYP/6-311+G* numbers have been corrected for zero-point energies (ZPEs) at their respective levels of theory while the CCSD(T) energies have been ZPE corrected using the PBE0/6-311+G* values. B23−: Both CK and CW searches revealed a perfectly planar C2v closed-shell structure I as the global minimum (Figure 3.6) with no competing close-lying isomers at both DFT levels of theory. This structure has a heart shape consisting of a 15-atom periphery, 8 interior atoms, and a pentagonal hole. The second low-lying isomer II is 6.98 and 23.74 kcal/mol higher in energy at PBE0 and B3LYP levels, respectively. The isomer is quasi-planar also with C2v symmetry and a buckled triangular lattice. The next isomer III has an elongated shape and is much higher in energy, ~19 kcal/mol relative to the global minimum at both PBE0 and B3LYP levels. Isomer IV at 20.76 kcal/mol is a low-symmetry 67 planar structure also with a pentagonal hole like the global minimum. Finally, the 3D double-ring-like structure V is found to be much higher in energy, ~22 kcal/mol higher in energy, than the global minimum at the PBE0 level. Figure 3.6 The low-lying isomers of B23−. Relative energies are given in kcal/mol at the PBE0/6- 311+G* and B3LYP/6-311+G* (in parenthesis) levels of theory and have been corrected for ZPEs at their corresponding levels of theory. B24−: Both restricted-open CCSD (ROCCSD) and restricted-open CCSD(T) [ROCCSD(T)] calculations show isomer I (C1, 2A) as the global minimum (Figure 3.7), which possesses a slightly puckered geometry and a filled pentagonal moiety with the central boron atom sticking out of the molecular plane by approximately 0.9 Å. For comparison, the same filled pentagonal moiety is found in B21− with an out of plane distortion of about 0.5 Å, whereas in B19− the filled pentagonal unit is found to be perfectly planar. Interestingly, the B-B bond lengths inside the pentagon vary from 1.61 to 1.68 Å, whereas the same bonds in the 3D α-boron icosahedral units are about 1.73 Å. 68 The manually built tubular isomer II was suggested as the most stable structure of B24− cluster at the DFT level,232 yet the more accurate and reliable ROCCSD and ROCCSD(T) calculations show that it is higher in energy than the quasi-planar isomer I, found via our global minimum searches. It was examined based on similar structures reported to be present among the low-lying isomers of several anionic boron clusters.103,104,106,108 The double ring structures have never been observed experimentally222 for any neutral or anionic boron clusters, even in cases where such isomers were found computationally to be rather low-lying.108,135 As will be discussed below, the comparison between the simulated PES spectra and the experiment supports our findings of the quasi- planar structure I as the global minimum of B24−. The next two lowest energy isomers (III and IV) possess pentagon-shaped cavities much like the global minimum structure I, but do not contain a filled pentagonal moiety. Structures III and IV are 4.59 and 6.24 kcal/mol higher in energy, at ROCCSD level, than isomer I, respectively. Isomer V has a triangular lattice, similar to the global minimum of B22−. All other structures in Figure 3.7 represent planar and quasi-planar high-energy isomers with relative energies >10 kcal/mol above the global minimum at the highest levels of theory. It is noteworthy that the robustness of planar geometry103,104,106,108,109,128-138 is seen for many boron clusters. 69 In order to compare the stability of the global minimum structure I with one of the most stable 2D sheet of boron atoms, the so-called α-sheet,142,145,147-149,151-153 and 3D α- rhombohedral bulk boron, we have performed additional calculations at the PBE/6-31G(d,p) level of theory to find a cohesive energy of the ground B24− isomer. It turned out that of the B24− cluster is 5.62 eV per boron atom. The values of the 2D α-sheet142,145,147- 149,151-153 and 3D α-rhombohedral bulk boron233 were previously calculated to be 5.93 eV145 (6.11 eV147) and 6.33 eV142, respectively. To assess the multi-reference character in the ROCCSD(T) method, we used an open-shell T1 diagnostic, which can produce a qualitative picture of the significance of non- dynamical (or static) correlation: the larger the T1 value, the less reliable the results of the single-reference coupled cluster wave function. In the current work, we obtained T1 diagnostic values using the open-shell T1 formalism of Jayatilaka and Lee,234 who suggested that open-shell T1 values may be larger than those of closed-shell systems, where T1 values greater than 0.02 are typically suspicious.235,236 Table 3.4 shows the T1 values at the ROCCSD(T) level of theory for all the isomers of B24− except isomer III, which is not presented due to the missing energy value at ROCCSD(T). As was suggested by Schaefer III and co-workers,237 the T1 values above 0.044 are considered somewhat less reliable for open-shell systems. According to our results, all the values are below 0.027, which supports 70 the reasonable assessment of our wave-function as single-configurational for all the studied species. Figure 3.7 The low-lying isomers of B24–. Relative energies are shown from single-point calculations at ROCCSD/6-311+G(d)//PBE0/6-311+G(d) and ROCCSD(T)/6-311+G(d)//PBE0/6-311+G(d) (in curly brackets), as well those from PBE0/6-311+G(2df)//PBE0/6-311+G(d) (in parentheses) and TPSSh238/6-311+ G(2df)//TPSSh/6-311+G(d) (in square brackets). All energies have been corrected for ZPEs at the corresponding levels of theory, aside from the CC methods, which have been corrected with the PBE0 ZPEs. The relative energy of isomer III at ROCCSD(T)/6- 311+G(d)//PBE0/6-311+G(d) could not be obtained. 71 3.3 Comparison between Experimental and Theoretical Results B21−: The calculated VDEs for isomers I and II at different levels of theory are compared with the experimental VDEs in Table 3.1. The pole strengths for the OVGF184-187 calculations are given in parentheses and they are all found to exceed 0.86, suggesting the single-electron description of the electron detachment processes for this system is a good approximation. Since the anion is a closed-shell system, electron detachment from each valence MO generates a final doublet electronic state within the one-electron picture. All three theoretical methods yield similar VDEs within 0.25 eV of each other for both isomers I and II (Table 3.1). Thus, the OVGF data will be used primarily in the following discussion. Isomer I: The first detachment channel occurs from the 13a" HOMO with a calculated VDE of 4.63 eV from OVGF, in excellent agreement with the first experimental VDE of 4.58 eV. The calculated second and third VDEs from HOMO−1 and HOMO−2 are nearly identical to each other (4.71 eV and 4.70 eV) and are in good agreement with the experimental feature A at 4.79 eV. The X and A bands are not well resolved experimentally and clearly the first three detachment channels are responsible for the intense broad band near 4.6 eV in the PES spectrum (Figure 3.3a). The OVGF VDEs for the next three detachment channels, 5.25, 5.39, and 5.54 eV agree well with the observed band B at 5.17 eV, band C at 5.43 eV, and band D at 5.72 eV, respectively (Table 3.1). The predicted 72 spectral pattern for isomer I is fairly simple. The somewhat congested spectral pattern observed experimentally suggests that there must be contributions from other isomers. Isomer II: At CCSD(T) level, isomer II is only 1.9 kcal/ mol higher in energy than isomer I and is expected to be significantly populated under our experimental conditions and contribute to the observed PES spectrum. The VDEs for the first three detachment channels for isomer II (Table 3.1) are very similar to those from isomer I and they should contribute to the intense broad band at 4.6 eV in the experimental spectrum (Figure 3.3a). The VDEs for the next four detachment channels range from 5.07 to 5.91 eV (Table 3.1); corresponding experimental features can be identified from the PES spectrum. We conclude that the calculated VDEs for isomers I and II are consistent with the experimental data and that it is the presence of the two nearly degenerate isomers that produced the somewhat congested PES spectrum observed experimentally. Isomers III, IV, and V: The calculated first VDE for isomers III (3.53 eV), IV (4.42 eV), and V (4.28 eV) are much smaller than the experimental value of 4.58 eV. However, these low VDEs are consistent with the weak low binding energy tail in the experimental spectrum (Figure 3.3a). This observation suggests that these isomers might be very weakly populated. 73 Overall, the good agreement between the experimental and theoretical results lends considerable credence to the planar structures and the energetics of the global minimum and low-lying isomers of B21−. Table 3.1 Comparison of the experimental VDEs with the calculated values for B21–. The calcualted values are based on the isomer I (Cs, 1A') and isomer II (Cs, 1A') of B21–. All energies are in eV. VDE (theo.) Feature VDE (expt.)a Final state and electronic configuration b TD-B3LYP TD-PBE0b OVGFc Isomer I (Cs, 1A') Xd 2 4.58 (4) A", 17a'218a'211a"212a"219a'213a"1 4.46 4.60 4.63 (0.88) 2 2 2 2 2 1 2 A', 17a' 18a' 11a" 12a" 19a' 13a" 4.50 4.68 4.71 (0.89) A 4.79 (6) 2 2 2 2 1 2 2 A", 17a' 18a' 11a" 12a" 19a' 13a" 4.60 4.75 4.70 (0.88) 2 2 2 1 2 2 2 B 5.17 (4) A", 17a' 18a' 11a" 12a" 19a' 13a" 5.00 5.12 5.25 (0.86) 2 2 1 2 2 2 2 C 5.43 (5) A', 17a' 18a' 11a" 12a" 19a' 13a" 5.24 5.40 5.39 (0.88) 2 1 2 2 2 2 2 D 5.72 (5) A', 17a' 18a' 11a" 12a" 19a' 13a" 5.53 5.73 5.54 (0.88) 1 Isomer II (Cs, A') 2 A", 23a' 4a" 24a' 5a"225a'226a'26a"1 2 2 2 4.46 4.67 4.59 (0.88) X 4.58 (4) 2 2 2 2 2 2 1 2 e A', 23a' 4a" 24a' 5a" 25a' 26a' 6a" 4.52 4.57 4.61 (0.89) 2 2 2 2 2 1 2 2 e A 4.79 (6) A', 23a' 4a" 24a' 5a" 25a' 26a' 6a" 4.66 4.77 4.81 (0.88) 2 2 2 2 1 2 2 2 B 5.17 (4) A", 23a' 4a" 24a' 5a" 25a' 26a' 6a" 4.86 5.05 5.07 (0.89) 2 2 2 1 2 2 2 2 A', 23a' 4a" 24a' 5a" 25a' 26a' 6a" 5.32 5.52 5.54 (0.87) C 5.43 (5) 2 2 1 2 2 2 2 2 A", 23a' 4a" 24a' 5a" 25a' 26a' 6a" 5.33 5.51 5.56 (0.88) 2 1 2 2 2 2 2 2 D 5.61 (5) A', 23a' 4a" 24a' 5a" 25a' 26a' 6a" 5.66 5.77 5.91 (0.87) 1 Isomer III (C1, A) 2 A, … 26a 27a 28a229a230a232a1 2 2 3.67 3.77 3.53 (0.89) 1 Isomer IV (C1, A) 2 A, … 26a 27a 28a229a230a232a1 2 2 4.23 4.27 4.42 (0.89) 1 Isomer V (C1, A) 2 A, … 26a 27a 28a229a230a232a1 2 2 4.15 4.23 4.28 (0.88) a Numbers in parentheses represent the uncertainty in the last digits. b Calculated at TD-DFT/6-311+G(2df)//B3LYP/6-311+G* level. c Calculated at ROVGF/6-311+G(2df)//B3LYP/6-311+G* level. Values in parentheses represent the pole strength, which characterizes the validity of the one-electron detachment picture. d − ADE of B21 is 4.38(5) eV. e Multiconfigurational value. 74 B22−: The double-ring tubular structure of B22– gives a first VDE of ~3.1 eV, significantly lower than the experimental first VDE at 3.48 eV. In addition, the calculated spectral pattern including the higher VDEs does not agree with the experimental spectrum.108 Thus, the tubular structure can be ruled out as a contributor to the observed spectrum of B22–. This situation is similar to B20–, for which a double-ring structure was computed to be nearly degenerate with a 2D structure, but had to be ruled out as a contributor to the observed PES spectra on the basis of the calculated VDEs and comparison between experiment and theory.135 The calculated VDEs of the quasi-planar C2 structure of B22– (isomer II) agree very well with the major PES features, as shown in Figure 3.3b and Table 3.2. Table 3.2 compares the calculated VDEs at B3LYP and PBE0 levels with the experimental data. The two levels of theory give similar VDEs, but the PBE0 values agree better with experiment and will be used in the following discussion. The first calculated VDE is 3.51 eV, in excellent agreement with the experimental value of 3.48 ± 0.05 eV. The electron detachment from the HOMO−1 produces the final neutral B22 species in the lowest triplet state. The calculated VDE of this detachment channel is 3.80 eV, in excellent agreement with band A at 3.87 eV. The corresponding singlet final state has a calculated VDE of 4.16 eV, contributing to the band B at 4.10 eV. The higher intensity for band A relative to those of bands X and B is consistent with its higher spin multiplicity. The calculated VDEs for 75 higher detachment channels from the quasi-planar C2 structure of B22– are all in reasonable agreement with the observed experimental features, as seen in Table 3.2. However, the X′ feature observed at ~3.6 eV cannot be accounted for by the C2 isomer of B22–. Both isomers III and IV are low in energy relative to the C2 isomer and are expected to be populated in the cluster beam. Indeed, the calculated first VDE for isomer III (3.84 eV) and isomer IV (3.70 eV) (Table 3.2) are in good agreement with the observed X′ feature at ~3.6 eV (Figure 3.3b). Therefore, both isomers III and IV should be present in the cluster beam, giving rise to the feature X′. In fact, the broad spectral features for B22– provide indirect evidence for the existence of multiple isomers in the cluster beam. Thus, the theoretical results are in good agreement with the experimental observations, lending credence to the identified global minimum C2 structure for B22– and the ranking of isomers II–IV. However, the absence of the double-ring isomer I in the cluster beam deserves some comments. The absence of this isomer in the cluster beam could be due to kinetic reasons because of its major structural differences with the planar structures. This argument has been used previously to interpret the absence of the similarly low-energy double-ring isomer for B20–.135 However, another more likely possibility concerns the actual stability of the different isomers. Due to the multiconfigurational nature of B22– as mentioned before, even the single-point CCSD(T) energy may not be reliable. Thus, based on the comparison 76 with experimental spectrum, we conclude that the C2 isomer is the main isomer we observed in the PES spectrum of B22–. B23−: We have calculated the VDEs of the two lowest structures identified for B23– (Table 3.2). The isomer II of B23– gives a very low first VDE (B3LYP: 3.21 eV, PBE: 3.33 eV) and can be ruled out to have any contribution in comparison to the observed spectrum (Figure 3.3c). The other isomers were found to be too high in energy (Figure 3.6) and they can be safely ruled out in our experiment condition. The calculated VDEs for the global minimum of B23– are compared with those of the experiment in Table 3.2. The agreement between theory and experiment is excellent. Clearly the X band (4.46 eV) contains two detachment channels (PBE0: 4.41 eV, 4.59 eV), corresponding to the electron removal from the HOMO and HOMO−1. The relatively simple spectral pattern of B23– (Figure 3.3c), compared with the broad spectrum of B22–, suggests that it comes only from one isomer, i.e., the global minimum of B23–, consistent with the fact that the heart-shaped structure is much more stable than any other structures. The very high electron binding energies of B23– also suggest that the heart-shaped structure is an exceptionally stable electronic system, which is borne out from the chemical bonding analyses, as discussed below. 77 Table 3.2 Comparison of the experimental VDEs with the calculated values for B22− and B23−. All energies are in eV. VDE (theoretical) VDE (exp)a final state and electronic configuration TD-B3LYPb TD-PBE0c B22− II (C2, 2B) 1 X 3.48 (5) A, …13b2 14a2 14b2 15b2 16a2 15b2 16b2 17a2 17b0 3.34 3.51 3 2 2 2 2 2 2 2 1 1 A 3.87 (4) B, …13b 14a 14b 15b 16a 15b 16b 17a 17b 3.73 3.80 1 2 2 2 2 2 2 2 1 1 B 4.10 (5) B, …13b 14a 14b 15b 16a 15b 16b 17a 17b 4.02 4.16 3 2 2 2 2 2 2 1 2 1 C 4.48 (5) A, …13b 14a 14b 15b 16a 15b 16b 17a 17b 4.36 4.53 1 2 2 2 2 2 2 1 2 1 D 4.64 (4) A, …13b 14a 14b 15b 16a 15b 16b 17a 17b 4.54 4.74 3 2 2 2 2 2 1 2 2 1 A, …13b 14a 14b 15b 16a 15b 16b 17a 17b 4.82 4.89 1 2 2 2 2 2 1 2 2 1 E 5.01 (5) A, …13b 14a 14b 15b 16a 15b 16b 17a 17b 4.97 5.10 3 2 2 2 2 1 2 2 2 1 B, …13b 14a 14b 15b 16a 15b 16b 17a 17b 5.02 5.14 1 2 2 2 2 1 2 2 2 1 B, …13b 14a 14b 15b 16a 15b 16b 17a 17b 5.29 5.42 F 5.51 (5) 3 2 2 2 2 1 2 2 2 1 B, …13b 14a 14b 15b 16a 15b 16b 17a 17b 5.38 5.51 1 2 2 2 2 1 2 2 2 1 d G 5.89 (4) B, …13b 14a 14b 15b 16a 15b 16b 17a 17b 5.66 5.89d 3 A, …13b2 14a2 14b2 15b1 16a2 15b2 16b2 17a2 17b1 6.17d 6.34d B22− III (C1, 2A) 1 X' ~3.6 eV A …24a2 25a2 26a2 27a2 28a2 29a2 30a2 31a2 32a0 3.67 3.84 − 2 B22 IV (C1, A) 1 A …24a 25a 26a 27a2 28a2 29a2 30a2 31a2 32a0 2 2 2 X' ~3.6 eV 3.51 3.70 − 2 B23 I (C2v, B) 2 B1, …11b2 14a1 3b1 12b2213b222a2215a123a224b11 2 2 2 4.32 4.41 X 4.46 (3) 2 2 2 2 2 2 2 2 1 2 A2, …11b2 14a1 3b1 12b2 13b2 2a2 15a1 3a2 4b1 4.38 4.59 2 2 2 2 2 2 2 1 2 2 A 4.95 (4) A1, …11b2 14a1 3b1 12b2 13b2 2a2 15a1 3a2 4b1 4.83 4.87 2 2 2 2 2 2 1 2 2 2 A2, …11b2 14a1 3b1 12b2 13b2 2a2 15a1 3a2 4b1 4.97 5.19 B 5.22 (5) 2 2 2 2 2 1 2 2 2 2 B2, …11b2 14a1 3b1 12b2 13b2 2a2 15a1 3a2 4b1 5.04 5.23 2 2 2 2 1 2 2 2 2 2 C 5.56 (3) B2, …11b2 14a1 3b1 12b2 13b2 2a2 15a1 3a2 4b1 5.45 5.61 2 2 2 1 2 2 2 2 2 2 D 6.06 (3) B1, …11b2 14a1 3b1 12b2 13b2 2a2 15a1 3a2 4b1 5.90 6.08 2 2 1 2 2 2 2 2 2 2 A1, …11b2 14a1 3b1 12b2 13b2 2a2 15a1 3a2 4b1 6.03 6.21 2 1 2 2 2 2 2 2 2 2 B2, …11b2 14a1 3b1 12b2 13b2 2a2 15a1 3a2 4b1 6.83 6.83 − 1 B23 II (C2v, A1) 2 B2 …9a1 5a2 6b2 10a126a2211a1210b1211b127b21 2 2 2 3.21 3.33 a Numbers in parentheses represent the uncertainty in the last digit. b VDEs were calculated at the TD-B3LYP/6-311+G(2df)//B3LYP/6-311+G* level of theory. c VDEs were calculated at the TD-PBE0/6-311+G(2df)//PBE0/6-311+G* level of theory. d VDE corresponds to transitions of multiconfigurational nature. 78 B24−: The calculated VDEs at the TPSSh and PBE0 levels of theory for isomer I are summarized in Table 3.3. Simulated spectra for isomer I using both functionals are compared with the experimental spectrum in Figure 3.8. The overall patterns at both functionals are in excellent agreement with the experimental data. The PBE0 data will be used in the following discussion. Isomer I: The first VDE of B24− corresponds to the electron detachment of the singly occupied HOMO (37a) resulting in the singlet neutral ground state 1A (Table 3.3). The calculated value of 3.79 eV is in excellent agreement with the experimental value of 3.75 eV. Detachment from HOMO−1 (36a) produces the first triplet neutral state with a calculated VDE of 4.46 eV, in good agreement with the experimental VDE of feature A at 4.61 eV. The next three detachment channels are calculated at 4.65, 4.65, and 4.75 eV, which contribute to the intense and broad feature B at 4.79 eV. Feature C at 5.12 eV is assigned to the singlet final states from electron detachment from HOMO−2 (4.93 eV) and HOMO−3 (5.05 eV). The next five detachments channels are assigned to contribute to the intense and broad feature D at 5.62 eV. Following a 0.4 eV gap in the theoretical values, two detachment channels calculated at 6.07 and 6.24 eV are assigned to feature E at 5.96 eV. No detachment channels are calculated to be in the gap between features X and A, which was not resolved to the baseline in the PES spectrum. This might be due to contributions of possible low-lying isomers in the cluster beam. 79 Table 3.3 Comparison of the experimental VDEs with the calculated values for B24−. The calcualted values are based on the isomer I (C1, 2A) of B24−. All energies are in eV. VDE VDE (theory) Feature a Final state and electronic configuration (Expt.) TD-TPSSh TD-PBE0 1 2 2 2 2 2 2 2 2 0 X 3.75(7) A…29a 30a 31a 32a 3 3a 34a 35a 36a 37a 3.70 3.79 3 A 4.61(8) A…29a2 30a2 31a2 32a2 3 3a2 34a2 35a2 36a1 37a1 4.29 4.46 1 2 2 2 2 2 2 2 1 1 A…29a 30a 31a 32a 3 3a 34a 35a 36a 37a 4.48 4.65 3 2 2 2 2 2 2 1 2 1 B 4.79(8) A…29a 30a 31a 32a 3 3a 34a 35a 36a 37a 4.51 4.65 3 2 2 2 2 2 1 2 2 1 A…29a 30a 31a 32a 3 3a 34a 35a 36a 37a 4.64 4.75 1 2 2 2 2 2 2 1 2 1 A…29a 30a 31a 32a 3 3a 34a 35a 36a 37a 4.73 4.93 C 5.12(8) 1 2 2 2 2 2 1 2 2 1 A…29a 30a 31a 32a 3 3a 34a 35a 36a 37a 4.89 5.05 3 2 2 2 2 1 2 2 2 1 A…29a 30a 31a 32a 3 3a 34a 35a 36a 37a 5.19 5.40 3 2 2 2 1 2 2 2 2 1 A…29a 30a 31a 32a 3 3a 34a 35a 36a 37a 5.34 5.59 1 2 2 2 1 2 2 2 2 1 D 5.62(6) A…29a 30a 31a 32a 3 3a 34a 35a 36a 37a 5.44 5.72 1 2 2 2 2 1 2 2 2 1 A…29a 30a 31a 32a 3 3a 34a 35a 36a 37a 5.36 5.65 3 2 2 1 2 2 2 2 2 1 A…29a 30a 31a 32a 3 3a 34a 35a 36a 37a 5.42 5.67 1 2 2 1 2 2 2 2 2 1 A…29a 30a 31a 32a 3 3a 34a 35a 36a 37a 5.85 6.07 E 5.96(5) 3 2 1 2 2 2 2 2 2 1 A…29a 30a 31a 32a 3 3a 34a 35a 36a 37a 6.02 6.24 a Numbers in the parentheses represent uncertainties in the last digit. Isomer II and other isomers: The first VDE calculated of isomer II at 2.88 eV is much lower than the observed first VDE and they do not correspond to any observable features in the experimental spectrum. Thus, we can rule out the presence of this isomer in any appreciable amount in the cluster beam. The calculated VDEs for the quasi-planar isomers III and IV show quite similar simulated spectral pattern109 as the global minima. Taking into account that their relative energies are quite low with respect to the global minimum, we could not completely rule out the possibility that they might be present in small amounts in the cluster beam and might make non-negligible contributions to the 80 overall width of the experimental spectrum. Isomer V has a detachment channel that could be responsible for the intensity in the gap between features X and A. Other isomers are too high in energy and can be safely ruled out. Thus, we believe that the global minimum isomer I is the main species responsible for the experimental PES spectrum. The excellent overall agreement between the simulated spectra of isomer I and the experiment lends considerable credence for the identified global minimum for B24−. Table 3.4 Open-shell T1 diagnostic values for B24−. Isomers T1 valuesa I 0.025 II 0.027 IV 0.025 V 0.023 VI 0.022 VII 0.019 VIII 0.025 a The values are obtained at the ROCCSD(T)/6-311+G(d)//PBE0/6-311+G(d) level of theory. 81 Figure 3.8 Comparison of the experimental and simulated PES spectrum of B24−. (a) The experimental PES spectra at 193 nm; the simulated PES spectrum from the global minimum isomer I at PBE0 (b) and TPSSh (c). 82 3.4 Chemical Bonding Analyses B21−: We performed chemical bonding analyses of the two low-lying isomers of B21− using the AdNDP method at the B3LYP/6-31G*//B3LYP/6-311+G* level of theory (Figure 3.9 and Figure 3.10). Isomer I: Similar to all the previously studied planar or quasi-planar boron clusters,103,104,128-138 all the peripheral boron atoms in isomer I of B21− are bonded by localized B-B σ-bonds. In this case, the peripheral ring is comprised of 14 B-B bonds (Figure 3.9). Surprisingly, we found a 2c-2e B-B σ-bond within the interior of the planar cluster, making B21− the first boron cluster to feature an internal localized σ-bond. The presence of this 2c-2e σ-bond is likely due to the neighboring holes in the lattice framework of the interior boron atoms. The holes allow room for a more localized bond analogous to that found in the BC3 honeycomb sheet.188 The remaining electron density is delocalized, forming bonds of three centers or higher. Isomer I is quasi-planar, therefore, the delocalized bonds can be approximately differentiated as “σ” or “π”. There are nine 3c-2e σ-bonds, two 4c-2e σ-bonds, and six delocalized π-bonds. The π-bonding pattern of isomer I is similar to that of the lowest energy structure of the B19− cluster,104 where one π-bond is responsible for the bonding in the internally centered pentagon of boron atoms and the other five π-bonds contribute to bonding between the interior boron atoms and the peripheral boron ring. 83 Figure 3.9 AdNDP analyses for isomer I of B21−. Isomer II: The chemical bonding analyses of the second lowest-lying structure II of B21− reveal a bonding picture very similar to that of isomer I, as shown in Figure 3.10. Once again, we see the presence of fourteen peripheral 2c-2e B-B σ-bonds and one internal 2c-2e B-B σ-bond. The delocalized σ-electrons form ten 3c-2e and one 4c-2e σ-bond in isomer II (Figure 3.10) versus the nine 3c-2e and two 4c-2e σ-bonds of isomer I (Figure 3.9). The delocalized π-bonds can be again split into two subsets: one 3c-2e π-bond delocalized across internal atoms and five π-bonds responsible for bonding between the inner and peripheral atoms. The π-bonding pattern of isomer II is reminiscent of that of the second lowest lying structure of B19−, too,104 as expected from their structural similarity. 84 Figure 3.10 AdNDP analyses for isomer II of B21−. B222−, an all-boron anthracene: The chemical bonding analyses of B22– were done on the basis of the CMOs. The C2 structure is not perfectly planar, and therefore, the division of the electron density into σ and π can be done only upon artificially flattening the structure to prevent mixing of σ and π orbitals. Since the out-of-plane distortion in the C2 B22– is relatively small, the analyses using the perfectly planar system should capture the main features of the chemical bonding in the C2 B22– species. As shown in Figure 3.11, the B222– contains seven CMOs reminiscent of those in anthracene (C14H10). Therefore, the planar B222– can be considered as an all-boron analogue of anthracene. AdNDP analyses (not shown) on the closed shell B222– reveal that the peripheral 14 boron atoms are bonded by 14 2c-2e bonds, whereas the bonding among the 8 interior atoms and between the 85 interior and the peripheral ring is via delocalized σ and π bonds. The B22– cluster is thus one electron short of an all-boron analogue of anthracene, or it can be viewed as an all-boron analogue of the anthracene cation (C14H10+). The C2 structure of B22– has a regular, but buckled, triangular lattice. The buckling in B22– is entirely due to the geometrical constraint of the 14-atom periphery, which cannot host 8 interior atoms. All 2D boron clusters possess a periphery characterized by strong 2c- 2e σ bonds, resulting in shorter B–B distances in the periphery than B–B distances in the interior, where only delocalized bonding exists (except B21–). A regular planar triangular boron lattice requires equal B–B distances throughout the 2D structure, which is incompatible with the strong peripheral bonding and weaker interior bonding. Therefore, either a 2D planar boron cluster buckles to give quasi-planar structures or holes will result in the interior of a perfectly planar boron cluster to release the geometrical strain caused by the strong peripheral B–B bonds. This is also why infinitely large planar boron sheets have to contain hexagonal holes, rather than a regular triangular lattice.142,145,147-149,151,152 In the current case, even the doubly charged B222– is not stable as a perfectly planar triangular lattice. Structural optimization shows that it is also slightly buckled similar to the C2 B22– monoanion. 86 Figure 3.11 Elucidation of the analogy between the π bonding in the flattened B222− and anthracene. B23−, an all-boron phenanthrene: We have performed a more thorough chemical bonding analyses of B23–, using both the CMOs and the AdNDP method, and discovered that the π bonding in B23– is almost identical to that in phenanthrene, as shown in Figure 3.12. First, we compared the π CMOs of B23– with those of phenanthrene in Figure 3.12a. The similarity between the π orbitals of the two molecules is extraordinary: they all have exactly the same irreducible representations and nodal structures. Such a high degree of semblance between the π bonding of a planar boron cluster and a hydrocarbon is unprecedented among all the planar boron clusters characterized so far. Hence, the B23– nano-heart can be considered as an all-boron analogue of phenanthrene, an isomer of anthracene (C14H10) also composed of three fused benzene rings. The AdNDP method allows us to obtain alternative chemical bonding representations, which reinforce the remarkable analogy between the B23– nano-heart and phenanthrene. 16 2c-2e C–C and 10 2c-2e C–H σ bonds are found for phenanthrene.108 However, the π density in phenanthrene can be partitioned in two ways: 1) the Kekule 87 representation with seven localized π bonds (Figure 3.12b); 2) the Clar representation with benzene-like delocalization of six π electrons over each of the outer benzene rings and one localized π bond in the central hexagon (Figure 3.12c). Comparison of the ONs of the AdNDP bonds suggests that the Clar representation of the chemical bonding is a more accurate model, in agreement with the chemical-bonding picture of phenanthrene proposed recently.239 Partitioning the π electron density in B23–, we also obtain two representations of the π-bonding pattern: the Kekule type (Figure 3.12b) and the Clar type (Figure 3.12c), which are analogous to the corresponding set in phenanthrene. Again, the Clar representation has higher ONs and should be considered a more accurate representation of the delocalized π bonding in the B23– nano-heart. According to the AdNDP analyses, the σ electrons in B23– form 15 2c-2e peripheral B–B σ bonds and 13 3c-2e σ bonds inside of the heart-shaped cluster, as shown in Figure 3.12. Therefore, both the delocalized π and σ electrons in B23– conform to the 4N + 2 Hückel rule, rendering the nano-heart doubly aromatic. The pentagonal hole and the double aromaticity underlie the perfectly planar structure and high stability of the B23– nano-heart. It is interesting to compare the electronic structures of the planar B23– with the predicted most stable form of a 2D boron sheet, i.e., the α-sheet.142,145,147-149,151-153 The α- sheet contains regular hexagonal holes, in which the ratio of σ and π electrons is 3 to 1, 88 identical to that in graphene. In B23–, the σ and π electron ratio is 4 to 1, whereas that in B22– is very close to 4 to 1. The lower π occupancy in the boron cluster is due to the fact that there is no hole in the B22– structure or only a pentagonal hole in the B23– nano-heart. It is expected that in larger planar boron clusters hexagonal holes may appear, which will increase the π occupancy because of reduced in-plane σ bonds. It would be interesting to see if such planar boron clusters exist and at what size. The existence of such planar clusters would confirm the viability of the predicted α-sheet.142,145,147-149,151-153 The analogy between the π bonding in B22–, B23–, and polycyclic aromatic hydrocarbons suggests that they may exhibit similar electronic properties in the bulk. Anthracene and phenanthrene are important organic molecular semiconductors. Both B22– and B23– have lateral dimensions over 1 nm. If these planar boron nanoclusters can be deposited on surfaces, their electrical properties can be potentially investigated by scanning tunneling microscopy. They are expected to display similar electrical properties. Neutral B22 is closed shell and should display semiconducting properties, whereas neutral B23 is open shell and should be a conductor. 89 Figure 3.12 Elucidation of the analogy between the π bonding in B23− and phenanthrene. (a) Comparison of the π CMOs, (b) comparison of the Kekule-type π-bonds obtained by the AdNDP method, (c) comparison of the Clar-type π-bonds obtained by the AdNDP method. 90 B24−: The global minimum of B 24 − (Figure 3.7) contains a tetragonal and a pentagonal hole. Previous investigations show that such defects are essential to keep the cluster flat because of the unique chemical bonding in all 2D boron clusters, which exhibit strong peripheral B-B bonding and delocalized interior bonding.103,104,106,109,128-138 However, the global minimum of B24− is quasi-planar owing to the out-of-plane distortion of the boron atom in the center of the filled pentagonal motif, similar to that observed in the global minimum of B21−. The appearance of such filled pentagonal units with ever increasing out- of-plane distortions for large boron clusters may hint at the onset to form icosahedral blocks found in bulk boron. The results of our chemical bonding analyses (Figure 3.13) using the AdNDP method provides further insight into this structural feature by revealing a separate bonding element (6c-2e π-bond with ON = 1.8 |e|) located over the filled pentagonal moiety. The chemical bonding analyses of the closed-shell neutral B24 (Figure 3.13a) and dianion B242− are shown in Figure 3.13. It should be pointed out that isomer I is not planar, and therefore, σ- and π-bonding could only be approximately assigned. The bonding elements obtained for B24 and B242− are the same, except for the additional 5c-2e π-bond pertaining to B242−, shown in Figure 3.13b (ON = 1.8 |e|). The addition of one electron to B24− can be seen as doubling ON value of the 5c π-bond in B242−. In other words, one can view the 5c-2e π-bond of B242− as a 5c-1e π-bond with an ON of 0.9 |e| in the B24− anion. 91 Similar to all the boron clusters studied previously,103,104,106,108,109,128-138 only classical localized 2c-2e B-B σ-bonds are found between the 14 peripheral boron atoms in B24− (Figure 3.13). The peripheral B-B bond distances are in the range of 1.52−1.63 Å, and their ON values are close to the ideal case of 2.0 |e|. All other σ-bonds associated with the 9 inner atoms are found to be delocalized: eleven 3c-2e and three 4c-2e σ-bonds with ON = 1.8−1.9 |e|. Interestingly, three 3c-2e σ-bonds are found inside the filled pentagon; four 3c- 2e and two 4c-2e σ-bonds are found to be responsible for the bonding between the filled pentagonal unit and its surrounding atoms. This delocalized σ bonding patter is exactly the same as those observed in the B21− (Figure 3.9). In addition to delocalized σ bonds, the 9 interior boron atoms in B24 are also bonded by seven delocalized π-bonds: six 4c-2e π-bonds and one 6c-2e π-bond. The B24− dianion contains an eighth delocalized 5c-2e π-bond, shown in Figure 3.13b. The four 4c-2e π- bonds found at the vertices of the filled pentagon in B24− look exactly the same as the corresponding ones in B21−. Furthermore, the unique 6c-2e π-bond delocalized over the six inner B atoms comprising the B-centered pentagon is also similar to that in B21−. An increase in the out-of-plane distortion of the filled pentagon fragment upon increasing the cluster size suggests the tendency to form icosahedral bulk-like structural features. The out- of-plane distortion in the filled pentagonal motif reduces the geometrical stress imposed by the periphery and may explain the energetic advantage of the global minimum of B24−. It is 92 also interesting to note that isomers I, III, and IV all contain a pentagonal cavity, which also helps release of geometrical stresses. All the other higher lying 2D structures (V, VI, VII, and VIII), however, possess more regular triangular lattices (Figure 3.7). These structures are higher in energy than isomers I, III, and IV, likely due to the geometric strain imposed by the uninterrupted triangular lattice motifs. Figure 3.13 AdNDP analyses of (a) the neutral B24 and (a and b) the dianion B242− at the geometry of B24−. 93 3.5 Conclusions The Bn− (n = 21 − 24) clusters were studies using combined photoelectron spectroscopy and ab initio calculation. Extensive searches for the global minimum structure were performed using the CK method and CW method independently and confirmed by comparing their computed ADEs and VDEs with the experimental ADEs and VDEs. Two isomers similar to the two lowest lying isomers of B19− were present in the experiment and contributed to the observed PES spectrum of B21−. Chemical bonding analyses performed revealed that the overall chemical bonding picture of these two of the B21− cluster are also similar to those of B19− and other smaller planar or quasi-planar boron clusters: all the peripheral atoms are bonded to each other through localized 2c-2e σ-bonds, while the bonding in the interior of the planar cluster is delocalized and multi-centered with one localized 2c-2e σ-bond in each isomer. The latter is unique to the B21− cluster, which is the first instance of a localized 2c-2e σ-bond in the interior of a planar boron cluster. Various “defects” or “holes,” such as four-membered or five-membered rings are found in the interior of the two lowest lying structures of B21−. The global minimum of B22– is found to be quasi-planar with a slightly buckled triangular lattice consisting of 14 peripheral and 8 interior boron atoms. Chemical bonding analyses for a flattened B222– reveal that its π- bonding pattern is similar to that in anthracene. The quasi-planar B22– cluster can thus be viewed as an all-boron analogue of an anthracene cation. The B23– cluster is found to 94 possess a perfectly planar and heart-shaped structure consisting of a 15-atom periphery with 8 interior atoms and a pentagonal hole. The π bonding pattern in B23– is found to be identical to that in phenanthrene. The B23– nano-heart is found to be particularly stable, derived from its perfectly planar structure and double aromaticity. The global minimum structure of B24− is quasi-planar, containing a filled pentagonal unit with the central boron atom distorted out of plane significantly. A double-ring 3D isomer was found to be higher in energy at the ROCCSD and ROCCSD(T) levels of theory, while it is the global minimum according to the DFT methods. Comparison of the simulated photoelectron spectra with the experimental data confirms unequivocally the quasi-planar global minimum identified for B24− at the higher levels of theory. Chemical bonding analyses revealed that the periphery of B24− is bonded only by classical 2c-2e B-B σ-bonds, whereas both delocalized σ- and π- bonds are found in the interior of the cluster with one unique 6c-2e π-bond responsible for the bonding in the B-centered pentagon. The current study extends the family of all-boron analogues of aromatic hydrocarbons and demonstrates that boron clusters provide a fertile ground to discover interesting structures and bonding. 95 Chapter 4 On the Way to Borophenes Influenced by the well documented incidence of carbon based nano-structures140 in the literature, theoreticians began to investigate similar concepts in boron chemistry as evidenced by work on the proposed boron buckyball, volleyball, and other fullerenes,141-145 two-dimensional sheets,146-154 nanotubes,155-157 nanoribbons,158 and core-shell stuffed boron fullerenes.159-162 Although boron is carbon’s neighbor in the Periodic Table and has similar valence orbitals, boron cannot form graphene-like structures with a honeycomb hexagonal framework because of its electron deficiency. Instead, boron prefers to adopt a rather buckled form.240-243 Recent computational studies suggest that a triangular planar boron lattice with hexagonal vacancies is more stable,147,148 which would be suitable to form the putative boron nanotubes and it underlies the stability of the proposed B80 fullerene.142 However, such structures await experimental studies to confirm or deny their viability as true nano-objects. Photoelectron spectroscopic studies combined with ab initio calculations have shown that boron clusters adopt planar or quasi-planar structures up to the size of 24 atoms.103,104,106,108,109,128-131,133-138 The propensity for planarity has been found to be a result of both σ- and π- electron delocalization over the molecular plane. To what size will boron clusters remain planar remains an open question. A more interesting question is if infinitely 96 large planar boron clusters are possible, giving rise to atom-thin boron nanostructures analogous to graphene. This chapter presents three boron clusters, B36−/0, B30−/0, and B35−/0, with hexagonal vacancies in the all-triangular lattices. The B36− cluster is the first boron cluster featuring a hexagonal vacancy in the central position and provides the first experimental evidence for the importance of hexagonal hole in stabilizing boron cluster and the viability of the 2D boron layers. The first inherently chiral cluster B30− is also reported, which has a slightly curved cluster plane and a hexagonal hole. The B35− cluster with double-hexagonal vacancy is a new and more flexible structural motif for borophene. It possesses similar structure as the B36− except missing an interior boron atom that creates two adjacent hexagonal holes. The experimental observations of these clusters with hexagonal vacancies provide the evidence for the viability of borophene. 4.1 Planar Hexagonal B36 as a Potential Basis for Extended Single‐Atom Layer Boron Sheets 4.1.1 Experimental Results Boron cluster anions with up to 24 atoms have been investigated previously.103,104,106,108,109,128-131,133-138 The PES spectra became more congested and complicated for clusters larger than 20 atoms (Figure 3.3),81-83 presenting considerable 97 challenges for both computational global minimum searches and comparison between experiment and theory. However, we found that the spectrum of B36– (Figure 4.1) is special, showing an unusually low electron-binding energy and well-resolved spectral features in the low binding energy side. We also measured the spectrum at 266 nm (not shown) with slightly higher resolution. The ADE of 3.12 eV measured from the sharp onset of the first detachment band X in the 266 nm spectrum also represents the EA of neutral B36. It is surprising that the EA of B36 is even smaller than that of B22 (3.34 eV) or B24 (3.55 eV), since the EA generally increases with increasing cluster size. The low EA of B36 is a result of the large energy gap, as revealed by the X–A separation, suggesting that neutral B36 is a highly stable cluster with a large energy gap between its highest occupied (HOMO) and lowest unoccupied molecular orbital (LUMO). The weak feature X′ observed in Figure 4.1a is due to contributions of a low-lying isomer (vide infra). VDEs of the observed detachment transitions are given in Table 4.1. VDEs are usually measured from the peak maxima from PES spectra. For small clusters or simpler systems, PES bands are well separated and each band represents a single detachment transition. In the current case, bands X and A are well resolved and they should each correspond to a single electron detachment channel, as given in Table 4.1. The VDEs for bands X (3.3. eV) and A (4.08 eV) are directly obtained from the band maximum in each case. Band B is relatively broad, which is likely a result of several overlapping detachment transitions. Consequently, a range of energy (4.2– 98 4.5 eV) is given for band B in Table 4.1. Following an energy gap, more congested detachment features are observed above 5 eV, suggesting a high density of electronic states. The label C is given to represent the signals from about 5.1 – 5.4 eV. An intense band D is observed at ~5.6 eV, which is also likely a result of overlapping detachment transitions. The sharp spikes on the higher binding energy side of band D cannot be assigned as individual detachment transitions because of the relatively low signal-to-noise ratios in this part of the spectrum. Finally, the label E represents the broad signals around 6.1 eV. Hence, all the labels from B to E do not represent individual detachment transitions and they are solely for the sake of discussion. The congested detachment transitions for such a large cluster are expected, as borne out from comparisons with the theoretical results (infra vide). The broad X band suggests a significant structural change from the anion to the neutral ground state. Despite the congested spectral features in the higher binding energy side, the relatively simple spectral pattern in the low binding energy side and the large HOMO−LUMO gap indicate that neutral B36 should be a highly symmetric cluster. 99 Figure 4.1 Photoelectron spectrum of B36– and comparison with simulation. (a) The experimental spectrum at 193 nm; (b) The simulated spectrum for the global minimum quasi-planar structure with a hexagonal hole (I in Figure 4.2a). (c) The simulated spectrum for the tubular isomer (II in Figure 4.2a); (d) The simulated spectrum for the quasi-planar structure with two holes (III in Figure 4.2a). The vertical bars in the simulated spectra represent the calculated VDEs. The simulated spectra were obtained by fitting the VDEs with a unit area Gaussian function of 0.05 eV width. 100 4.1.2 Theoretical Results We searched for energetically low-lying isomers of B36– with the CW method and TGmin. Among the 3,000 or so trial structures in our search, a quasi-planar pseudo-C6v structure with a hexagonal hole was found to be much more stable than any other isomers. We also considered a ring-type structure, which was shown to be stable for large boron clusters.108,135,139,244-246 Refined geometry optimizations and vibrational frequency calculations were performed using DFT method with the hybrid PBE0 exchange- correlation functional with the 6-311G* basis set on all structures within 70 kcal mol−1 of the pseudo-C6v global minimum structure. ZPE corrections were included for all the isomers at the PBE0/6-311G* level. The effect of including the zero-point corrections was small for isomers of similar structures but could be substantial (shifting relative energy values by around 2 kcal mol−1 for isomers of different structural types (that is, 2D versus 3D). We found that the hexagonal global minimum structure of B36– and its corresponding neutral species exhibit C2v (pseudo-C6v) and C6v symmetries, respectively (Figure 4.2). The nearest isomers of B36–, a triple ring and a double-hole quasi-planar structure, lie at 10.5 and 14.7 kcal mol−1 higher in energy at the PBE0 level of theory. Our global search also led to a number of other 3D structures, such as cage-like structures and two-layer structures, which are all much higher in energy. 101 Figure 4.2 The global minimum and low-lying isomers of B36− and B36. (a) Relative energies for the isomers of B36− are given in kcal/mol at the PBE0/6-311G* and CCSD/6-31+G*//PBE0/6-311G* (in parenthesis) levels of theory. (b) Relative energies for the isomers of B36 are given in kcal/mol at the PBE0/6-311G* level of theory. All energies have been corrected for ZPEs at the PBE0/6-311G* level. 4.1.3 Comparison between Experimental and Theoretical Results To confirm the global minimum of B36–, we compare its simulated spectrum with the experimental data in Figure 4.1 and Table 4.1. The relatively simple spectral pattern can act as an electronic fingerprint. The overall simulated spectral pattern of the C2v global 102 minimum of B36–(Figure 4.1b) is in good accord with the experimental spectrum. In particular, the calculated first and second VDEs are in excellent agreement with the experimental observation, confirming the large HOMO−LUMO gap observed and the unusually low EA of B36. The LUMO of the hexagonal B36 (C6v) is doubly degenerate with e2 symmetry. The C2v symmetry of B36– is, hence, due to the Jahn–Teller effect as a result of the occupation of the degenerate LUMO in the anion. The broad X band is consistent with a significant geometry change between the anionic and neutral B36, primarily involving the distortion of the hexagonal hole in the anion. However, the higher binding energy side of the experimental spectrum (Figure 4.1a) is complicated and is not reproduced well by the simulated spectrum of the C2v global minimum of B36– (Figure 4.2b). Furthermore, the weak peak labelled as X′ observed experimentally was not reproduced by the simulated spectrum of the C2v B36–, consistent with the suggestion that it might be due to a low-lying isomer. We further tested the possibility of isomer contributions by computing the VDEs for the two lowest-lying isomers (II and III in Figure 4.2a), as presented in Figure 4.1c and Figure 4.1d, respectively. The first five detachment channels of the tubular isomer II are close to each other around 3.7 eV (Figure 4.1c ), corresponding to the gap region between bands X and A. Thus, isomer II can be ruled out as a discernible contributor to the observed spectrum. On the other hand, the first detachment channel of isomer III is in good agreement with the X′ band (Figure 4.1d). 103 Furthermore, the second and third detachment channels of isomer III agree well with the broad band B, and the higher detachment channels of isomer III also seem to coincide with the congested higher binding energy part of the experimental spectrum. However, isomer III is 14.7 kcal mol−1 higher than the global minimum isomer I at the PBE0 level and it is not expected to be populated in any significant amount because our cluster beam is expected to be fairly cold. Under similar experimental conditions, van der Waals complexes of Ar and anionic gold clusters were observed,172 indicating a vibrational temperature of < 200 K. We then calculated the energies of the first three isomers using the more accurate, but computationally more demanding, CCSD level of theory with the 6-31+G* basis set (Figure 4.2) and found that the double hole quasi-planar isomer III became more stable, only 1.17 kcal mol−1 above the global minimum C2v isomer. Thus, isomer III would be expected to be substantially populated experimentally. The tubular isomer became 23.97 kcal mol−1 above the global minimum and its presence in our experiment can be safely ruled out. The combination of the simulated spectra of isomers I and III and their close energetic stability provide a much satisfying agreement with the experimental observations, lending considerable credence for the identified C2v global minimum with a hexagonal hole for B36–. 104 Table 4.1 Comparison of the experimental VDEs with the calculated values for B36−. The calcualted values are based on the C2v (2A1) lowest energy hexagonal B36–. All energies are in eV. Observed VDEa VDE features (exp.) final state and electronic configuration (theo.)b 1 X 3.3 (1) A1, …14a12 12b22 13b12 15a12 10a22 14b12 13b22 16a12 11a22 17a10 3.15 3 2 2 2 2 2 2 2 1 2 1 A 4.08 (3) A1, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 4.03 3 2 2 2 2 2 2 2 2 1 1 A2, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 4.08 1 2 2 2 2 2 2 2 2 1 1 B 4.2~4.5 A2, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 4.26 1 2 2 2 2 2 2 2 1 2 1 A1, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 4.47 3 2 2 2 2 2 2 1 2 2 1 B2, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 5.10 C 5.1~5.4 3 2 2 2 2 2 1 2 2 2 1 B1, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 5.23 1 2 2 2 2 2 2 1 2 2 1 B2, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 5.48 1 2 2 2 2 2 1 2 2 2 1 B1, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 5.56 3 2 2 1 2 2 2 2 2 2 1 B1, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 5.60 3 2 2 3 2 1 2 2 2 2 1 A2, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 5.68 D ~5.6 1 2 2 2 2 1 2 2 2 2 1 A2, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 5.73 3 2 2 2 1 2 2 2 2 2 1 A1, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 5.74 1 2 2 2 1 2 2 2 2 2 1 A1, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 5.85 1 2 2 1 2 2 2 2 2 2 1 B1, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 5.89 3 2 1 2 2 2 2 2 2 2 1 B2, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 6.29 3 1 2 2 2 2 2 2 2 2 1 A1, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 6.35 E ~6.1 1 2 1 2 2 2 2 2 2 2 1 B2, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 6.42 1 1 2 2 2 2 2 2 2 2 1 A1, …14a1 12b2 13b1 15a1 10a2 14b1 13b2 16a1 11a2 17a1 6.65 a Numbers in parenthesis represent uncertainty in the last digit. b VDEs were calculated at the TD-PBE0/6-311+G(2df)//PBE0/6-311G* level of theory. 4.1.4 The Electronic Structure and Stability of the Hexagonal B36 Our calculations show that neutral B36 has perfect hexagonal symmetry (C6v) and is overwhelmingly stable relative to the closest-lying isomers II or III (Figure 4.2b). The hexagonal B36 has an out-of-plane distortion with the shape of a bowl, and its valence CMOs are shown to be similar to those of a planar structure optimized with D6h constraint. 105 DFT calculations at the PBE0/6-311G* level of theory show that the D6h structure is a saddle point at ~9 kcal mol−1 above the C6v global minimum. The peripheral B–B bonding is enhanced upon shortening the B–B distance, which induces the out-of-plane bending in B36 to the C6v bowl shape. The bowl height is 1.16 Å with two different types of peripheral B–B distances, which are reduced from 1.61 and 1.72 Å in D6h to 1.58 and 1.67 Å, respectively, in the C6v structure (I0 in Figure 4.2b). The shorter bond length occurs between the six apex B atoms and their neighbors (1.58 Å), while the remaining six peripheral B–B bonds are slightly longer (1.67 Å). We analyzed the chemical bonding of the hexagonal C6v B36 as well as the D6h form of the cluster using AdNDP method. The AdNDP analyses of the D6h structure are shown in Figure 4.3; an analysis of the C6v structure leads to similar results. AdNDP displays 12 2c-2e σ bonds describing the shorter B–B bonds involving the six apex B atoms, 12 3c-2e σ bonds, 18 4c-2e σ bonds, six 4c-2e π bonds and six completely delocalized 36c-2e π bonds. The bonding pattern suggests that the B36 cluster can be viewed as six hexagonal B7 (B©B6) units bound together by the 12 3c-2e σ bonds and the six 36c- 2e π bonds. The totally delocalized 36c-2e π bonds in B36 are interesting, which may be partly responsible for the remarkable stability of this hexagonal boron cluster. The necessity of hexagonal holes in stable planar 2D boron sheets was analyzed in detail by Tang and Ismail-Beigi,147 who considered the electronic structures of a graphene- like hexagonal boronsheet and a triangular boron lattice. They also showed a model 106 B32 cluster with a hexagonal hole to be more stable than a double ring structure. To explore the effect of the hexagonal hole on the stability of the B36 cluster, we also optimized the structure of a B37 cluster with C6v symmetry by filling the hexagonal hole in B36 with an extra B atom. We found that this B37 cluster with a triangular lattice has an open-shell quartet electronic state with a (a1)1(e2)2 configuration. The optimized structure is found to have changed significantly from the C6v B36 cluster: buckling of certain boron atoms was observed in contrast to the smooth bowl shape in the parent B36. This buckling of the B37 cluster is similar to the buckled 2D boron sheets with triangular lattices.147,240-243 The calculated atomization energy per B atom at the PBE/TZ2P level reduces from 130.8 kcal mol−1 (5.67 eV per atom) for the C6v B36 cluster to 128.9 kcal mol−1 (5.59 eV per atom) for the C6v B37 cluster. Interestingly, the difference in the atomization energy (~0.08 eV per atom) between the hexagonal C6v B36 and the buckled B37 cluster is also similar to that of the most stable 2D boron sheet with hexagonal holes and the buckled triangular 2D sheet (~0.11 eV per atom) at the DFT the generalized gradient approximation (GGA) level.147 107 Figure 4.3 Chemical bonding analyses for the hexagonal D6h structure of B36. The analyses were done using the AdNDP method. 4.1.5 The Relationship of the Hexagonal B36 and 2D Boron Sheets The hexagonal hole in the B36 cluster is reminiscent of the hexagonal vacancies in the 2D boron sheets recently predicted.147,148 The B36 cluster can be viewed as the analogous boron unit of the hexagonal C6 unit in graphene to form extended graphene- like boron nanostructures with hexagonal holes, as shown schematically in Figure 4.4. The structure shown in Figure 4.4 represents a hexagonal hole density of η=1/27 (one vacancy per 27 lattice sites in a triangular lattice), as defined for the 2D boron sheet.147 The structure 108 in Figure 4.4 is constructed by sharing a row of B atoms between two neighboring B36 units. The apex atoms (circled in Figure 4.4) are shared by three neighboring B36 units. If these atoms are removed, one arrives at the more stable α-sheet with η=1/9 (refs 147, 148). Interestingly, a B30 model has been used to analyze the bonding in the proposed α-sheet,151 which is equivalent to removing all six apex B atoms in the B36 cluster. Hence, the B36 cluster can be viewed as the embryo for the various proposed stable 2D boron sheets. However, it should be pointed out that Figure 4.4 is only schematically showing the relationship between the hexagonal B36 cluster and the stable 2D boron sheet. It does not represent the growth mechanism of the putative boron sheet, as it has been shown computationally that large boron clusters exhibit polymorphism with close-lying 3D cage- like structures.247,248 Liu et al.153 have considered computationally possible synthesis of 2D boron sheets on coinage metal surfaces as substrates, analogous to the synthesis of graphene. Thus, B36 or other small boron clusters with hexagonal holes may serve as the nuclei for the formation of large-scale 2D boron sheets on the substrate. 109 Figure 4.4 Relationship between B36 and borophene. A schematic view of part of an extended one- atom thick boron sheet, named borophene, as constructed from the planar hexagonal B36 unit. The circles represent the apex atoms in the B36 unit that are shared by three units. Removal of these atoms would lead to the α-sheet.147 The present study provides the first experimental evidence for the viability of novel boron nanostructures with hexagonal vacancies. These structures can indeed exist and may be synthesized using appropriate substrates.153 The potential large-scale synthesis of the new atom-thick boron nanosheets calls for an appropriate name: “borophene” is proposed here, in analogy to graphene. The electronic structure of the 2D boron sheets can be either metallic or semiconducting, according to theoretical calculations.147,148,152,163 Because of the 110 hexagonal holes, various chemical modifications are possible to tune the electronic and chemical properties of borophenes.149,249 Thus, borophene may constitute a new class of atom-thick nanostructures complementary to graphene. 4.2 B30−: Quasiplanar Chiral Boron Cluster Chirality is vital in chemistry. Its importance in atomic clusters has been recognized since the discovery of the first chiral fullerene, D2-C76.250 A number of gold clusters have been found to be chiral,251,252 raising the possibility to use them as asymmetric catalysts. The discovery of clusters with enantiomeric structures is essential to design new chiral materials with tailored chemical and physical properties.7 In the previous section, we have found that the B36 cluster is a quasi-planar cluster with hexagonal symmetry and a perfect hexagonal hole in its center, providing the first experimental evidence that the 2D atom-thin boron layer with hexagonal holes is viable.110 What is the smallest boron cluster for an interior hexagonal hole to appear? The studies on boron clusters have shown that tetragonal and pentagonal defects appear in the small boron clusters (Figure 3.1). Hexagoanal defects are observed in the low-lying isomers of B21− (Figure 3.4) and B22− (Figure 3.5), the B36 and B36− (Figure 4.2) represent the first boron clusters to feature an interior hexagonal hole. It is expected that hexagonal holes should be a defining feature for large planar boron clusters. 111 This section presents the first inherently chiral boron cluster of B30− in a joint photoelectron spectrosocpy and theoretical study. The most stable structure of B30− is found to be quasi-planar with a hexagonal hole. Interestingly, a pair of enantiomers due to different positions of the hexagonal hole are found to be degenerate in our global minimum searchs and both should co-exist experimentally because they have identical electronic structures and give rise to identical simulated photoelectron spectra. 4.2.1 Experimental Results The spectrum of B30− at 193 nm (Figure 4.5a) shows four well-defined bands (X, A, B, C) in the low binding energy region and more bands (D, E, F) in the high binding energy region, which are tentatively labeled due to the poorer signal-to-noise ratios. The VDE of band X is measured to be 3.69 ± 0.05 eV. The relatively sharp X band suggests there are probably only small geometry changes of the cluster upon electron detachment to neutral B30. The ADE is measured to be 3.59 ± 0.07 eV. Following a gap of about 0.65 eV, three intense and broad bands, A, B, and C are observed with VDEs of 4.34 ± 0.05, 4.61 ± 0.05, and 5.03 ± 0.08 eV, respectively. Band C is particularly broad, which must contain multiple detachment transitions. The VDEs for bands D, E and F are tentatively measured and all VDEs are given in Table 4.2, where they are compared with theoretical data (vide infra). The large X-A gap suggests that neutral B30 should be a closed-shell species and the X-A separation is an approximate measure of the gap between the HOMO and LUMO of B30. 112 The non-zero intensity in the gap region between bands X and A may be due to a weakly populated low-lying isomer. Figure 4.5 (a) Photoelectron spectrum of B30− at 193 nm and simulated spectra of (b) isomer I/II and (c) isomer III. The simulated spectra were obtained at TD-PBE0/6-311+G(2df) level of theory. 113 Figure 4.6 The global minimum and low-lying isomers of B30−. The relative energies are given in kcal/mol at LPNO-CCSD (in braces) and PBE0 levels of theory. The relative energies at PBE0 level are corrected by ZPEs. Figure 4.7 The global minimum and low-lying isomers for B30. The relative energies are given in kcal/mol at DLPNO-CCSD(T)/Def2-SVP/C (in braces) and PBE0/6-311G* levels of theory. 114 4.2.2 Theoretical Results To determine the global minimum of B30−, we searched more than 3600 isomeric forms using the TGMin code.177 The calculations were carried out using the DFT formalism with the PBE exchange-correlation functional and the Goedecker-Teter-Hutter (GTH) pseudopotential with the associated double- valence plus polarization (DZVP) basis set for boron via the CP2K program. We further refined the energies by reoptimizing the geometries of low-lying isomers within 20 kcal/mol using DFT method with the hybrid PBE0 functional and the 6-311G* basis set. Vibrational frequencies were calculated for each isomer and all the structures were ensured to be minima on the potential energy surface without imaginary frequencies. Single-point PBE0/6-311+G(2df) calculations and LPNO-CCSD/def2-SVP/C calculations were performed on the optimized structures obtained at the PBE0/6-311G* level of theory to get more accurate relative energies. The DLPNO-CCSD(T) energies were also calculated for the low-lying isomers of the closed- shell neutral B30. Figure 4.6 displays the structures, symmetries and electronic states of the lowest 11 isomers at the PBE0 and LPNO-CCSD levels of theory. Interestingly, the global minima of B30− are found to consist of two degenerate quasi-planar structures I and II with a hexagonal hole and C1 symmetry. A close examination of these two structures finds that they correspond to a pair of enantiomers identified by the position of the hexagonal hole. The enantiomers have exactly the same electronic structures, and thus should have the same 115 PES spectrum. Isomer III (Cs, 2A") with a hexagonal hole in the middle lies 1.90 kcal/mol above the global minima. A 3D isomer IV is found to be 3.97 kcal/mol higher, while the double ring structure V is 4.99 kcal/mol higher than the global minima. Isomer IX, which is highly non-planar with a bow-structure and a pentagonal hole, is 16.75 kcal/mol above the global minima. However, this structure is found to be the global minimum for neutral B30 (Figure 4.7), as reported in a recent theoretical study.255 Such divergence in global minimum structures for anions and neutrals has been observed previously for B20 and B22,108,135 whose global minima were found to be planar in the anions, but the double rings in the neutral. However, no experimental evidence is available for the predicted neutral structures. A previous infrared-UV double resonance experiment on neutral boron clusters failed to detect B20.222 4.2.3 Comparison between Experimental and Theoretical Results To verify the anionic global minimum structures, we computed the VDEs of the low-lying isomers. The calculated VDEs of isomer I/II using the ΔSCF-TDDFT method with PBE0 and TPSSh functionals are compared with the experiment in Table 4.2. The VDEs from the two methods are in general consistent with each other, and we will only use the PBE0 values in the following discussion. The B30− anion has a doublet ground state and thus both singlet and triplet neutral final states are accessible upon one electron detachment. The first VDE refers to electron detachment from the SOMO 46a, corresponding to the 116 LUMO of neutral B30, to produce the singlet neutral ground electronic state of the chiral isomers. The VDE of this detachment channel is calculated to be 3.72 at PBE0, in excellent agreement with the experimental VDE of band X at 3.69(7) eV. The calculated ADE of 3.60 eV at PBE0 is also in excellent agreement with the experimental ADE of 3.59(7) eV. The detachment channel from the HOMO (45a) yields the neutral triplet state, and the calculated VDE is 4.23 eV at PBE0, consistent with band A at 4.34(5) eV. The next two detachment channels have VDEs of 4.43 eV and 4.49 eV at PBE0, which should both contribute to band B at 4.61(5) eV. Seven detachment channels are calculated to be within 4.74 eV and 5.35 eV, which are responsible for the broad band C around 5 eV. The calculated VDEs for higher detachment channels are also consistent with the experiment. The simulated spectrum of isomer I at PBE0 is shown in Figure 4.5b. It should be stressed that isomer II gives identical simulated spectrum. Isomer III (Cs, 2A") lies only 1.90 kcal/mol higher in energy than isomer I, and is likely to be present in the cluster beam. Its simulated spectrum is shown in Figure 4.5c. The calculated first VDE of isomer III is higher than that of isomer I and occurs in the X-A gap region of the PES spectrum. The non-zero intensity in the gap of bands X and A provides tentative evidence for the weak population of this isomer. We also simulated the spectra of isomers IV-VI and IX (not shown). None of these agrees with the experiment. In particular, isomer IX exhibits an extremely low first VDE and its presence in the experiment can be 117 safely ruled out. The overall good agreement between the simulated spectrum of the chiral isomer I and the experiment lends considerable credence to the obtained chiral global minimum for B30−. Table 4.2 Comparison of the experimental VDEs with the calculated values for B30−. The calcualted values are based on the C1 (2A) lowest energy chiral B30–. All energies are in eV. Observed VDEa VDEb Final state and electronic configuration features (Expt.) PBE0 TPSSh 1 2 2 2 2 2 2 2 2 0 X 3.69(7) A …38a 39a 40a 41a 42a 43a 44a 45a 46a 3.72 3.65 3 2 2 2 2 2 2 2 1 1 A 4.34(5) A …38a 39a 40a 41a 42a 43a 44a 45a 46a 4.23 4.07 1 2 2 2 2 2 2 2 1 1 A …38a 39a 40a 41a 42a 43a 44a 45a 46a 4.43 4.24 B 4.61(5) 3 2 2 2 2 2 2 1 2 1 A …38a 39a 40a 41a 42a 43a 44a 45a 46a 4.49 4.37 3 2 2 2 2 2 1 2 2 1 A …38a 39a 40a 41a 42a 43a 44a 45a 46a 4.74 4.64 1 2 2 2 2 2 2 1 2 1 A …38a 39a 40a 41a 42a 43a 44a 45a 46a 4.80 4.63 3 2 2 2 2 1 2 2 2 1 A …38a 39a 40a 41a 42a 43a 44a 45a 46a 4.89 4.75 3 2 2 2 1 2 2 2 2 1 C 5.03(8) A …38a 39a 40a 41a 42a 43a 44a 45a 46a 4.99 4.82 1 2 2 2 2 2 1 2 2 1 A …38a 39a 40a 41a 42a 43a 44a 45a 46a 5.14 4.96 1 2 2 2 1 2 2 2 2 1 A …38a 39a 40a 41a 42a 43a 44a 45a 46a 5.23 5.17 1 2 2 2 2 1 2 2 2 1 A …38a 39a 40a 41a 42a 43a 44a 45a 46a 5.35 5.05 3 2 2 1 2 2 2 2 2 1 A …38a 39a 40a 41a 42a 43a 44a 45a 46a 5.77 5.32 D ~5.6 1 2 2 1 2 2 2 2 2 1 c A …38a 39a 40a 41a 42a 43a 44a 45a 46a 5.49 3 E ~5.9 A …38a239a140a241a242a243a244a245a246a1 5.91 5.79 3 1 2 2 2 2 2 2 2 1 F ~6.2 A …38a 39a 40a 41a 42a 43a 44a 45a 46a 6.51 6.44 a The numbers in parentheses represent the uncertainty in the last digit. b Calculated at TD-DFT/6-311+G(2df)//DFT/6-311G* level of theory. c This value cannot be obtained at this level of theory. 118 4.2.4 Chemical Bonding Analyses and Stability of Enantiomers To understand the chemical bonding in the chiral B30− global minimum, we carried out AdNDP analyses for the closed-shell 2D B30. The results for B30 are shown in Figure 4.8. The AdNDP analyses of B30 reveal seventeen 2c-2e σ bonds on the periphery of the quasi- planar cluster. The remaining σ electron densities are partitioned into two sets of σ delocalized bonds: thirteen 3c-2e σ bonds and six 4c-2e σ bonds. All the π electron density could be localized into eight 4c-2e and one 5c-2e π delocalized bonds, rendering π aromaticity for B30 according to the 4N+2 Hückel rule for π electrons. Despite the aromatic character of planar B30, it remains to be a high energy isomer in the neutral potential energy surface (Figure 4.7). Thus, we further analyzed the chemical bonding of the planar B302− by adding an electron to the global minimum of B30−. The chemical bonding in B302− is almost identical to that in B30 except one additional 9c-2e π bond in B302−. This result reinforces the importance of delocalized π bonds in stabilizing planar boron clusters. To understand the stability of the two enantiomers of B30−, we searched possible transition barriers between them by using the dimer method.256 The lowest transition state is located for the inversion pathway (Figure 4.9), with an inversion barrier of 6.21 kcal/mol calculated at the LPNO-CCSD/Def2-SVP/C level. Vibrational analyses on the transition state geometry show that there is only one imaginary frequency at 71i cm-1. The barrier between the two enantiomers of B30− is not overwhelming, and it is possible for them to 119 convert through the out-of-plane inversion at elevated temperatures. However, when depositing the clusters onto a proper surface, such out-of-plane inversion will be inhibited, yielding two enantiomers with distinct optical activities. Figure 4.8 AdNDP chemical bonding analyses of the closed-shell B30 (C1, 1A). Figure 4.9 Potential energy curve showing the transition state between the two enantiomers of B30− via a bending mode. 120 4.2.5 Conclusions We report the first inherently chiral boron cluster at B30− using photoelectron spectroscopy and quantum chemical calculations. Excellent agreement between the calculated and experimental spectra of B30− has confirmed the global minimum structure located by using an improved Basin-Hoping algorithm. The global minimum of B30− is found to be a pair of 2D enantiomers characterized by different positions of the hexagonal hole. Chiral boron clusters have not been observed before, except in the boron hydride clusters B4H5 and B4H5− considered theoretically.257 It is possible chiral structures may exist for larger boron clusters and such chiral clusters may be obtainable experimentally by deposition on suitable surfaces using size-selected cluster beams. 4.3 The B35 Cluster with a Double‐Hexagonal Vacancy (DHV): A New and More Flexible Structural Motif for Borophene Two-dimensional atomic-thin boron sheets have attracted increasing attention. Various forms of monolayer boron structures have been considered with different vacancy densities and arrangements.152,154,163,258-260 The role of the hexagonal hole in the borophenes has been rationalized in term of chemical bonding.151 In the previous sections, I have demonstrated that the B36–/0 and B30–/0 clusters feature isolated hexagonal holes, and thus can be viewed as the embryo for the formation of borophene in the arrangement of α-sheet. 121 The hexagonal vacancy seems to be the defining structural feature of medium-sized boron clusters above n = 30. Here I describle a joint PES and computational study on the B35– and B35 clusters, which are found to be the smallest planar boron clusters containing two adjacent hexagonal holes or a DHV. This structure is similar to the hexagonal B36 cluster with a missing interior B atom. Chemical bonding analyses reveal a triple π aromatic system for the closed-shell B35–, analogous to the benzo(g,h,i)perylene (C22H12) molecule. Most significantly, the B35 cluster can be viewed as a new and more flexible motif to construct various types of borophene, containing DHVs or mixed hexagonal holes and DHVs. 4.3.1 Experimental Results The photoelectron spectrum of B35– at 193 nm is shown in Figure 4.10. The low binding energy band X, which represents the electron detachment transition from the ground state of B35– to that of neutral B35, occurs at a VDE of 4.06  0.05 eV. The ADE is 3.96  0.05 eV, which also represents the EA of neutral B35. Band A appears at ~5.0 eV, which is separated from band X by an energy gap of ~0.9 eV as evaluated from the VDE difference of the two bands. Band B is prominent and broad, centering at 5.35  0.05 eV and hinting it may contain multiple detachment transitions. A well-separated band C is observed at 5.93  0.05 eV. The overall spectral pattern is well-structured and relatively simple, providing a definitive electronic fingerprint for B35– and the corresponding neutral 122 B35. It is interesting to note that the spectrum of B35– is somewhat similar to that of B36– (Figure 4.1), except the latter contains an extra low binding energy feature at a VDE of 3.3 eV. This observation suggests that the structure of B35– may be related to the hexagonal B36–. 4.3.2 Theoretical Results Global minimum searches were accomplished using the Minima Hopping algorithm and TGmin, in combination with manual structural constructions. The global minimum of B35– (Cs, 1A) is shown in Figure 4.11, along with its corresponding neutral structure (Cs, 2 A). These structures are quasi-planar with an overall hexagonal shape, in which the B atoms are triangular close-packed except for the two adjacent hexagonal holes. The nearest competing structures are 0.52 eV and 0.27 eV higher in energy for the anion and neutral, respectively, suggesting that the B35– (Cs, 1A) and B35 (Cs, 2A) structures with the DHV are quite stable species. The relative energies at the CCSD(T) level are 0.56 eV and 0.38 eV for the anion and neutral, respectively, further confirming the stability of the Cs B35– (1A) and Cs B35 (2A). The lowest-energy 3D structures are cage-like, being 0.85 eV and 0.72 eV above the global minima, respectively, for the anion and neutral. 123 Figure 4.10 (a) Experimental photoelectron spectrum of B35– at 193 nm, in comparison with (b) simulated spectrum. The simulation was done for the global-minimum Cs (1A) structure by fitting the calculated VDEs with unit-area Gaussian functions of 0.05 eV half-width. . Figure 4.11 The optimized global-minimum structures of B35– (Cs, 1A) and neutral B35 (Cs, 2A) at the PBE0/6-311+G* level. 124 4.3.3 Comparison between Experimental and Theoretical Results To confirm the Cs (1A) structure is the true global minimum for B35–, we calculated its VDEs, using the TD- DFT method with the PBE0 functional, to compare with the experimental data. As shown in Table 4.3, the calculated ground state VDE is 3.99 eV, in excellent agreement with the experimental value of 4.06 eV. The ground state ADE is calculated to be 3.91 eV, corresponding to the experimental value of 3.96 eV. The calculated VDE for the second detachment channel (4.89 eV) is in good agreement with band A at ~5.0 eV. The computed VDEs for the next five detachment channels are closely spaced ranging from 5.07 to 5.47 eV, which should correspond to the broad and prominent band B covering the same energy range. Following a small energy gap, the next calculated detachment transition is at 5.87 eV, in good agreement with band C at 5.93 eV. The simulated spectrum (Figure 4.10b), obtained by fitting the calculated VDEs with unit-area Gaussians, is almost in quantitative agreement with the experimental spectrum, lending considerable credence to the identified global minimum of the quasiplanar hexagonal B35– with the DHV. 125 Table 4.3 Comparison of the experimental VDEs with the calculated values for B35−. The calcualted values are based on the global-minimum structure of B35– (Cs, 1A). All energies are in eV. Observed VDEa Final state and electronic configuration VDE (TD-PBE0) features (Expt.) 4.06 (5)b 2 X A", ...26a'2 27a'2 21a"2 22a"2 28a'2 23a"2 29a'2 24a"1 3.99c ~5.0d 2 A A', ...26a'2 27a'2 21a"2 22a"2 28a'2 23a"2 29a'1 24a"2 4.89 2 2 2 2 2 1 2 2 2 A', ...26a' 27a' 21a" 22a" 28a' 23a" 29a' 24a" 5.07 2 2 2 2 2 2 1 2 2 A", ...26a' 27a' 21a" 22a" 28a' 23a" 29a' 24a" 5.18 e 2 2 2 2 1 2 2 2 2 B 5.35 (5) A", ...26a' 27a' 21a" 22a" 28a' 23a" 29a' 24a" 5.27 2 A", ...26a'2 27a'2 21a"1 22a"2 28a'2 23a"2 29a'2 24a"2 5.29 2 2 1 2 2 2 2 2 2 A', ...26a' 27a' 21a" 22a" 28a' 23a" 29a' 24a" 5.47 1 2 2 2 2 2 2 2 C 5.93 (5) 2A', ...26a' 27a' 21a" 22a" 28a' 23a" 29a' 24a" 5.87 a Numbers in parentheses represent the experimental uncertainty in the last digit. b Ground-state ADE is 3.96 (5) eV, which represents the EA of the corresponding neutral B35 species. c Calculated ground-state ADE is 3.91 eV at the PBE0 level. d Experimental ADE for band A is estimated to be 4.82 (5), defining an X-A excitation energy of ~0.9 eV for the B35 neutral. e Broad PES band covering roughly the binding energy regime of 5.15.6 eV. 4.3.4 Chemical Bonding Analyses and Stability of B35− The structure of neutral B35 is similar to the anion with little geometry change. The overall structures of B35– and B35 resemble closely the structures of the hexagonal B36– and B36, respectively, except the additional hexagonal hole in the former. Both B36– and B36 possess perfect hexagonal structures with C6v symmetry and a central hexagonal hole. They can also be viewed as consisting of three concentric hexagonal boron rings: an inner B6 ring, a middle B12 ring, and an outer B18 ring. The structures of B35– and B35 can be viewed as removing a boron atom from the middle B12 ring of B36– and B36, generating an extra hexagonal hole adjacent to the central hexagonal hole such that the two hexagonal holes share a B–B bond to give rise to the DHV. Amazingly, the B–B distances in B35– and B35 126 exhibit very little change relative to their 36-atom counter parts. In comparison to the symmetric C6v B36, the maximum in-plane dimension in the DHV direction expands by only 0.06 Å in B35– and shrinks by only 0.09 Å in the perpendicular in-plane direction. The twin holes make the B35– cluster slightly more planar with an out-of-plane distortion of 1.12 Å, slightly smaller than that in B36 (1.16 Å).110 To understand the structure and stability of the 35-atom boron cluster, we analyzed the bonding in the closed-shell B35– system. All π CMOs of B35– are plotted in Figure 4.12. Of the eleven CMOs, HOMO29, HOMO22, HOMO26, HOMO13, and HOMO15 are the bonding and partial bonding combinations. These CMOs can be transformed to five 5c- 2e π bonds, as shown in Figure 4.13a, using the AdNDP method. These five bonds mainly describe π interactions between the outer B18 ring and the middle B11 ring. The remaining six π CMOs can be transformed into two sets of π systems (Figure 4.13a): three 11c-2e bonds primarily responsible for π bonding between the inner and middle rings, and three 35c-2e global π bonds delocalized over the whole cluster. There are 42 σ CMOs in B35–. AdNDP analyses (Figure 4.13a) yielded 19 2c-2e B–B σ bonds involving the 18 peripheral atoms and the B–B bond shared by the double-hexagonal holes, nine 3c-2e σ bonds around the DHV, and 14 4c-2e σ bonds. 2c-2e σ bonds are found for all peripheral atoms in planar boron clusters.103,104,106,108,109,128-131,133-138 However, it is rare to see a localized 2c-2e σ bond 127 in the interior of planar boron clusters. It was only observed previously in B21– between a pair of boron atoms shared by two adjacent pentagonal vacancies.106 The π bonding in B35– is quite interesting. The eleven π bonds from the AdNDP analyses can be viewed to form three different π systems: the five 5c-2e bonds, three 11c-2e bonds, and three 35c-2e bonds, each obeying the 4N+2 Hückel rule for aromaticity. Thus, the B35– cluster can be considered to be a unique triply π aromatic system. More interestingly, we found that the π bonding in B35– is nearly identical to that in the polycyclic aromatic hydrocarbon, benzo(g,h,i)perylene (C22H12), as shown in Figure 4.13b. AdNDP analyses reveal that the eleven π bonds in C22H12 can also be classified into three separate π systems, just like that in B35–. Specifically, the five peripheral CC 2c-2e π bonds in C22H12 are localized and they correspond to the five 5c-2e π bonds in B35–. This observation is reminiscent of previous findings that a B5 unit in boron nanoribbons, called polyboroenes, is equivalent to a CC unit in polyacetylenes.262-265 The B35– clusters provides another example of the hydrocarbon analogs of boron clusters: the π bonding in many planar boron clusters has been found to resemble those of aromatic hydrocarbons.28-42,69-71 The central hexagonal hole in the C6v B36 is critical for its 2D structure. The slight out-of-plane distortion is really due to the peripheral effect, i.e., the peripheral B–B bonds tend to be stronger or slightly shorter than the interior B–B bonds.110 It is interesting to note that the second hexagonal hole in B35– or B35 induces very little structural distortion and in 128 fact makes the cluster to be slightly more planar, reinforcing the importance of hexagonal vacancies in the stabilization of borophene. The B36 cluster has been considered as a motif for borophene consisting of isolated hexagonal holes or the α-sheet. The β-sheet refers to boron monolayers with adjacent hexagonal holes.147,150 Since the initial predictions of stable α- and β-sheets, many monolayer boron sheets with different hexagonal hole densities and arrangements have been considered.8-13 We find that the planar B35 cluster is in fact a more flexible motif to construct borophenes with DHVs or mixed hexagonal holes and DHVs. Figure 4.14 shows schematically two such arrangements. Other arrangements of the B35 clusters are possible, allowing the creation of borophenes with different hole-densities. 129 Figure 4.12 Comparison of the canonical π CMOs of (a) B35– (Cs, 1A) and (b) C22H12 (C2v, 1A1). 130 Figure 4.13 Results of AdNDP analyses for (a) B35– (Cs, 1A), (b) C22H12 (C2v, 1A1). 131 Figure 4.14 Schematic drawings of borophenes constructed from two different arrangements of the planar hexagonal B35 motif. The brown shaded areas represent a single B35 unit and the yellow shaded areas in (a) indicate mono-hexagonal vacancies as a result of the arrangement of the B35 units. 4.3.5 Conclusions In conclusion, we report the structures and bonding of the B35– and B35 clusters, which are found to be quasi-planar structures with a double-hexagonal vacancy or DHV. The structures of B35 can be viewed as removing an interior boron atom from the hexagonal 132 B36 cluster. Chemical bonding analyses show that the closed-shell B35– cluster possess three distinct π systems and can be considered to be triply aromatic. The π bonding in B35– is shown to be analogous to the polycyclic aromatic hydrocarbon, benzo(g,h,i) perylene (C22H12). The B35 cluster with the DHV is shown to be new and flexible structural motif, which can be used to construct borophenes related to the b-sheet with DHVs or mixed hexagonal holes and DHVs. The unique structure of B35 and its relationship to the β-sheet provide further evidence for the viability of borophene. 4.4 Structural Evolution of Anion Boron Clusters The structures of the main contributors to the photoelectron spectra of boron clusters (Bn−, n = 3 – 24, 30, 35, 36) are shown in Figure 4.15. The clusters with n > 6 can be considered to be quasi-planar structures derived from the familiar triangular grid motif of smaller boron clusters. Tetragonal defects start to show up in the B11− clusters and are also found in many other larger clusters. The smallest boron cluster contains a pentagonal vacancy is the B21− cluster. Previous investigations103,104,128-138 show that such defects are essential to keep the cluster flat, because of the unique chemical bonding in all 2D boron clusters, which exhibit strong peripheral B−B bonding and delocalized interior bonding. There seems to be a tendency for larger defect sizes from tetragonal → pentagonal → hexagonal holes as the cluster size increases. The presence of low-lying isomers with hexagonal holes seems to be a ubiquitous feature of the potential energy surface for anionic 133 boron clusters of n > 20. Our studies revealed four structures containing hexagonal holes within 20 kcal/mol of the global minimum for B21− (Figure 3.4) and within 15 kcal/mol for B22− at the PBE0/6-311+G(d) level of theory. The first experimentally and theoretically resolved cluster with hexagonal hole is B36−, which has hexagonal symmetry and a central vacancy. In an effort to search for the smallest boron cluster featuring a hexagonal hole, we have found B30− is a chiral cluster, consisting of a pair of quasiplanar enantiomers both with a hexagonal hole. Adjacent hexagonal holes were observed in the cluster B35−, which has similar structure as the B36−. It is expected that hexagonal holes will be a defining feature for the planar boron clusters in the range of B30− to B36−. Figure 4.15 The structures of the main contributors to the photoelectron spectra of boron clusters (Bn−, n = 3 − 24, 30, 35, 36). 134 Chapter 5 An All‐Boron Fullerene After the discovery of buckminsterfullerene (C60),5 the existence of a similar B60 fullerene was not considered for over two decades, mainly because of the electron deficiency of boron. Even with a recent interesting theoretical proposition,266 heretofore there has been no experimental evidence for boron fullerenes. Early mass spectra of boron clusters showed no special abundance of the B60 cluster.164 Over the past decade, joint experimental and theoretical efforts have been used to systematically elucidate the electronic and structural evolution of elemental boron clusters, and have uncovered a new world of flat boron.104,109,132,133,135,139 Planar or quasi-planar (2D) boron clusters were shown to be the most-stable structures for anionic Bn− clusters up to at least n = 24, governed by σ and π delocalized bonding.109,267 Most recently, B36− was discovered to possess a 2D structure with a perfect hexagonal hole in its center (Figure 4.2),110 which suggested that extended 2D atomically thin boron sheets (borophene) might be viable experimentally. Low- dimensional boron nanostructures have also been studied theoretically.147,148,268 In particular, the proposal of a B80 fullerene142 spurred renewed interest in all-boron fullerenes,154,161,269-274 although further theoretical work showed that core–shell structures are much lower in energy.162,247,248,275 Thus, whether all-boron fullerenes exist or not has remained an open question. Here we report the experimental observation and characterization of an all-boron fullerene cluster at B40−, along with a 2D isomer. The 2D B40− with two adjacent hexagonal holes represents the global minimum, whereas the nearly degenerate fullerene-like B40− cage 135 is slightly higher in energy. However, for neutral B40 the fullerene structure is overwhelmingly the global minimum with unprecedented delocalized bonding over the cage surface. Here we report experimental observation and characterization of an all-boron fullerene cluster at B40–, along with a 2D isomer. The 2D B40– with two adjacent hexagonal holes represents the global minimum, whereas the nearly degenerate fullerene-like B40– cage is slightly higher in energy. For neutral B40, the fullerene structure is overwhelmingly the global minimum with unprecedented delocalized bonding over the cage surface. The current finding marks the onset of all-boron fullerenes, suggesting that a new class of related boron nanostructures may exist. 5.1 Experimental Results The PES spectra at 266 nm and 193 nm photon energy are shown in Figure 5.1. B40– distinguishes itself from other boron clusters with exceptional electronic properties. Its leading PES band X has an extremely low VDE of 2.62  0.05 eV. The overall spectral pattern is unusually simple for such a large cluster: PES bands X, X (VDE: 3.63  0.05 eV), and A (VDE: 4.24  0.03 eV) are well separated, suggesting a remarkably stable neutral B40 cluster with a sizable energy gap between its HOMO and LUMO. Higher binding energy bands are also observed at B (5.10 eV), C (5.55 eV), and D (6.08 eV). The well-resolved PES features serve as electronic fingerprints, making it possible to determine the structure of B40– by comparison with theoretical calculations, as done for B36– recently110 or other smaller boron clusters.104,109,132,133,135 Furthermore, the intensity ratio of bands X and X can be varied slightly upon changes of the supersonic expansion conditions, hinting that they may originate from coexisting isomers in the B40– cluster beam. The ADEs for bands X and X are 136 evaluated from their onsets to be 2.50  0.05 and 3.51  0.05 eV, respectively, which represent the EAs of their corresponding neutral species. The ADE of the X band is exceptionally low, in comparison with the already low ADE of B36– (3.12 eV)110 or that of the B24– (3.55 eV)109, indicating a major structural change at B40–. Figure 5.1 Experimental photoelectron spectra of B40– at (a) 266 nm, (b) 193 nm, in comparison with simulated spectra based on the (c) quasi-planar structure 1 (Cs, 2A'), and (d) cage-like fullerene structure 2 (D2d, 2B2). The weak band X' is magnified by 10 times to show the details. The simulations were done by fitting the distribution of calculated VDEs at PBE0 with unit-area Gaussian functions of 0.1 eV half-width. 137 5.2 Theoretical Results Unbiased global-minimum searches were performed for B40– and B40 using both the Stochastic Surface Walking276 and Basin Hopping algorithms. Low-lying structures were then fully optimized and their relative energies comparatively evaluated at three DFT levels with the 6-311+G* basis set: PBE, PBE0, and TPSSh. Relative energies at the PBE0/6- 311+G* level should be reliable for the current systems, because it has been tested extensively in prior works to be suitable for boron clusters.104,109,110,135,139,162 For more accurate relative energies, single-point CCSD calculations with the optimized PBE0 geometries and 6-31G* basis set were performed for the two lowest isomers. All the DFT levels of theory predict a quasi-planar global-minimum structure 1 (Cs, 2A) for B40– along with a low-lying cage-like fullerene structure 2 (D2d, 2B2), within ~2 kcal/mol at PBE0 level (Figure 5.2). The CCSD calculations show that structure 2 is 1.7 kcal/mol above structure 1, consistent with DFT results. Configurational energy spectrum of B40– at PBE0 level is shown in Figure 5.3a, where representative configurations (quasi-planar, cage-like, double-ring, and triple-ring structures) are depicted according to their relative energies. Only ten low-lying structures located within ~1 eV above the global minimum for B40–, which are either quasi- planar or cage-like. The double-ring and triple-ring structures are much higher in energy (Figure 5.3a). For the neutral B40 cluster (Figure 5.3b), the cage structure 4 (D2d, 1A1) becomes well separated from other isomers and clearly defines the global minimum. The next three isomers also possess cage-like structures (positional isomers of structure 4), being at least ~0.5 eV higher in energy at PBE0 level, and the nearest quasi-planar isomer 3 (Cs, 1 A) corresponding to the anion global minimum is ~1.0 eV higher in energy (Figure 5.3b). 138 Apparently, the B40– cluster favors slightly the quasi-planar geometry, whereas the B40 neutral favors cage-like structures. Figure 5.2 Top and side views of the global minimum and low-lying isomers of B40– and B40 at PBE0/6-311+G* level. 1 (Cs) is the quasi-planar global minimum and 2 (D2d) is the nearly degenerate low-lying fullerene structure of B40– (see Figure 5.3a). 3 (Cs) is the low-lying isomer and 4 (D2d) is the global minimum of B40 (see Figure 5.3b). 139 Figure 5.3 Configurational energy spectra at PBE0/6-311+G* level. a, B40–. b, B40. The energies of the global minima are taken to be zero. Black-quasi-planar structures; red-fullerene-like cages; violet- double-ring tubular structures; blue — triple-ring tubular structure. 140 5.3 Comparison between Experimental and Theoretical Results To confirm the global minimum and low-lying structures of B40–, we calculated their ADEs and VDEs using the TD-DFT formalism.182 The simulated spectra for 1 and 2 are compared with the experimental PES spectrum in Figure 5.1. Clearly, neither structure 1 nor 2 can reproduce the observed PES spectrum. However, their combination is in excellent agreement with the experimental data. Structure 1 gives a ground state ADE/VDE of 3.51/3.60 eV at PBE0 level, consistent with the experimental data of 3.51/3.63 eV for the X band. Higher binding energy transitions from structure 1 also agree well with the observed PES bands AD, which each clearly contain multiple detachment channels. On the other hand, the calculated ground state ADE/VDE from structure 2 are 2.39/2.39 eV at PBE0 level, in close agreement with band X (ADE/VDE: 2.50/2.62 eV). Because of the overlap of the higher binding energy transitions from 2 with those of 1, detailed assignments are not feasible. But contributions of structure 2 are expected to be minor due to its slightly higher energy. Additional PES simulations at the TPSSh, B3LYP, and PBE levels produce similar spectral patterns. Interestingly, all the four lowest-lying cage-like B40– isomers (positional isomers of 2) produce calculated low first VDEs close to 2.6 eV, while all the four lowest- lying quasi-planar isomers give much higher first VDEs close to 3.6 eV, lending further support that the coexisting cage-like and quasi-planar isomers are responsible for the observed PES spectra. 5.4 The Electronic Structure and Stability of B40–/0 The experimental observation of structure 2 of B40– represents the first all-boron fullerene ever produced and characterized, even though boron cages have long been speculated and computationally explored.142,162,164,247,248,277 Both structure 2 and its 141 corresponding neutral 4 have D2d symmetry, with 16 tetracoordinated and 24 pentacoordinated B atoms. The all-boron fullerenes 2 and 4 are elongated slightly along the two-fold main molecular axis, with two hexagonal holes on top and bottom and four heptagonal holes on the waist. These structures are akin to a perforated Chinese red lantern, with two concentric convex caps supported by four double-chain ribs.164 Alternatively, the B40 cage can be built from two B6 rings on top and bottom linking four B7 rings, which form the body of the lantern. The all-boron fullerenes follow the Euler’s rule: E (92 edges) = F (48 triangular + 2 hexagonal + 4 heptagonal faces) + V (40 vertices)  2. It should be noted that the heptagonal holes observed in 2 and 4 are not known in boron clusters or any previously proposed boron nanostructures. Figure 5.4 Chemical bonding analyses for the D2d B40 fullerene. The analyses was done using the AdNDPmethod. 142 The exceptional stability of the neutral B40 fullerene is evident by the large energy gap, as revealed in the simulated spectrum (Figure 5.1d). Due to the overlap of the higher binding energy features of 2 with those from 1, we could not obtain the experimental energy gap for 2. We were able to compute an extremely large HOMO−LUMO gap of 3.13 eV for the neutral cage 4 at the PBE0 level, which is comparable to that of C60 (3.02 eV) calculated at the same level. The LUMO of 4 is a non-degenerate b2 orbital, where the extra electron resides in the B40– cage, explaining why both 2 and 4 can have the same D2d symmetry without symmetry breaking when an electron is added or detached. We analyzed the bonding in the closed-shell neutral 4 fullerene using the AdNDP.107 Of the 60 pairs of valence electrons in 4, a total of 48 delocalized σ bonds are readily identified (Figure 5.4): forty 3c-2e σ bonds on the B3 triangles and eight 6c-2e σ bonds on the quasi-planar close-packed B6 units. As the central B3 triangles make major contributions to the 6c-2e σ bonds, the 48 σ bonds can all be practically viewed as 3c-2e bonds, which match exactly the number of B3 triangles on the surface of 4, completely and uniformly covering the cluster surface, one on each B3 triangle. The remaining 12 bonds in 4 can be essentially characterized as delocalized π bonds: four 5c-2e π bonds, four 6c-2e π bonds, and four 7c-2e π bonds evenly distributed over the cage surface. Thus, all the valence electrons in 4 are completely delocalized as either σ or π bonds, and there is no localized 2c-2e bond, unlike the 2D boron clusters. According to our AdNDP analyses, on average, each B atom contributes 0.6 electron in the π framework. The completely delocalized σ and π bonding in the B40 fullerene is unprecedented, underlying its exceptional stability. Molecular dynamics simulations278 for 4 show that it is highly robust even at high temperatures, dynamically stable at 700 and 1000 K for the 30 ps duration used in the simulation. We also find that the B40 fullerene possesses three- 143 dimensional aromaticity with calculated nucleus independent chemical shifts (NICS)279 of 43 and 42 ppm at the cage centers for 2 and 4, respectively. The quasi-planar B40– isomer 1 (Cs, 2A) is also extremely interesting. The 2D-to-3D transition occurs at B16+ for cationic boron clusters,139 but it is still unresolved for neutral boron clusters.222 The Bn– anionic clusters are known to adopt 2D structures up to at least n = 2429-41,81-83 and remain 2D at n = 30 and 36, as discovered recently.110,111 The current results suggest that the critical size for 2D-to-3D transition for the anionic boron clusters is probably around n = 40. The stability and planarity of 1 may be understood on the basis of concentric dual π aromaticity, analogous to the planar hydrocarbon C27H13+ (Figure 5.5) and the doubly  aromatic B19– Wankel motor cluster.104,218 The AdNDP analyses (Figure 5.5) show that, in quasi-planar B402– (Cs, 1A), there exist three delocalized π bonds for the inner-ring surrounding the double-hexagonal holes and three delocalized π bonds for the global outer- ring, which is an all-boron analogue of the model hydrocarbon molecule C27H13+. The inner- ring and outer-ring sets of π bonds each conform to the (4n + 2) Hückel rule for aromaticity, rendering B402– doubly π aromatic. The remaining seven 4c-2e and 5c-2e π bonds are similar to the seven peripheral 2c-2e and 3c-2e π bonds in C27H13+. The  framework of B402– consists of 2c-2e and 3c-2e  bonds associated with the periphery and the twin- holes, respectively, along with 4c-2e  bonds in between, which essentially cover the whole surface. B40– has a singly occupied HOMO and also possesses dual π aromaticity, similar to B402–. The  bonding pattern based on AdNDP analyses of the closed-shell doubly charged 1 is almost identical to the model C27H13+ unsaturated hydrocarbon. It is also interesting to note that the quasi-planar Cs B402– dianion appears to be thermodynamically stable in the gas phase, with a calculated ADE of ~0.7 eV at PBE0 level. It is 1.46 eV more stable than the 144 D2d B402– fullerene. More interestingly, the two adjacent hexagonal holes in the triangular lattice of 1 are reminiscent of a 2D boron β-sheet.147 If B36 can be viewed as the embryo of the boron α-sheet,110 then different types of β-sheets may be constructed from isomer 1 of B40–, suggesting the viability of extended boron β-sheets, i.e., different types of borophene. Figure 5.5 Comparison of the AdNDP bonding patterns of (a) Cs B402– and (b) C2v C27H13+. 5.5 Discussion Because of the electron deficiency of boron, strong covalent interactions are anticipated between neighboring fullerene B40 units in the condensed phase, making it 145 difficult to form B40-based materials, like the fullerite,6 with the B40 cage as isolated building blocks. However, chemical modification and functionalization of the B40 fullerene should be possible. Initial calculations indicate that doping 4 with a metal atom M (= Ca, Y, La) results in endohedral boron fullerenes M@B40 with M slightly off-center along the two-fold 280 molecular axis, analogous to Ca@C60 (ref. ). In fact, because all-boron fullerenes 2 and 4 possess a slightly smaller diameter (6.2 Å relative to 7.1 Å for C60), they can more comfortably accommodate an endohedral M atom than even C60. Preliminary calculations also suggest that 2 and 4 offer valuable model systems for hydrogen storage. For example, an H2 molecule can be activated in an encapsulated H2@B40–/0 and up to 16 hydrogen atoms can be terminally bonded at the 16 tetra-coordinate B sites of 2 and 4. In particular, Ca-coated B40 may serve as promising materials for H2 chemisorption.281 Notably, every B atom in 2 and 4 is on the edge of a hexagonal or heptagonal hole, which facilitates H and/or H2 adsorption and release. Only a handful of free-standing elemental cage clusters5,282-284 have been characterized experimentally thus far: the fullerenes, Au16–, the stannaspherene Sn122–, and the plumbaspherene Pb122–. The observation of the all-boron fullerene enriches the chemistry of boron and may lead to new boron-based nanomaterials. 146 Chapter 6 Transition Metal Centered Boron Monocyclic Molecular Wheels The study of atomic clusters, with structures and properties intermediate between individual atoms and bulk solids, has a profound impact on the understanding of chemical bonding, and the rational design of nanosystems with tailored physical and chemical properties.7 Small boron clusters have been discovered to possess planar structures stabilized by electron delocalization both in the σ and π frameworks.103,104,106,108-111,128-133,135,138 All planar boron clusters confirmed experimentally thus far consist of an outer ring, featuring strong 2c-2e B-B bonds, and one or more inner atoms interacting with the peripheral ring via delocalized σ and π bonding.103,104,106,108,109,133,135,138,215 To emphasize the role electron delocalization plays in the stability of planar boron clusters, we note that the inner boron atoms in the anionic clusters (n ≤ 24) are bonded to the outer ring almost exclusively by multi-center two-electron bonds (nc–2e). One prototypical example is the circular B19− cluster, which consists of two different delocalized π systems,9 in addition to σ delocalized bonding. These delocalized bonding characterize the interactions between the central B atom and the middle B5 ring and between the B5 ring and the outer B13 ring. Interestingly, the inner B©B5 moiety has been found to rotate almost freely inside the B13 outer ring, akin to an aromatic Wankel motor.218 Similar fluxional behavior has also been found for the inner B3 ring in the planar B13+ cluster, entirely owing to delocalized bonding between the B3 unit and the outer B9 ring.219 147 The planar boron clusters that provided the inspiration for metal doping are the 8- and 9-atom boron clusters.132,134 These two clusters stand out as perfectly symmetric molecular wheels: B82− (D7h) and B9− (D8h), each with 6 σ and 6 π electrons conforming to the (4N + 2) Hückel rule for aromaticity.132,134 Chemical bonding analyses using the AdNDP method107 confirmed that both clusters are doubly aromatic with unprecedented multi-center electron delocalization. However, attempts to substitute the central B atom with C to form carbon- centered wheel structures285-288 were not successful and yielded only higher energy structures, because C avoids hyper-coordination in BxCy clusters and prefers to participate in localized 2c-2e σ bonding on the periphery in the B-C mixed clusters.289-291 One interesting question was whether it would be possible to substitute the central B atom with a metal atom to create clusters with a central metal atom coordinated by a monocyclic boron ring (M©Bn). It was shown that simple valence isoelectronic substitution by Al was not possible, only resulting in “umbrella”–type structures in AlB7− (C7v) and AlB8− (C8v)292, in which Al interacts with a concave B7 or B8 unit primarily through ionic bonding and does not participate in delocalized bonding within the 2D boron frameworks. Similar ionic interactions have also been observed in larger AlBn− (n = 9–11) clusters.293,294 Gold was also considered in a prior experiment, but it was found to form a covalent bond with a corner boron atom on the periphery of a planar B10 in AuB10−, whereas the D10h-Au©B10− is a high- energy local minimum.295 Hence, doping boron clusters with transition metals with open d- shells became the natural choice for potentially creating M©Bn-type molecular wheels. In the meantime, the transition-metal atom centered in a planar monocyclic ring appears to be Fe©Sn5+ and Fe©Bi5+, although these structures are not the global minima on their respective potential energy surfaces.296 148 This chapter presents a series of transition metal centered molecular wheel produced in a supersonic cluster beam by laser vaporization and characterized using joint PES and quantum chemistry studies. All these clusters have been shown to be the global minima on their respective potential energy curves. A design principle based on doubly aromaticity has been proposed and verified for electronically stable M©Bnk–-type compounds. The © sign is proposed to designate the central position of the doped atom in monocyclic structure in M©Bn-type planar clusters. These novel molecular wheels represent a new series of structural motifs for boron nanomaterials. 6.1 The Design Principle for Metal Centered Boron Wheel Clusters (M©Bnk−) Despite numerous theoretical reports on molecular wheel-type clusters,285-288 only the pure boron clusters, B82− and B9−, with hepta- and octa-coordinated boron atoms were proved to be thermodynamically stable.6,23 The chemical bonding of these two clusters involves classical 2c-2e bonds for the peripheral boron rings (7 for B82− and 8 for B9−) and 6 delocalized σ electrons and 6 delocalized π electrons. Thus, the bonding in these molecular wheels can be viewed as a monocyclic boron ring interacting with a central B atom entirely through delocalized bonds. Because the number of σ or π electrons each satisfies the 4N+2 Hückel rule for aromaticity, these molecular wheels are considered to be doubly aromatic. Thus, each peripheral B atom contributes two valence electrons to the 2c-2e bonds of the outer ring and one electron to the delocalized bonding between the outer ring and the central atom, whereas the central B atom contributes all three of its valence electrons to the delocalized bonding. Replacing the central B in B82− by C would result in an isoelectronic D7h-CB7−, which was found to be a local minimum.289 In fact, all group-14 elements were 149 found to give stable minima for D7h-MB7− clusters.287 However, C has been confirmed experimentally to avoid the central position and the global minimum of CB7− has C2v 289 symmetry, in which the C atom is on the periphery. Because C is more electronegative than B, it prefers the peripheral position, where it is involved in strong 2c-2e bonding, rather than the central position, where only delocalized multi-center bonding is possible. A D9h- AlB9+ has been found to be a local minimum,297 but we have shown that Al also does not favor the central planar position.293 Once the main-group elements came out of favor as potential substituents for the central B atom to create molecular wheels, the focus of theoretical studies shifted to transition-metal-doped boron systems.298-302 Two previous reports showed that D8h-CoB8−, D9h-FeB9−, and D8h-FeB82− were global minima, while a number of other transition metal doped boron rings (MBn) with n = 7 − 10 were found to be only local minima.299,301 Nucleus- independent-chemical-shift calculations showed that all these clusters were highly aromatic. The introduction of the AdNDP method greatly simplified the bonding analyses and revealed that all planar wheel-type boron clusters featured double σ and π aromaticity.41 Based on the double aromaticity requirement, (4N1+2) delocalized σ electrons and (4N2+2) delocalized π electrons to fulfill the Hückel aromaticity rule, a general electronic design principle has been proposed that involves the formal valence of the transition metal (x), the number of peripheral boron atoms (n), and the cluster’s charge (k). To form electronically stable and doubly aromatic wheel-type clusters (Mx©Bnk−), the design principle requires that the total number of bonding electrons present in the system, 3n + x + k, participate in n 2c-2e B-B peripheral σ bonds and two sets of aromatic delocalized bonds (12 e for 6 σ and 6 π electrons), i.e. 150 3 2 12 Eq. 13 In other words, for an electronically stable Mx©Bnk− cluster with double aromaticity, 12 Eq. 14 For singly charged Mx©Bn− clusters (k = 1) 11 Eq. 15 However, geometric or steric considerations should probably limit the ring size to be at least 7 atoms. For pure boron clusters, it was found that the B7 cluster has a hexa- pyramidal structure, 5 which suggests that even the boron atom is too large to fit inside a B6 ring. The smallest molecular wheel structure found experimentally is the D7h-B82− cluster,134 while B8− has a slightly distorted planar structure with a D2h symmetry due to the Jahn-Teller effect.132 When applied to a hypothetical D7h-M©B7− cluster, the design principle requires a valence IV element. For large boron rings, we have shown that a B10 ring is already too large to fit Au,295 even though Au has the right valence to make an electronically stable Au©B10− wheel. 6.2 Case Studies of M©B8− Molecular Wheels: Co©B8− and Fe©B8− When applied to a D8h-M©B8− cluster (n = 8, k = 1), the design principle requires that the transition metal atom should contribute 3 valence electrons to delocalized bonding. Given the small size of the B8 ring, the best candidate for such a cluster should be a 3d metal. Indeed, D8h-CoB8− and FeB82− were calculated to be stable minima,299,300 and in this thesis, they were experimentally confirmed as D8h-M©B8− molecular wheels.113,114 151 6.2.1 Experimental Results CoB8−: The 266 nm spectrum (Figure 6.1b) reveals an intense feature X at 3.84 ± 0.01 eV and a weak feature A at 4.23 ± 0.02 eV. The feature X corresponds to the electron detachment from the ground state of CoB8− to produce its neutral ground state. Two vibrational modes are observed for feature X: one with a frequency of 1200 ± 50 cm−1 and another with a frequency of 520 ± 50 cm−1. The ADE value is measured from the 0-0 vibrational peak at 3.84 ± 0.01 eV. The weak feature A becomes slightly stronger in the 193 nm spectrum (Figure 6.1a). Two more features B and C are observed for CoB8− at 4.83 ± 0.03 eV and 5.21 ± 0.04 eV. Overall, the 193 nm spectra of CoB8− (Figure 6.1a) displayed relatively high electron binding energies and simple spectral patterns, suggesting a high symmetry of the CoB8− cluster. All the VDEs are summarized and compared with the computed VDEs in Table 6.1. FeB8−: The 266 nm spectrum of FeB8− (Figure 6.2b) displays a broad and weak low binding energy band X', an intense vibrationally resolved band X, and a weak band A. As will be shown below, the first band X' represents probably a transition from a higher energy isomer. The strong feature X in the 266 nm spectrum has a VDE value of 3.75 ± 0.03 eV and is a partially resolved vibrational progression. Two vibrational modes are tentatively assigned with average spacing of 510 ± 50 cm−1 and 1300 ± 100 cm−1, respectively. Since this band does not have a sharp rise, it is likely that there may be unresolved low frequency vibrational excitations associated with each resolved peak. The ADE of band X is evaluated to be 3.65 ± 0.03 eV. The third weak feature, A, with a VDE of 4.15 eV, was not well resolved at 266 nm, but it is better defined in the 193 nm spectrum (Figure 6.2a). At the high binding energy side, we observed three additional bands B–D with VDEs of 4.60 ± 0.05, 5.21 ± 0.05, and 5.6 ± 152 0.1 eV, respectively. All the spectral features of FeB8− are broad, suggesting that there are significant geometry changes between FeB8− and its neutral states. The VDEs of all the spectral are given in Table 6.2 and are compared with theoretical calculations. Figure 6.1 Photoelectron spectra of CoB8− at (a) 193 nm and (b) 266 nm. Figure 6.2 Photoelectron spectra of FeB8− at (a) 193 nm and (b) 266 nm. 6.2.2 Theoretical Results The simple spectral patterns of CoB8− and FeB8− and the resolved vibrational structures for such complicated systems suggest that they should have high symmetries. To 153 confirm that the D8h structures are indeed the global minima of CoB8– and FeB8–, we compared the computed VDEs with the experimental data and analyzed the vibrational structures resolved in the 266 nm spectrums. CoB8–: The optimized structures of Co©B8– and Co©B8 at PBE0/6-311g* level of theory are shown in Figure 6.3a. The Co©B8– (1A1g, …3a1g22e1u4) has a perfect D8h symmetry with the Co atom in the center of an eight-membered boron ring. The B-B bond length is 1.556 Å and the Co-B bond length is 2.033 Å. Our result for Co©B8– is consistent with previous calculations.299 The neutral CoB8 has a slightly distorted structure with D2h symmetry. The two types B-B peripheral bond lengths are 1.545 Å and 1.572 Å, while the Co-B bond lengths are 2.010 Å, 2.033 Å and 2.069 Å. The valence canonical MOs of the Co©B8– are presented in Figure 6.3b. FeB8–: The unbiased global minimum structures of FeB82−, FeB8− and FeB8 are presented in Figure 6.4a. The FeB8− cluster is an octa-coordinate wheel with the central Fe atom slightly shifted out of the boron ring plane (∼0.2 Å). The extent of distortion could be evaluated by noting that the largest B-Fe-B angle in the C8v structure is 160.0°. The valence CMOs of the anionic species are presented in Figure 6.4b. The global minimum of FeB8− has one unpaired electron in the singly occupied MOs (HOMO, 4a1) giving rise to the lowest doublet 2A1 state of the C8v structure (Figure 6.4a). The optimized geometries of the dianionic and neutral FeB82−/0 cluster at BP86/aug-cc-pVTZ are compared in Figure 6.4a. It can be clearly seen that the peripheral B-B distance becomes somewhat shorter (1.572 Å for Fe©B82−; 1.563 Å for Fe©B8−; 1.548 Å for Fe©B8) while the central iron atom gets more and more out of plane as we gradually remove two electrons from the octa-coordinate Fe©B82− cluster introduced by Pu et al.300 154 Figure 6.3 (a) Optimized structures and (b) CMOs of Co©B8− and Co©B8. All bond lengths are given in Å. 155 Figure 6.4 (a) Optimized structures for Fe©B82/−/0, (b) CMOs of Fe©B8−. All bond lengths are given in Å 156 6.2.3 Comparison between Experimental and Theoretical Results CoB8–: The calculated VDE values are three levels of theory are shown in Table 6.1, where they are comparing with the experimental values. The first VDE of 3.88 eV at ROCCSD(T) level, which corresponds to the electron detachment from the double degenerate HOMO orbital (2e1u), is in excellent agreement with the feature X at 3.84(1) eV. As a result of the electron removal from a doubly degenerate orbital, the geometry of the neutral CoB8 cluster undergoes a small Jahn-Teller distortion leading to a lower D2h symmetry. The geometry change was, also, reflected by the observation of the two vibrational modes of CoB8 that are responsible for the D8h to D2h distortion. The experimental values, 520(50) cm−1 and 1200(100) cm−1 (Figure 6.1b), are indeed in good agreement with the theoretical values: 549 cm−1 (ν2) and 1160 cm−1 (ν4), respectively. The calculated ADE of 3.78 eV is also in excellent agreement with the experimental value of 3.84(1) eV. The electron detachment from the HOMO−1 (3a1g) produces the 2A1g final states with a VDE of 4.20 eV, which is assigned to feature A. The next two detachment channels are assigned to features B and C, respectively. Overall, the theoretical results and the experimental observations are in excellent agreement, confirming unequivocally that the D8h- Co©B8– (1A1g) structure is highly stable and should be the global minima in its respective potential energy surface. The good agreement between the theoretical VDEs and the experimental data lends support for the D8h molecular wheel structure as the global minimum for CoB8−. FeB8–: The calculated VDE values are three levels of theory are shown in Table 6.2. The ground state detachment transition is from the removal of an electron from the doubly degenerate 3e1 orbital (HOMO−1) to produce the triplet 3E1 final state. The calculated VDE 157 of 3.84 eV at ROCCSD(T) is in excellent agreement with the X band at 3.75 eV. A small Jahn-Teller distortion due to electron detachment from the doubly degenerate orbital leads to a lower C2v symmetry of the neutral FeB8. The vibrational modes (516 cm−1 and 1286 cm−1) are responsible for this C8v to C2v distortion are also in excellent agreement with the experimental values (510 (50) cm−1 and 1300 (100) cm−1). The B band corresponds to electron detachment from the 4a1 orbital. All of the other transitions are explained as electron detachments from the 3a1, 2a1, and 2e1 orbitals with final triplet states. All of the VDE values calculated for the photodetachment transitions are in good agreement with the experimentally measured values (Table 6.1) with the exception of the transition marked as X' in Figure 6.2, which is assigned to a low-lying isomer.114 Table 6.1 Observed VDEs for CoB8– compared with theoretical values. The calculated values are from the D8h Co©B8– (1A1g) cluster. All energies are in eV. Observed VDE (theoretical) VDE (exp)a Final State and Electronic Configuration b features PBE0 B3LYPc ROCCSD(T)d Xe 2 3.84 (1) E1u … 2a1g2 1b2g2 1e1g4 2e2g4 1a2u2 3a1g2 2e1u3 3.81 3.72 3.88 2 A 4.23 (2) A1g … 2a1g2 1b2g2 1e1g4 2e2g4 1a2u2 3a1g1 2e1u4 3.90 3.97 4.20 2 B 4.82 (3) E2g … 2a1g2 1b2g2 1e1g4 2e2g3 1a2u2 3a1g2 2e1u4 4.60 4.58 4.82 2 C 5.21 (4) E1g … 2a1g2 1b2g2 1e1g3 2e2g4 1a2u2 3a1g2 2e1u4 5.12 5.17 5.58 2 A2u … 2a1g2 1b2g2 1e1g4 2e2g4 1a2u1 3a1g2 2e1u4 5.27 5.15 a Numbers in parentheses represent the uncertainty in the last digit. b – VDEs for Co©B8 were calculated at ROPBE0/6-311+G(2df)//PBE0/6-311+G*. c – VDEs for Co©B were calculated at ROB3LYP/6-311+G(2df)//B3LYP/6-311+G. 8 d – VDEs for Co©B were calculated at ROCCSD(T)/6-311+G(2df)//PBE0/6-311+G. 8 e Measured ADE is the same as the VDE. 158 Table 6.2 Observed VDEs for FeB8– compared with theoretical values. The calculated values are from the Fe©B8− (C8v, 2A1) cluster. All energies are in eV. Observed VDE (theoretical) VDE (exp)a Final State and Electronic Configuration b features UBP86 ROPBE0c ROCCSD(T)d 3 X 3.75(3) E1 … 2e14 2a12 3a12 2e24 3e13 4a11 3.62 (0.80) 3.71 3.84 (1.41) 3 4 2 2 3 4 1 A 4.15(4) E2 … 2e1 2a1 3a1 2e2 3e1 4a1 4.17 (2.04) 3.81 4.06 (1.34) 1 4 2 2 4 4 0 B 4.60(5) A1 … 2e1 2a1 3a1 2e2 3e1 4a1 4.58 (0.00) 4.79 5.06 (1.68)f 3 A1 … 2e14 2a12 3a11 2e24 3e14 4a11 5.17 (2.03) 5.16 5.30 (1.33) C 5.21(5) 3 3 2 2 4 4 1 e E1 … 2e1 2a1 3a1 2e2 3e1 4a1 5.35 (2.07) 5.24 (1.36) 3 4 1 2 4 4 1 D 5.6(1) A1 … 2e1 2a1 3a1 2e2 3e1 4a1 5.60 (2.08) 5.78 5.66 (1.37) a Numbers in parentheses represent the uncertainty in the last digit. b 2 VDEs were calculated at UBP86/aug-cc-pVTZ. The values of are given in parentheses following the computed VDE values. c VDEs were calculated at ROPBE0/aug-cc-pVTZ//UBP86/aug-cc-pVTZ. d VDEs were calculated at ROCCSD(T)/6-311+G(2df)//UBP86/aug-cc-pVTZ. The NORM values are given in parentheses following the computed VDE values. e We couldn’t achieve convergence for this particular state. f The validity of this VDE value is questionable due to the high NORM value. 6.2.4 Discussion CoB8–: The CMOs responsible for the B-B bonding in the circumference, the delocalized π bonding (HOMO−2 (1a2u) and HOMO−4 (1e1g) and the delocalized σ bonding (HOMO (2 e1u) and HOMO−6 (2a1g) can be readily recognized. The CoB8– cluster contains six delocalized π and six delocalized σ electrons, thus resulting in double aromaticity and high electronic stability. The CoB8– cluster has three primarily d-based orbitals ( , , ), which can also be readily recognized. The AdNDP analyses show the bonding situations in the two complexes more clearly (Figure 6.5). These results show the lone pairs of electrons in the d orbitals, the B-B peripheral bonds, and the double aromaticity in both clusters. The occupation numbers for the localized and delocalized MOs are all close to 2. However, the two d-based MOs ( and ) have occupation numbers significantly less than 2 (1.81|e|), thus suggesting that these MOs are involved in covalent interactions between 159 the monocyclic ligands and the central metal atoms with the contribution of the 3d element. Co is formally trivalent in Co©B8−, consistent with our electronic design principle. Figure 6.5 AdNDP analyses for Co©B8−. FeB8–: The CMO of the open-shell global minimum of Fe©B8− are presented in Figure 6.4b. The Fe©B8− has one less electron than Co©B8− and it has very similar CMO as Co©B8−. We expect that the 33 valence electrons of Fe©B8− could form the following bonds and lone pairs: 1) three π delocalized bonds making this cluster π aromatic; 2) three σ delocalized bonds making this cluster σ aromatic; 3) two lone pairs of d-type participating in a minor covalent bonding with the peripheral boron ring; 4) a singly occupied 1c-2e bond of -type localized on the central atom; 5) eight 2c-2e peripheral B-B σ bonds. The double aromaticity of the FeB8− global minimum explains its stability and presence in the photoelectron spectrum. 6.3 Case Studies of M©B9− Molecular Wheels: Fe©B9− and Ru©B9− When applied to a D9h-M©B9− cluster, the design principle requires that the transition metal atom should contribute 2 (x = 2) valence electrons to delocalized bonding. All the 3d, 160 4d and 5d transition metal elements have been examined for the D9h-M©B9− cluster. Indeed, the Fe©B9− was computed to be a stable minimum.298,299,301,302 In this section, two D9h- M©B9− (M = Fe and Ru) molecular wheels characterized both experimentally and theoretically will be discussed.113,114 6.3.1 Experimental Results RuB9−: Four well-resolved bands (X, A–C) were observed in the spectrum of RuB9− (Figure 6.6). At 266 nm, the X band (3.85 ± 0.01 eV) was observed to be fairly sharp without any resolved vibrational structures, thus suggesting that a very low frequency mode was involved and that there was little geometry change between the anion and the neutral ground state. The A band was vibrationally resolved with three vibrational modes (Figure 6.6, right): 550 ± 50, 1240 ± 50, and 1560 ± 50 cm−1. After a gap of ~0.6 eV, features B and C are observed at 5.11 ± 0.03 eV and 5.21 ± 0.03 eV, respectively. FeB9−: The 266 nm photoelectron spectrum of FeB9− (Figure 6.7b) displays two detachment bands: X and A. The first band, X, is weak but sharp with a VDE value of 3.42 eV and does not show any resolved vibrational structure, suggesting that this transition should involve the removal of one electron from a non-bonding orbital. The ADE is 3.38 (3) eV. The second band, A, is intense and has a VDE value of 4.22 eV. The A band has a sharp rise and shows a short vibrational progression with an average spacing of 440 ± 40 cm−1. We assign the most intense peak of the A band to the 0-0 vibrational transition, as the measured ADE and VDE values are equal. At 193 nm (Figure 6.7a), two more features are identified, B and C, with VDE values of 5.03 and 5.23 eV. No discernable spectral features were observed beyond 6 eV. All detachment transitions were relatively 161 sharp, suggesting that there are only minor geometry changes between the anion and the neutral states. Figure 6.6 Photoelectron spectra of RuB9− at (a) 193 nm and (b) 266 nm. Figure 6.7 Photoelectron spectra of FeB9− at (a) 193 nm and (b) 266 nm. 6.3.2 Theoretical Results RuB9−: The optimized structures of RuB9– and RuB9 are shown in Figure 6.8a. The D9h-Ru©B9– (2A1' ...2a1'2 1e1''4 2e2'4 1a2''2 2e1'4 3a1'2) is indeed the minima on the potential energy surface. The B-B bond length is 1.536 Å and the Rh-B bond length is 2.245 Å. The 162 neutral RuB9 has a C9v symmetry that the Ru is only approximately 0.1 Å out of plane. The B-B bond length in the neutral (2.256 Å) is slightly larger than that in the anion, as well as the Ru-B bond length (2.256Å in the neutral). FeB9−: The lowest planar wheel-type structure featuring a nona-coordinate iron (Figure 6.9a) was identified in previous work using stochastic searches of both singlet and triplet potential energy surfaces of FeB9−.299 All other structures were found to lie higher in energy.299 Therefore, in the current study we did not perform a global minimum search for FeB9−. Instead we reoptimized the D9h global minimum structure of FeB9− at UBP86/aug-cc- pVTZ, further calculated its VDEs at the U(RO)BP86, ROPBE0, and ROCCSD(T) levels, and compared the VDEs with the experimental data to confirm the calculated structure. All the calculated VDE values were found to be in good agreement with the experimental values. 6.3.3 Comparison between Experimental and Theoretical Results RuB9−: The calculated VDEs for the D9h Ru©B9− (1A1′, …2e1′4 3a1′2) at several levels of theory is shown in Table 6.3 and found excellent agreement with the experimental data. The HOMO of the D9h-Ru©B9– is 3a1', which is primarily of Ru 4 character (Figure 6.8b). Electron detachment from this orbital produces the neutral ground state, the VDE of which is calculated at 3.80 eV (ROCCSD(T)), agreeing with the experimental values of 3.85(1) eV. The out-of-plane distortion is consistent with the nature of this HOMO. This structural distortion suggests that the vibrational mode, which is active upon detaching an electron from the HOMO, should involve the Ru atom moving up and down. This mode has a calculated frequency of 36 cm−1, in agreement with the unresolved low frequency vibration of the X band (Figure 6.6b). The HOMO−1 (2e1') of Ru©B9– is degenerate and Jahn-Teller distortions are expected for detachment from this orbital, in agreement with the observed vibrational 163 features in the A band (Figure 1d). The calculated ADE of Ru©B9– is also in good agreement with the experimental value (Table 6.3). Overall, the theoretical results and the experimental observations are in excellent agreement, confirming unequivocally the D9h-Ru©B9– as the global minima in its respective potential energy surface. FeB9−: The previously reported global minima stochastic searches revealed that the wheel-type structure is the lowest energy isomer of FeB9−.299 The first low-lying isomer (Cs) was shown to be 14.9 kcal/mol higher in energy at the BP86/TZVPP level of theory299 and, therefore, we expect that only the wheel structure should contribute to the photoelectron signal in the photodetachment spectra. The theoretical first VDE corresponds to the photodetachment transitions occur from the HOMO (3a1′), which is computed at BP86 (3.58 eV) or at PBE0 (3.40 eV), is in good agreement with the experimental feature X at 3.42 eV (Table 6.4). The sharpness of feature X is also consistent with the non-bonding character of the HOMO. The next four transitions occur from HOMO−1, HOMO−2, HOMO−3, and HOMO−4. The calculated VDEs for these transitions also show good agreement with the experimental data, confirming that the Fe-centered wheel structure is the global minimum of FeB9−.299,302 164 Figure 6.8 (a) Optimized structures, and (b) MOs for Ru©B9− and Ru©B9. Bond lengths are given in Å. 165 Figure 6.9 (a) Optimized structures, and (b) MOs for Fe©B9− and Fe©B9. All bond lengths are given in Å. 166 Table 6.3 Observed VDEs for RuB9– compared with theoretical values. The calculated values are from the Ru©B9– (D9h, 1A1') cluster. All energies are in eV. Observed VDE (theoretical) VDE (exp)[a] Final State and Electronic Configuration b features PBE0 B3LYPc ROCCSD(T)d Xe 2 3.85 (1) A1' ...2a1'2 1e1''4 2e2'4 1a2''2 2e1'4 3a1'1 3.68 3.70 3.80 f 2 2 4 4 2 3 2 A 4.15 (1) E1' ...2a1' 1e1'' 2e2' 1a2'' 2e1' 3a1' 4.17 4.05 4.28 2 2 4 3 2 4 2 B 5.11 (3) E2' ... 2a1' 1e1'' 2e2' 1a2'' 2e1' 3a1' 5.22 5.12 5.30 2 2 4 4 1 4 2 C 5.29 (3) A2” ...2a1' 1e1'' 2e2' 1a2'' 2e1' 3a1' 5.30 5.16 5.45 a Numbers in parentheses represent the uncertainty in the last digit. b – VDEs for Ru©B9 were calculated at ROPBE0/Ru/Stuttgart/B/aug-cc-pvTZ. c – VDEs for Ru©B were calculated at ROB3LYP/Ru/Stuttgart/B/aug-cc-pvTZ. 9 d – The first VDE for Ru©B9 was calculated at ROCCSD(T)/Ru/Stuttgart/B/aug-cc-pvTZ. e Measured ADE = 3.83 ± 0.02 eV. Calculated ADE at ROCCSD(T)/Ru/Stuttgart/B/aug-cc-pvTZ//PBE0/Ru /Stuttgart/B/aug-cc- pvTZ with ZPE correction = 3.75 eV. f −1 Observed vibrational frequencies: 550 ± 50, 1240 ± 1240 ± 50, and 1560 ± 50 cm . Table 6.4 Observed VDEs for FeB9– compared with theoretical values. The calculated values are from the Fe©B9− (D9h, 1A1') cluster. All energies are in eV. Observed VDE (theoretical) VDE (exp)a Final State and Electronic Configuration features UBP86b ROPBE0c 2 2 4 4 4 1 X 3.42(3) A1’ … 1a2'' 1e1'' 2e2' 2e1' 3a1' 3.58d 3.40 2 2 4 4 3 2 E1’ … 1a2'' 1e1” 2e2' 2e1' 3a1' 4.05 (0.77) 4.19 A 4.22(3) 2 2 4 3 4 2 E2’ … 1a2'' 1e1” 2e2' 2e1' 3a1' 4.42d 4.10 2 2 3 4 4 2 B 5.03(4) E1” … 1a2'' 1e1” 2e2' 2e1' 3a1' 5.08 (0.80) 4.69 2 1 4 4 4 2 C 5.23(4) A2” … 1a2'' 1e1'' 2e2' 2e1' 3a1' 5.26d 5.26 a Numbers in parentheses represent the uncertainty in the last digit. b 2 VDEs were calculated at UBP86/aug-cc-pVTZ. The values of are given in parentheses following the computed VDE values. c VDEs were calculated at ROPBE0/aug-cc-pVTZ//UBP86/aug-cc-pVTZ. d 2 In these cases high spin contamination of the final neutral states was encountered (with higher than 0.8). Therefore the VDEs were calculated at ROBP86/aug-cc-pVTZ. 6.3.4 Discussion We present the CMOs of Ru©B9− in Figure 6.8 and Fe©B9− in Figure 6.9. Both of the two clusters are indeed 1) π aromatic with six delocalized π electrons (HOMO−2, HOMO−4, HOMO−4′ for Ru©B9−; HOMO−3, HOMO−3′, and HOMO−4 for Fe©B9− satisfying the 167 4N + 2 rule for π-aromaticity; 2) σ aromatic with six delocalized σ electrons (HOMO−1, HOMO−1′, and HOMO−5 for both clusters) satisfying the 4N + 2 rule for σ aromaticity. In both cases, the HOMO is a completely non-bonding lone pair of 4 /3 -type centered on the Ru/Fe atom, whereas the HOMO−3 and HOMO−3′ (Ru©B9−) and HOMO−2 and HOMO−2′ (Fe©B9−) can be viewed as mainly composed of metal d lone pairs with some minor contributions to electron density from the peripheral boron atoms. The remaining nine valence CMOs are responsible for the bonding of the peripheral boron atoms with each other. The AdNDP analyses of Ru©B9− are shown in Figure 6.10, which is almost identical to that of the FeB9− reported before.302 The AdNDP analyses showed that both clusters doubly aromatic (σ + π) and that Ru/Fe acts as valence 2 element. The six 4d/3d electrons are localized as lone pairs ( , , ), however, there is some bonding interaction between the peripheral boron ring and the and electrons (ON < 2.00|e|). Even though this system is valence isoelectronic to Ru©B9− we note that there are differences between their MO patterns (Figure 6.8b and Figure 6.9b). In the case of Ru©B9− the HOMO (3a′) is essentially the 4 atomic orbital of Ru and does not contribute to bonding (ON = 2.00|e|). Removal of a single electron from the 4 HOMO does not lead to a large geometry change and causes only a slight out-of-plane displacement of the Ru atom. In the Fe©B9−, electron removal from the non-bonding 3a1′ HOMO results in a D9h-Fe©B9 neutral ground state, which is at least a minimum on the potential energy surface of FeB9. The difference in neutral geometry suggests that the Ru atom was found to be slightly too large to fit inside a neutral B9 ring and was pushed outside the ring and formed a highly symmetric C9v symmetry structure. 168 Figure 6.10 AdNDP analyses for Ru©B9−. 6.4 Case Studies of M©B9 Molecular Wheels: Rh©B9 and Ir©B9 According to the design principle, n + x + k = 12, the central atom should contribute 3 valence electrons to delocalized bonding for a neutral D9h-M©B9 cluster. In this section, the first two neutral molecular wheels will be discussed, which are the photodetachment products of their anionic counterparts. 6.4.1 Experimental Results RhB9−: The PES spectra of RhB9− are shown in Figure 6.11 at the three photodetachment laser energies. The 355 nm spectrum (Figure 6.11b, inset) of RhB9− displays a nicely resolved short vibrational progression with an average spacing of 380 ± 50 cm–1. The 0-0 transition defines the ADE or the EA of neutral RhB9 at 2.86 ± 0.03 eV. The short vibrational progression suggests that there is a very small geometry change between the anionic and neutral ground state. The 266 nm spectrum (Figure 6.11b) reveals four more features A, B, C, and D with VDEs of 4.07 ± 0.03 eV, 4.18 ± 0.03 eV, 4.33 ± 0.04 eV, and 4.39 ± 0.04 eV, respectively, following a large energy gap (1.21 eV) from band X. 169 Both features A and B are very sharp, and feature B is vibrationally resolved with a spacing of 350 ± 50 cm–1. Two relatively weak features E (VDE: 4.54 eV) and F (VDE: 4.80 eV) are observed in the 193 nm spectrum (Figure 6.11a), followed by nearly continuous spectral features starting at band G at a VDE of 5.13 ± 0.04 eV. No other definitive bands can be labeled in the high binding energy side due to the spectral congestion. IrB9−: The IrB9− shows similar spectral pattern as RhB9−, as shown in Figure 6.11. The 355 nm spectrum of IrB9− (Figure 6.11d, inset) exhibits a sharp peak with discernible vibrational structures. The 0-0 peak defines an ADE of 2.59 ± 0.03 eV, which is also the EA of the neutral IrB9 cluster. Following a large energy gap (1.59 eV), a sharp and intense band A with a VDE of 4.18 ± 0.03 eV is observed in the 266 nm spectrum (Figure 6.11d). Two more sharp features, B and C, are also observed in the 266 nm spectrum with VDEs of 4.27 ± 0.03 eV and 4.48 ± 0.03 eV, respectively. At 193 nm (Figure 6.11c), more transitions are observed. Features D and E are observed at 4.60 ± 0.04 eV and 4.65 ± 0.04 eV, respectively. The weak feature F at 4.79 eV is similar to the corresponding feature in the 193 nm spectrum of RhB9−. Again, following an energy gap, a strong band G is observed at 5.31 ± 0.04 eV, beyond which the signal-to-noise ratios are poor, but there appear to be continuous signals similar to the spectrum of RhB9−. There is a weak feature at 3.5 eV in the 193 nm spectrum of IrB9− in the band gap region. This feature is most likely due to autodetachment,303,304 because of its photon energy dependence. The large X–A gaps in the PES spectra of RhB9− and IrB9− suggest that their corresponding neutrals must be closed shell with large HOMO−LUMO gaps, and they should be electronically stable and chemically inert. The simplicity of the spectra and the sharpness 170 of the various electronic bands indicate high-symmetry cluster species and minimum geometry changes during photodetachment transitions. Figure 6.11 Photoelectron spectra of RhB9− and IrB9− at 355, 266, and 193 nm. The vertical lines in the 355 and 266 nm spectra of RhB9− indicate vibrational structures. 6.4.2 Theoretical Results The global minimum structures of the RhB9− and IrB9− are shown in Figure 6.12, along with their optimized neutral structures. Our geometry optimizations showed that the perfectly symmetric D9h structures are minima on the potential energy surfaces of the neutral species. Both clusters have almost the same B-B bond length and M-B bond length regardless of the different central atoms. On the other hand, the presence of an unpaired 171 electron in the anion’s doubly degenerate HOMO (the LUMO for neutral species) lowers the symmetry to C2v due to the Jahn–Teller effect. Figure 6.12 Optimized geometries of (a) Rh©B9−, (b) Ir©B9−, (c) Rh©B9, (d) Ir©B9 and valence CMOs of (e) Rh©B9 and (f) Ir©B9. The calculations are performed at PBE0/M/Stuttgart’97/B/aug-cc- pVTZ (M = Rh, Ir) level. Bond lengths are given in Å. 6.4.3 Comparison between Experimental and Theoretical Results We calculated the ab initio VDEs using four different methods to confirm that the C2v structures are the global minima for RhB9– and IrB9–. PBE0/M/Stuttgart’97/B/aug-cc-pVTZ and B3LYP/M/Stuttgart’97/B/aug-cc-pVTZ (M = Rh, Ir) were used at their respective optimized geometries. VDEs were calculated also with the ROHF-UCCSD(T) /M/Stuttgart’97/B/6-311+G(2d) and EOM-CCSD(T)305-309/M/Stuttgart’97/B/6-311+G(2d)310 methods at the PBE0/M/Stuttgart’97/B/aug-cc-pVTZ optimized geometries. On the basis of the literature and our previous work with transition-metal-doped boron clusters,114,308 we believe that this basis set combination provides a reasonable balance between accuracy and 172 computational efficiency for these approaches. EOM neutral excitation energies were used to offset the ΔCCSD(T) VDE for the lowest singlet state. The frozen core approximation was utilized in all CCSD(T) and EOM-CCSD(T) calculations. Because of the open-shell nature of the Rh©B9− and Ir©B9− anions, the detachment transitions are quite complicated, in qualitative agreement with the congested spectral features at the higher binding energy range. The computed VDEs are compared with the experimental data in Table 6.5. For Rh©B9−, the first and second VDEs at CCSD(T) level are 2.87 and 4.22 eV, in good agreement with features X and A observed in the experimental spectra at 2.86 and 4.07 eV, respectively. The next two calculated VDEs correspond to the transition to the 3A2 and 3B1 final states with electrons detached from HOMO−2 (6b2) and HOMO−3 (8a1). We were not able to calculate these detachment channels at CCSD(T), but the VDEs calculated at the UPBE0 and UB3LYP are in good agreement with the experimental data (features B and C). The next three detachment channels correspond to singlet final states resultant of detachment from the fully occupied HOMO−1, HOMO−2, and HOMO−3 orbitals. These detachments correspond to the observed features D, E, and F. We were not able to calculate these values at UPBE0 and UB3LYP levels, but the VDEs calculated using EOM-CCSD(T), 4.40, 4.55, and 4.60 eV, are in reasonable agreement with the experimental data. The next major detachment channel is from HOMO−4 (2b1), resulting in the 3A1 final state. Electron detachment from HOMO−4 gives a VDE of 5.04 and 4.94 eV at UPBE0 and UB3LYP, respectively, compared to 5.13 eV in the experimental spectrum. As seen from Table 6.5, the congested spectral features beyond the F band are consistent with the high density of detachment channels beyond HOMO−4. For IrB9–, the observed spectral features and assignments are very similar to those of RhB9–, as can be seen in Table 6.5. In 173 some cases, the spectra of IrB9– are better resolved, for example, the C band. Overall, for both species, the computational results are in excellent agreement with the experimental data, lending considerable credence to the molecular wheel structures for Rh©B9− and Ir©B9−. 6.4.4 Discussion The ground state of M©B9– (M= Rh, Ir) is 2B1 with C2v symmetry due to the Jahn– Teller effect. The neutral ground state of M©B9 is 1A1 with perfect D9h symmetry. The observed vibrational mode in the ground state transition should correspond to the distortion from the D9h symmetry to the C2v symmetry. The observed frequency of 380 cm–1 for Rh©B9 is in excellent agreement with the calculated frequency for this mode, 386 cm–1. The neutral Rh©B9 and Ir©B9 clusters are valence isoelectronic to Ru©B9– and Fe©B9–, and they exhibit similar bonding patterns and strength (Figure 6.8 and Figure 6.9). Valence CMOs of Rh©B9 and Ir©B9 are presented in e and f of Figure 6.12. Similar to Ru©B9–, we can understand the chemical bonding as follows. HOMO−2 (1a2″) and HOMO−4 (1e1″) of Rh©B9 as HOMO−2 (1a2″) and HOMO−5 (1e1″) of Ir©B9 are responsible for delocalized π-bonding (rendering π-aromaticity in the systems); HOMO (2e1′) and HOMO−6 (2a1′) of both clusters are responsible for delocalized σ-bonding (rendering their σ-aromaticity). HOMO−1 (3a1′) and HOMO−3 (2e2′) of both clusters are formed mainly by d electron lone-pairs of the central atoms and the remaining nine valence MOs are responsible for the B-B bonding in the circumference. Thus, both clusters are doubly aromatic, and the central metal has a formal valence of 3. 174 Table 6.5 Observed VDEs for and IrB9− compared with the calculated values for the lowest energy isomer in each case. All energies are in eV. VDE VDE (theoretical) a Final State and Electronic Configuration b Feature (exp) UPBE0 UB3LYPc CCSD(T)d Rh©B9− 1 X 2.86(3) A1 …6a12 1a22 1b12 5b22 7a12 2b12 8a12 6b22 9a12 3b10 2.88 2.78 2.87 (2.69)e 3 A 4.07(3) B1 …6a12 1a22 1b12 5b22 7a12 2b12 8a12 6b22 9a11 3b11 4.06 3.97 4.22 (4.40) 3 B 4.18(3) A2 …6a12 1a22 1b12 5b22 7a12 2b12 8a12 6b21 9a12 3b11 4.17 4.08 f 3 C 4.33(4) B1 …6a12 1a22 1b12 5b22 7a12 2b12 8a11 6b22 9a12 3b11 4.16 4.16 f 1 D 4.39(4) B1 …6a12 1a22 1b12 5b22 7a12 2b12 8a12 6b22 9a11 3b11 f f (4.40) 1 E 4.54(4) A2 …6a12 1a22 1b12 5b22 7a12 2b12 8a12 6b21 9a12 3b11 f f (4.55) 1 F 4.80(4) B1 …6a12 1a22 1b12 5b22 7a12 2b12 8a11 6b22 9a12 3b11 f f (4.60) 3 G 5.13(4) A1 …6a12 1a22 1b12 5b22 7a12 2b11 8a12 6b22 9a12 3b11 5.04 4.94 (5.33) 3 B1 …6a12 1a22 1b12 5b22 7a11 2b12 8a12 6b22 9a12 3b11 f 5.40 f 5.2 3 A2 …6a12 1a22 1b12 5b21 7a12 2b12 8a12 6b22 9a12 3b11 5.51 5.43 f ~ 3 A1 …6a12 1a22 1b11 5b22 7a12 2b12 8a12 6b22 9a12 3b11 5.57 5.54 (5.66) >6 3 B2 …6a12 1a21 1b12 5b22 7a12 2b12 8a12 6b22 9a12 3b11 6.12 f (6.14) Ir©B9− 1 X 2.59(3) A1 …6a12 1a22 1b12 5b22 7a12 2b12 8a12 6b22 9a12 3b10 2.56 2.48 2.50 (2.29)e 3 A 4.18(3) B1 …6a12 1a22 1b12 5b22 7a12 2b12 8a12 6b22 9a11 3b11 4.20 4.40 4.40 (4.56) 3 B 4.27(3) A2 …6a12 1a22 1b12 5b22 7a12 2b12 8a12 6b21 9a12 3b11 4.31 4.21 f 3 C 4.48(3) B1 …6a12 1a22 1b12 5b22 7a12 2b12 8a11 6b22 9a12 3b11 4.41 4.43 f 1 D 4.60(4) B1 …6a12 1a22 1b12 5b22 7a12 2b12 8a12 6b22 9a11 3b11 f f (4.60) 1 E 4.65(4) A2 …6a12 1a22 1b12 5b22 7a12 2b12 8a12 6b21 9a12 3b11 f f (4.63) 1 F 4.79(4) B1 …6a12 1a22 1b12 5b22 7a12 2b12 8a11 6b22 9a12 3b11 f f (4.67) 3 G 5.31(4) A1 …6a12 1a22 1b12 5b22 7a12 2b11 8a12 6b22 9a12 3b11 5.20 5.09 (5.46) 3 B1 …6a12 1a22 1b12 5b22 7a11 2b12 8a12 6b22 9a12 3b11 f f f 5.5 3 A2 …6a12 1a22 1b12 5b21 7a12 2b12 8a12 6b22 9a12 3b11 5.65 5.55 (5.61) ~ 3 A1 …6a12 1a22 1b11 5b22 7a12 2b12 8a12 6b22 9a12 3b11 5.91 5.85 (5.99) >6 3 B2 …6a12 1a21 1b12 5b22 7a12 2b12 8a12 6b22 9a12 3b11 f f (6.32) a Numbers in parentheses represent the uncertainty in the last digit b VDEs were calculated at PBE0/M/Stuttgart’97/B/aug-cc-pVTZ, M=Rh, Ir c VDEs were calculated at B3LYP/M/Stuttgart’97/B/aug-cc-pVTZ, M=Rh, Ir d VDEs were calculated at ROHF-UCCSD(T)/M/Stuttgart’97/B/6-311+G(2d)//PBE0/M/Stuttgart‘97/B/aug-cc-pVTZ, M=Rh, Ir e VDEs in parenthesis were calculated at EOM-CCSD(T)/M/Stuttgart’97/B/6-311+G(2d)//PBE0/M/Stuttgart’97/B/aug-cc-pVTZ, M=Rh, Ir f VDE could not be calculated at this level of theory 175 6.5 Case Studies of M©B92− Molecular Wheels: V©B92−, NbB92−, TaB92− The design principle says for double charge nine-member wheel clusters, the central atoms should contribute one electron to the delocalized bonds. In the following section, we will show the results of a perfect D9h-V©B92− and two C9v-NbB92−, TaB92− cluster. Their singly charged anion counterparts are produced in the molecular beam and chartered with C2v symmetry due to Jahn-Teller distortion. 6.5.1 Experimental Results The photoelectron spectra of VB9−, NbB9−, and TaB9− are presented in Figure 6.13, respectively, at two photodetachment energies. All the measured VDEs are given in Table 6.6, where they are compared with theoretical calculations at various levels of theory. VB9−: The 266 nm photoelectron spectrum of VB9− (Figure 6.13b) displays intense and congested features around 4 eV and a weak feature at lower binding energies (labeled as X′). The congested main spectral region consists of at least five relatively sharp bands, labeled as X, A, B, C, and D. The C and D bands are very closely spaced. The ADE of the ground state detachment transition is 3.64 eV, obtained by drawing a straight line along the leading edge of band X and taking the intersection with the binding energy axis plus the spectral resolution. The ADE also represents the EA of neutral VB9. The VDE of band X measured from the peak maximum is 3.70 eV. The 193 nm spectrum (Figure 6.13a) seems to exhibit continuous and relatively weak signals throughout the higher binding energy region. Only one prominent band F with a VDE of 5.03 eV can be identified in this range, whereas congested features appear to be present around 4.5 eV (E). The signal-to-noise ratios are too poor beyond the F band to allow identifications of definitive spectral bands. The X′ feature at the low binding energy range is 176 probably due to a low-lying isomer. The weak signals throughout the low binding energy range (<3.5 eV) are probably all due to the same weakly populated low-lying isomer. NbB9−: The photoelectron spectra of NbB9− (Figure 6.13c,d) are somewhat similar to those of VB9−. In the 266 nm spectrum (Figure 6.13d), a weak feature (X′) at the low binding energy side, probably due to a low-lying isomer, is followed by a series of intense and congested features at higher binding energies around 4 eV. An intense and relatively sharp band X defines the transition from the ground state of NbB9− to that of neutral NbB9. The ADE of band X, measured from its leading edge, is 3.58 eV, which represents the EA of NbB9. The VDE of band X is measured to be 3.64 eV. Beyond band X, the spectral features become more congested and slightly weaker in intensity. Four bands (A, B, C, and D) are assigned. In the 193 nm spectrum (Figure 6.13c), only one additional broad band is observed at 4.88 eV (E), which is somewhat similar to band F of VB9−. TaB9−: The spectra of TaB9− (Figure 6.13e, f) are almost identical to those of NbB9−, except the spectral features are slightly better separated and resolved. In addition, the weak low binding energies features, attributed to a low-lying isomer, are almost negligible in the spectra of TaB9−. The 266 nm spectrum of TaB9− displays three intense bands (X, A, and B) and a weaker, broader band C. The ADE of band X, measured to be 3.57 eV, defines the EA of neutral TaB9, which is identical to that of NbB9 within our uncertainty. The 193 nm spectrum (Figure 6.13e) reveals two more bands, a relatively weak band D, and a broad band E, both of which are similar to those observed in the 193 nm spectrum of NbB9−. 177 Figure 6.13 Photoelectron spectra of VB9− at (a) 193 nm and (b) 266 nm, NbB9− at (c) 193 nm and (d) 266 nm, and Ta B9− at (e) 193 nm and (f) 266 nm. 6.5.2 Theoretical Results Our global minimum search and geometry optimization show that the wheel-like structures are the global minima for all the MB9− clusters considered here, as presented in Figure 6.14. The boron rings in all clusters are slightly distorted from a perfect circle, 178 because of the Jahn-Teller effect.311,312 VB9− has a planar C2v structure; while NbB9− and TaB9− both have non-planar Cs structures with the Nb and Ta atoms located approximately 0.7 Å out of the averaged boron plane. Energies from single-point CCSD(T) calculations are given for selected low-lying isomers, assuring that the M©B9− molecular wheel structures are the global minimum in each case. Figure 6.14 Global minimum structures of VB9−, NbB9−, and TaB9−. Bond lengths are given in Å at the (RO)PBE0/V,Nb,Ta/Stuttgart/B/aug-cc-pVTZ level. Geometry optimization of the neutral M©B9 (M = V, Nb, Ta) clusters in the D9h symmetry leads to an imaginary frequency corresponding to out-of-plane distortions of the central metal atom in each case. Following the imaginary mode, C9v structures were obtained (Figure 6.15, upper row) for all three clusters with an open-shell triplet ground electronic state. Consequently, we considered the closed-shell doubly charged M©B92− clusters (Figure 6.15, lower row). The V©B92− cluster was found to be a perfect D9h planar cluster, whereas NbB92− and TaB92− were found to have C9v symmetry with the central metal atom slightly out-of-plane. 179 Figure 6.15 Optimized structures of neutral VB9, NbB9, and TaB9 and the doubly charged VB92−, NbB92−, and TaB92− clusters. Bond lengths are given in Å at the PBE0/V,Nb,Ta/Stuttgart/ B/ aug-cc- pVTZ level. 6.5.3 Discussion and Interpretation of the Photoelectron Spectra Because of the open-shell nature of the anion and neutral ground states, both singlet and triplet final states can be accessed during photodetachment, consistent with the complicated photoelectron spectra observed experimentally. In particular, the open-shell anions and neutrals make it challenging to compute the detachment channels. Thus, we calculated the VDEs for the global minimum structures of M©B9− using three different methods: PBE0, CCSD(T), and EOM-CCSD. The theoretical results are compared with the 180 experimental data in Table 6.6. We found that the three methods give consistent results and together they allow almost quantitative interpretation of the experimental data. The X′ feature and possible presence of low-lying isomers: According to the relative energies calculated at the CCSD(T) level of theory, the global minima of these clusters are significantly more stable compared to the nearest low-lying isomers.115 Despite the relatively high energies of the “boat”-like isomers found at the CCSD(T) level, we find that their calculated VDEs are in agreement with the experimental values for the peaks labeled as X′ in the spectra of VB9− and NbB9−, suggesting that the boat-like isomers were weakly populated in the cluster beams. The fact that the boat-like isomers were present in all of the current cases suggests that the stability of the boat-like isomers relative to the global minima was probably underestimated. Nevertheless, the trend is consistent with the experimental observation: the energy of the boat-like isomer relative to the molecular wheel global minimum increases from VB9− to TaB9−, and experimentally, the relative intensities of the weak low binding energy features due to the boat-like isomer decrease in the same direction (Figure 6.13). We focus our discussion on the global minimum molecular-wheel structures (Figure 6.14), which are responsible for the main spectral features observed experimentally. The photoelectron spectral data are compared with the calculated VDEs in Table 6.6, where the final states and MO configurations for the final states are also given. The MOs and bonding in the closed-shell M©B92− (M = V, Nb, Ta) dianions: Given the similarity of the electronic and the geometrical structures of these clusters, we will discuss in more detail the assignments of the photoelectron spectra of VB9−. The geometry of VB9− can be best understood by considering one electron removal from the closed-shell 181 V©B92− cluster. The valence MOs of the D9h V©B92− cluster are plotted in Figure 6.16 and they can be understood as follows: the degenerate HOMO (2e2′) and HOMO−1 (2e1′), plus HOMO−4 (2a1′), are delocalized σ bonding orbitals between the central V atom and the B9 ring; the degenerate HOMO−2 (1e1″) and HOMO−3 (1a2″) are delocalized π bonding orbitals between the V atom and the B9 ring; and remaining nine valence orbitals are responsible for the nine 2c-2e peripheral B-B bonds. Thus, V©B92−is doubly aromatic, with 10 σ (Nσ = 2) and 6 π (Nπ = 1) electrons and the formal valence of V in V©B92− is 5. For the closed-shell Nb©B92− and Ta©B92− clusters, we found that the size of the central metal atom is too big to fit inside a B9 ring and these clusters have quasi-planar structures and a C9v symmetry (Figure 6.16, bottom), even though they obey the modified electronic design principle and display bonding features almost identical to the non- distorted D9h structure. The MOs of Nb©B92− and Ta©B92− (not shown) are similar to those of V©B92−. Interpretation of the photoelectron spectra of M©B9− (M = V, Nb, Ta): Removal of one electron from the degenerate 2e2′ HOMO of the D9h V©B92− results in the low symmetry C2v V©B9−, owing to the Jahn-Teller effect. The MOs of the C2v V©B9− are shown in Figure 6.17a and they bear close resemblance to those of V©B92−, except that its 6b2 HOMO is now singly occupied to give the 2B2 ground electronic state (Figure 6.16). The other component of the degenerate 2e2′ orbital becomes the 7a1 (HOMO−3) orbital in V©B9− (Figure 6.17a). Similarly, removal of an electron from the doubly degenerate HOMO orbitals of Nb©B92− and Ta©B92− results in slightly distorted pyramidal structures with Cs symmetry for Nb©B9− and Ta©B9− (Figure 6.17), due to the Jahn-Teller effect. The MOs of Nb©B9− and Ta©B9− are given in Figure 6.17b and Figure 6.17c, respectively, and 182 their similarities to those of V©B9− ((Figure 6.17a) are evident. In the case of Nb©B9−, the degenerate HOMOs in the closed-shell dianion transform into 10a′ (HOMO) and 6a″ (HOMO−3) (Figure 6.17b), whereas in Ta©B9− they transform into 10a′ (HOMO) and 7a″(HOMO−1) (Figure 6.17c). These MOs together with the calculated VDEs in Table 6.6 are used to interpret the photoelectron spectra. The calculated neutral states all have C9v symmetry and triplet spin state (3A2, Figure 6.15), with their doubly degenerate σ HOMOs half-occupied. The lack of a HOMO−LUMO gap in the photoelectron spectra (Figure 6.13) is consistent with the triplet configuration of the neutral clusters for all three cases. Therefore, the first detachment channel from M©B9− should be from electron removal from the fully occupied σ delocalized orbital that corresponds to one of the 2e2′ orbitals in V©B92− (Figure 6.16), i.e., the 7a1 orbital in V©B9−, the 6a″ orbital in Nb©B9−, and the 7a″ orbital in Ta©B9−. The calculated first VDE in each case is in very good agreement with the experimental data, except for the case of Nb©B9−, where the calculated VDE from the 9a′ orbital is the same as the first VDE (Table 6.6). In reality, the top four CMOs in all M©B9− anions (Figure 6.17b) lie very close in energy and they give rise to seven detachment channels in a narrow energy range, accounting for the congested spectral features from about 3.6 eV to 4.8 eV in the photoelectron spectra (Figure 6.13). Overall, the calculated spectral features are in good agreement with the observed features in these congested spectral regions, as shown in Table 6.6. Remarkably, the feature around 5 eV (band F in Figure 6.13a and band E in Figure 6.13c, e) is very similar in all three cases. As shown in Table 6.6, this feature is from detachment from the same orbitals in all three cases, i.e., the 2b1 and 1a2 orbitals in V©B9− (Figure 6.17a) and 8a′ and 5a″ for Nb©B9− (Figure 6.13b) and Ta©B9− (Figure 6.13c), which correspond to the degenerate 183 delocalized π orbitals (1e1″ in Figure 6.17). The splitting of these MOs in the M©B9− anions seems to be very small, giving rise to the same calculated VDEs, consistent with the experimental band around 5 eV in each case. The excellent agreement and consistency between theory and experiment for this feature in all three anions provide an anchoring point for the validity of the spectral assignment. Overall, the agreement between the calculated VDEs and the experimental data, as shown in Table 6.6, is almost quantitative, confirming unequivocally the obtained global minima for all three clusters. Figure 6.16 Valence CMO plots of V©B92− (D9h, 1A1'). The calculations were performed at the PBE0/V/Stuttgart/B/aug-cc-pVTZ level. 184 Figure 6.17 Valence CMO plots of (a) V©B9−, (b) Nb©B9− and (c) Ta©B9−. The calculations were performed at ROPBE0/M/Stuttgart/B/aug-cc-pVTZ level of theory. The HOMO−7 to HOMO−14 of Nb©B9− and Ta©B9− are the same as those of the V©B9−’s and thus are not shown. 185 Table 6.6 Observed VDEs of VB9−, NbB9− and TaB9− compared with the calculated values for the lowest energy isomer in each case. All energies are in eV. Observed VDE VDE (theoretical) a Final State and Electronic Configuration b bands (exp) PBE0 CCSD(T)c EOM-CCSDd VB9− (C2v, 2B2) 3 B2 … 1b121a222b127a115b228a126b21 e X 3.70 (3) 3.72 3.79 3 B2 … 1b121a222b127a125b228a116b21 e A 3.79 (3) 3.87 3.98 3 A1 … 1b121a222b127a125b218a126b21 e B 3.93 (3) 3.86 3.98 1 C 4.03 (3) A1 … 1b121a222b127a125b228a126b20 4.17 4.09 4.04 1 2 2 2 2 2 1 1 D 4.10 (3) B2 … 1b1 1a2 2b1 7a1 5b2 8a1 6b2 4.14 1 2 2 2 1 2 2 1 B2 … 1b1 1a2 2b1 7a1 5b2 8a1 6b2 4.57 E ~4.6 1 2 2 2 2 1 2 1 A1 … 1b1 1a2 2b1 7a1 5b2 8a1 6b2 4.57 3 2 2 1 2 2 2 1 e A2 … 1b1 1a2 2b1 7a1 5b2 8a1 6b2 4.92 5.14 F 4.94 (4) 3 B1 … 1b121a212b127a125b228a126b21 e 4.92 1 A2 … 1b121a222b117a125b228a126b21 5.22 1 2 1 2 2 2 2 1 B1 … 1b1 1a2 2b1 7a1 5b2 8a1 6b2 5.22 1 1 2 2 2 2 2 1 A2 … 1b1 1a2 2b1 7a1 5b 8a 6b2 5.45 − 2 NbB9 (Cs, A‘) 3 A'' … 7a' 5a''28a'26a''29a'27a''110a'1 2 3.65 3.73 3.67 X 3.64 (3) 3 2 2 2 2 1 2 1 A' … 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 3.64 3.78 3.67 3 2 2 2 1 2 2 1 A 3.84 (3) A'' … 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 3.77 3.78 3.74 1 2 2 2 2 2 2 0 B 3.93 (3) A' ... 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 4.06 3.97 3.98 1 2 2 2 1 2 2 1 C 4.12 (4) A' ... 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 4.08 1 2 2 2 2 2 1 1 A'' ... 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 4.38 D ~4.4 1 2 2 2 2 1 2 1 A' ... 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 4.38 3 2 2 1 2 2 2 1 A' … 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 4.94 5.06 5.01 E 4.88 (5) 3 2 1 2 2 2 2 1 A'' … 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 4.94 5.01 3 1 2 2 2 2 2 1 A' … 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 5.26 1 2 1 2 2 2 2 1 A'' ... 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 5.32 1 2 2 1 2 2 2 1 A' ... 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 5.32 1 1 2 2 2 2 2 1 A' ... 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 5.40 − 2 TaB9 (Cs, A') 3 A'' … 7a' 5a''28a'26a''29a'27a''110a'1 2 X 3.64 (3) 3.72 3.71 3.70 3 2 2 2 2 1 2 1 A' … 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 3.70 3.85 3.75 A 3.89 (4) 3 2 2 2 1 2 2 1 A'' … 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 3.70 3.85 3.75 1 2 2 2 2 2 2 0 B 4.03 (3) A' ... 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 4.04 3.89 3.90 1 2 2 2 2 2 1 1 C 4.36 (5) A'' ... 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 4.01 1 2 2 2 2 1 2 1 A' ... 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 4.54 D 4.68 (5) 1 2 2 2 1 2 2 1 A'' ... 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 4.54 186 3 A' … 7a'25a''28a'16a''29a'27a''210a'1 f 5.08 5.06 E 5.07 (5) 3 2 1 2 2 2 2 1 f A'' … 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 5.08 5.06 1 2 2 1 2 2 2 1 A' … 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 5.32 1 2 1 2 2 2 2 1 A'' ... 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 5.32 3 1 2 2 2 2 2 1 A' … 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 5.26 5.38 5.50 1 1 2 2 2 2 2 1 A' ... 7a' 5a'' 8a' 6a'' 9a' 7a'' 10a' 5.61 a Numbers in parentheses represent the uncertainty in the last digit. The ADEs of the X band or the electron affinities of the neutral VB9, NbB9, and TaB9 clusters are measured to be 3.64 ± 0.04 eV, 3.58 ± 0.04 eV, and 3.57 ± 0.04 eV, respectively. b VDEs were calculated at ROPBE0/V, Nb, Ta /Stuttgart/B/aug-cc-pVTZ//(RO)PBE0/V, Nb, Ta/Stuttgart/ B/aug-cc-pVTZ. c VDEs were calculated at ROCCSD(T)/V, Nb, Ta/Stuttgart/B/aug-cc-pVTZ//(RO)PBE0/V, Nb, Ta/ Stuttgart/B/aug-cc-pVTZ. d VDEs were calculated at EOM-CCSD/V, Nb, Ta/Stuttgart/B/6-311+G(d)// (RO)PBE0/V, Nb, Ta/ Stuttgart/B/aug-cc-pVTZ. e - EOM-CCSD values for triplet states of VB9 are not presented because of high spin contamination observed in the calculations. f VDEs could not be calculated at this level of theory. 6.6 Observation of the Highest Coordination Number in Planar Species: Nb©B10− and Ta©B10− Coordination number is one of the most fundamental characteristics of molecular structures. Molecules with high coordination numbers often violate the octet and the 18 electron rules and push the boundary of our understanding of chemical bonding and structures. We have been searching for the highest possible coordination number in a planar species with equal distances between the central atom and all peripheral atoms. In the previous sections, a series of octa-, nona- coordinated molecular wheels have been discussed. The quest for higher coordination numbers was limited primarily to theoretical calculations.287,300,301 The highest coordination number considered computationally was ten for a broad range of metal atoms. Though some of the proposed species satisfy our electronic design principle, none was known to be the global minimum. Among these species, only AuB10− has been experimentally observed,295 but its global minimum was shown to be an Au atom interacting with a B10− cluster on the outside: the wheel-type structure is a high-energy isomer, around 45 kcal mol−1 above the ground state. 295 The instability of the 187 Au©B10− wheel isomer is caused by the fact that only the 6s valence electron participates in the delocalized bonding in this species while the 5d orbitals of the central Au atom are completely filled and have little interaction with the peripheral B10 ring. The finding of the nonacoordinated Ru©B9− complex shows that the interactions of the 4d orbitals with the B9 ring play an important role in stabilizing the wheel structure. Early 4d and 5d transition metals have larger atomic sizes and more diffused d orbitals, conducive to participation in bonding with the peripheral boron rings. Thus, our search for higher coordination metal- doped boron clusters has been focused on the early 4d or 5d transition metals. Here we show that Nb and Ta fit into the B10 decagonal ring and the resulting singly charged wheel-type anions Nb©B10− and Ta©B10− are closed-shell and doubly aromatic systems. Furthermore, all five valence electrons of Nb and Ta participate in the delocalized bonding, providing considerable stability to the wheel structures, which were found to be the lowest energy isomers by unbiased global minimum searches. The theoretical results are in excellent agreement with the experimental photoelectron data, confirming the first decacoordinated 2D chemical species. 6.6.1 Experimental Results The photoelectron spectra of TaB10− and NbB10− at two different photon energies are shown in Figure 6.18. The spectrum of TaB10− at 193 nm (Figure 6.18a) shows a fairly simple spectral pattern with three strong peaks (X, A, B) between 3.9 – 4.7 eV and two weak bands (C, D) between 5.2–5.6 eV. At 266 nm (Figure 6.18b), an additional peak was resolved between the X and A band. This peak is due to a vibrational feature of the X band, yielding a vibrational spacing of (1050 ± 50) cm−1. The first ADE and the VDE for TaB10−, both defined by the 0-0 transition of the X band, are (4.04 ± 0.03) eV, which also represents the 188 EA of neutral Ta©B10. The spectra of NbB10− (Figure 6.18c and d) are very similar to those of TaB10− except for the weak low binding energy features labeled as X′, A′, B′, and C′. This observation suggests the presence of a higher energy isomer in the beam of NbB10−, whereas the main isomer of NbB10− should be similar to that of TaB10−. The X, A, B features in the NbB10− spectra are more congested and fine features are also resolved at 266 nm (Figure 6.18d), yielding a vibrational frequency for the ground state of NbB10 as (600 ± 50) cm−1. The vibrationally resolved X band yields an accurate ADE for NbB10− as (4.10 ± 0.03) eV, very close to that for TaB10−. The observed VDEs for all spectral features for TaB10− and NbB10− are given in Table 6.7, where they are compared with the computational data. Figure 6.18 Photoelectron spectra of TaB10− at (a) TaB10− 193 nm, (b) 266 nm, NbB10− at (c) TaB10− 193 nm, (d) 266 nm. 189 6.6.2 Theoretical Results and Comparison with Experimental Results According to the highest level of theory we used, the wheel-type structures (D10h- M©B10−) are the global minima for both anions (Figure 6.19). The second lowest isomers of both species possess 3D ‘boat’-like structures involving the metal atom interacting with the B10 cluster from above (C2v). In the TaB10−, the C2v boat isomer is 8.6 kcal/mol above the wheel structure and in the NB10− the boat is only 5.4 kcal/mol above the wheel structure. To verify the wheel-type structures we computed VDEs for the two lowest isomers of each species. Theoretical VDEs calculated for the M©B10− structures at two non-relativistic levels of theory predict two detachment channels in the 4.0 – 4.5 eV binding energy range (Table 6.7), though there are more peaks in the experimental spectra in this region. As shown in Figure 6.20a, both the HOMO (e2g) and HOMO−1 (e1u) of the M©B10− clusters are doubly degenerate involving interactions between the d orbitals and the B10 ring. Thus, spin–orbit coupling is expected to yield two photoelectron bands from electron detachment from each orbital, thereby resulting in four detachment bands in this energy region. Hence, the three observed peaks could result from the overlap of the four expected spin-orbit split peaks. Indeed, spin–orbit calculations for Ta©B10− revealed a splitting of around 0.2 eV in these peaks, in excellent agreement with the experiment. The calculated VDEs from HOMO−2 and HOMO−3 are also in excellent agreement with the observed bands C and D. We also calculated the vibrational frequencies for the neutral Ta©B10 species, the symmetry of which is reduced by the Jahn–Teller effect. The frequency for one of the totally symmetric mode [ω4(ag)=1050 cm−1] is in excellent agreement with the observed vibrational frequency for the X band. On the other hand, the predicted VDEs for the higher energy C2v isomer of TaB10− totally disagree with the experimental spectra. Overall, the theoretical results for 190 the D10h Ta©B10− structure are in excellent agreement with the experimental data, confirming unequivocally that the molecular wheel is the global minimum for TaB10−. The VDEs calculated for the D10h structure of Nb©B10− can explain the high energy features (Table 6.7, X, A–D), which are similar to those of the features in the Ta©B10− spectra. The smaller spin– orbit effects expected in Nb©B10− result in the more congested spectral features in the 4.0– 5.4 eV energy range (Figure 6.18c and d). The additional features (X′, A′, B′, C′) observed for NbB10− are in excellent agreement with the calculated VDEs for the C2v isomer. The lower intensities of these features suggest that the C2v isomer is energetically less stable than the wheel-type structure, again confirming that the global minimum of NbB10− is also the D10h molecular wheel. 191 Figure 6.19 Structures of the two lowest energy isomers of a) TaB10− and b) NbB10−. The their point group symmetries, spectroscopic states, and ZPE corrected relative energies are given at RCCSD(T)/Ta, Nb/Stuttgart/B/aug-cc-pVTZ//PBE0/Ta, Nb/Stuttgart/B/aug-cc-pVTZ level of theory. 192 Table 6.7 Observed VDEs for TaB10− and NbB10− compared with theoretical values. The calculated values are based on the two lowest isomers of TaB10− and NbB10−. All energies are in eV. Features VDE (theoretical) VDE (exp)a Final State and Electronic Configuration PBE0b ROCCSD(T)c TaB10− (D10h, A1g) 1 Xd 2 4.04(3) E2g …2a1g2 1b2u2 1a2u2 1e1g4 2e1u4 2e2g3 4.13 4.16 A 4.29(3) 2 e E1u …2a1g2 1b2u2 1a2u2 1e1g4 2e1u3 2e2g4 4.37 4.46 B 4.55(5) 2 C 5.36(5) E1g …2a1g2 1b2u2 1a2u2 1e1g3 2e1u4 2e2g4 5.37 5.47 2 A2u …2a1g2 1b2u 1a2u1 2 1e1g4 2e1u 2e2g4 4 D 5.51(5) 5.49 5.61 − 1 TaB10 (C2v, A1) 2 A1 … 5a1 4b22 4b12 3a22 6a12 7a11 2 2.52 2.64 2 2 2 2 2 1 2 f A1 … 5a1 4b2 4b1 3a2 6a1 7a1 2.70 2 A2 … 5a12 4b22 4b12 3a21 6a12 7a12 3.34 3.42 2 2 2 1 2 2 2 B1 … 5a1 4b2 4b1 3a2 6a1 7a1 4.37 4.43 2 2 1 2 2 2 2 B2 … 5a1 4b2 4b1 3a2 6a1 7a1 5.00 5.06 − 1 NbB10 (D10h, A1g) g 2 E2g … 1b2u 2a1g2 1a2u2 1e1g4 2e1u4 2e2g3 2 X 4.12(3) 4.16 4.21 A 4.26(3) 2 e E1u … 1b2u2 2a1g2 1a2u2 1e1g4 2e1u3 2e2g4 4.29 4.36 B 4.34(5) 2 C 5.28(5) E1g … 1b2u2 2a1g2 1a2u2 1e1g3 2e1u4 2e2g4 5.32 5.44 2 1b2u 2a1g2 2 1a2u 1e1g4 1 2e1u 2e2g4 4 D 5.41(5) A2u … 5.42 5.50 − 1 NbB10 (C2v, A1) 2 A1 … 5a1 4b22 4b12 3a22 6a12 7a11 2 X' 2.65(4) 2.48 2.57 2 2 2 2 2 1 2 A' 2.89(4) A1 … 5a1 4b2 4b1 3a2 6a1 7a1 2.69 2.84 2 2 2 2 1 2 2 A2 … 5a1 4b2 4b1 3a2 6a1 7a1 3.23 3.30 B' 3.4(1) 2 2 2 1 2 2 2 B1 … 5a1 4b2 4b1 3a2 6a1 7a1 4.33 4.37 2 2 1 2 2 2 2 C' 4.91(5) B2 … 5a1 4b2 4b1 3a2 6a1 7a1 4.95 4.99 a Numbers in parentheses represent the uncertainty in the last digit. b VDEs were calculated at ROPBE0/Ta,Nb/Stuttgart/B/aug-cc-pvTZ. c VDEs were calculated at ROCCSD(T)/Ta,Nb/Stuttgart/B/aug-cc-pvTZ//PBE0/Ta,Nb/Stuttgart/B/aug-cc-pvTZ. d Measured ADE = 4.04(3) eV. Calculated ADE at ROCCSD(T)/Ta/Stuttgart/B/aug-cc-pvTZ//PBE0/Ta/Stuttgart/B/aug-cc-pvTZ with ZPE correction: 4.05 eV. e 2 The peak is assigned to the transition to the second spin-orbit component of the E1u electronic state. f We were not able to calculate this VDE at this level of theory. g Measured ADE = 4.10(3) eV. Calculated ADE at ROCCSD(T)/Nb/Stuttgart/B/aug-cc-pvTZ//PBE0/Nb/Stuttgart/B/aug-cc-pvTZ with ZPE correction: 4.03 eV. 193 Figure 6.20 (a) CMOs and (b) chemical bonding pattern of Ta©B10−. 194 6.6.3 Discussion According to the design principle that we proposed recently for stable M©Bnk−-type molecular wheels, the valence of the central metal atom should be one for a B10 ring. However, both Ta and Nb are known to have five valence electrons. To understand the bonding in the M©B10−molecular wheels, we present results of the AdNDP analyses for Ta©B10− in Figure 6.20b. The advantage of the AdNDP analyses is the ability to recover simultaneously both localized and delocalized bonding in chemical species. The AdNDP analyses revealed ten 2c-2e peripheral σ bonds, five delocalized σ bonds (satisfying the 4N+2 rule for aromaticity with N = 2), and three delocalized π bonds (satisfying the 4N+2 rule for aromaticity with N = 1). A similar bonding pattern was found for Nb©B10−. Thus, both clusters are doubly σ and π aromatic and satisfy the construction model. However, in contrast to the previous discussed molecular wheels, there are 10 delocalized σ electrons for the current M©B10− molecular wheels owing to the strong bonding between the 4d/5d orbitals of Nb/Ta with the peripheral B10 ring. Therefore, in these cases, the electronic design principle needs to be revised as x = 16 – n − k to account for the 10 delocalized σ electrons. This result suggests that more delocalized bonding electrons are required; either in the σ or π framework, to build ever highly coordinated planar molecular wheels. The two delocalized σ bonds involving the Ta 5d orbitals can be alternatively shown by the AdNDP analyses with low threshold values as and lone pairs on the Ta atom with low occupation number of 1.11 |e| (compared to the ideal value of 2.00 |e|) and therefore the estimated contribution of the Ta 5d atomic orbitals to the delocalized bonding is 55 %. On the contrary, the molecular wheel structure of the above-mentioned Au©B10− anion 195 is not the global minimum because the Au 5d AOs remain atom-like and do not participate in delocalized bonding. The availability of d AOs in Nb and Ta for participation in the σ- delocalized bonding with the peripheral ring leads to substantial stabilization of the decagonal doubly aromatic structures of Nb©B10− and Ta©B10− and makes them the global minimum structures. Thus, it is conceivable that other early 4d or 5d elements will be able to form not only decagonal M©B10k−-type species, but also species with even higher coordination numbers. 6.7 Geometrical Requirements for Transition‐Metal‐Centered Aromatic Boron Wheels: the Case of VB10− In the photoelectron spectrum of NbB10−, minor contributions from a low- lying C2v “boat”-like structure was observed, suggesting it is energetically close to the global minimum D10h-Nb©B10− molecular wheel, whereas for TaB10−, the Ta©B10− molecular wheel is overwhelmingly favored. The change in the relative stability of the low-lying isomers of TaB10− and NbB10− prompted us to further investigate the effects of the atomic size of the transition metal on the stability of the molecular wheels using the valence isoelectronic substitution of Ta and Nb by V. The VB10− cluster fulfills the electronic design principle to form a doubly aromatic V©B10− molecular wheel. Indeed, a previous theoretical report showed that V©B10− was a minimum on the potential energy surface of VB10−.300 In the present study, we show that V©B10− is a local minimum, which is significantly higher in energy above the global minimum “boat”-like three-dimensional structure. The “boat”-like structure was identified as the second low-lying isomer for NbB10− and TaB10− (Figure 6.19). We find that the molecular wheel D10h-M©B10− becomes less favored going up the periodic table from Ta to V, as a result of decreasing atomic size. The current experimental 196 and computational results demonstrate that the V atom is too small to stabilize the 10- membered boron ring. 6.7.1 Experimental Results The PES spectra of VB10− are shown in Figure 6.18 at three photon energies. The measured VDEs are summarized in Table 6.8, where they are compared with theoretical calculations. The 355 nm spectrum (Figure 6.18a) of VB10− displays three detachment bands: X, A, and B. Band X has a VDE of 2.47 eV without any fine features resolved. The ADE or the EA of the neutral VB10 is measured to be 2.24 ± 0.08 eV. Band A has a VDE of 2.91 eV, closely followed by band B with a VDE of 3.27 eV. All these features are broad even at 355 nm, indicating that there is either more than one detachment transition in each band or a large geometry change between the anionic and neutral cluster. The 266 nm spectrum (Figure 6.18b) contains one sharp feature (“*”) at a VDE of 3.77 eV and a broad band C at a VDE of 4.16 eV. Closely following band C, a shoulder labeled with “**” was observed at a VDE of 4.4 eV. Two additional bands are observed in the 193 nm spectrum (Figure 6.18c), a broad band D at a VDE of 4.96 eV and band E at a VDE of 5.62 eV. Due to the low signal-to-noise ratios, no other detachment bands can be definitively identified in the higher binding energy side. The features labeled with * and ** are relatively weak and, as will be shown below, they do not belong to the global minimum, which gives rise to the main bands labeled with the letters. 197 Figure 6.21 Photoelectron spectra of VB10– at (a) 355 nm, (b) 266 nm, and (c) 193 nm. 198 6.7.2 Theoretical Results and Comparison with Experimental Results Figure 6.22 presents all the calculated isomers of VB10− within 20 kcal mol−1 of the global minimum at the BP86 and PBEPBE levels of theory. The singlet boat-like structure, isomer I, is found to be the global minimum of VB10− according to the BP86 functional. Isomer II, a C2v triplet boat-like structure, is only 0.45 kcal mol−1 higher than isomer I. The PBEPBE functional suggests the opposite ordering, with isomer II being slightly more stable than isomer I by 0.50 kcal mol−1. Thus, these two isomers can be viewed as degenerate within the accuracy of the theoretical methods and are both expected to contribute to the observed photoelectron spectra. The next higher-lying isomer is 7 kcal mol−1 higher than the global minimum at the BP86 level and 15 kcal mol−1 higher at the PBEPBE level, which is unlikely to be present in the supersonic cluster beam. The anticipated V©B10− wheel structure is found to be a much higher energy isomer, more than 13 kcal mol−1 higher in energy than the global minimum at the BP86 level and 27 kcal mol−1 at the PBEPBE level. The calculated VDEs of both isomers I and II at BP86 and PBEPBE levels of theory are compared with the experimental VDEs in Table 6.8. Isomer I (C2, 1A): Isomer I has a closed-shell electronic configuration (1A, C2) and only doublet final states are expected upon one electron detachment. The first electronic band corresponds to electron detachment from the HOMO (10a, Table 6.8) of the ground state of the anion to produce the neutral 2A ground state. The calculated first VDE, 2.37 eV at the BP86 level and 2.28 eV at the PBEPBE level, is in good agreement with the experimental value of 2.47 eV. Optimization of the corresponding neutral cluster gives a structure with C2v symmetry (Figure 6.23c). The energy difference between the optimized neutral and anion yielded a calculated ADE value of ~2.2 eV at different levels of theory, in good agreement with the experimental ADE of 2.24 eV. 199 The large difference between the ADE and VDE is a result of the geometry change between the anion and neutral ground states, consistent with the broad ground state PES band (X) (Figure 6.21). The second and third detachment channels correspond to electron removal from the HOMO−1 (9a) and HOMO−2 (8a), respectively. The VDEs calculated for these two detachment channels are 2.90 and 3.24 eV at the BP86 level, in excellent agreement with features A (2.91 eV) and B (3.27 eV). Electron detachment from HOMO−3 (8b) results in a calculated VDE of 4.06 eV, agreeing well with band C at 4.16 eV. The next two detachment channels were calculated to have very close VDEs at 4.74 and 4.80 eV (BP86), comparing well to the broad band D at 4.96 eV. The VDEs of the next three detachment channels are calculated also to be close, at 5.24, 5.33, and 5.41 eV (BP86), consistent with band E or possible features not definitively identified beyond band E in the higher binding energy region (Figure 6.21). The calculated VDEs at the BP86 level are fitted with Gaussians to produce a simulated spectrum, as shown in Figure 6.24a, displaying pictorially the good agreement with the experimental spectrum (Figure 6.24c). This good agreement lends considerable credence that the closed-shell C2 boat-like 3D structure I is the global minimum of VB10−. Isomer II (C2v, 3A2): Isomer II has an open-shell electronic configuration (3A2, C2v) and both doublet and quartet neutral states are expected to be produced upon one electron detachment. The first VDE is calculated to be 2.27 eV (BP86) and 2.19 eV (PBEPBE), which are lower than the first VDE of isomer I and are not in good agreement with the experiment. However, this isomer may contribute to the lower binding energy tail in the PES spectra (Figure 6.21). Geometry optimization of the doublet neutral ground state led to the structure as that derived from isomer I. There is little structure change between isomer II (Figure 200 6.23b) and its corresponding neutral state (Figure 6.23c). Thus, relatively sharp detachment transitions are expected from isomer II. The sharp peak labeled as “*” does not correspond to any detachment channel from isomer I and may come from isomer II. Our calculation shows that detachment from HOMO−4 produces a 4B2 final state with a VDE of 4.15 eV (BP86), which is the closest to the “*” feature. Detachment from the same orbital also produces a low-spin 2B2 state with a VDE of 4.29 eV, which may account for the feature labeled as “**” at 4.4 eV (Figure 6.21). The calculated VDEs for isomer II are fitted with Gaussians to produce a simulated spectrum, as shown in Figure 6.24b. Clearly, most of the features from isomer II would be buried in the more dominating spectral features of isomer I and we cannot rule out minor contributions of this isomer to the observed PES spectra. The weak features “*” and “**” are likely evidence of the presence of isomer II. These observations suggest that the BP86 energies are in better agreement with the experiment, i.e., the closed- shell C2 boat structure should be the global minimum of VB10− and the triplet C2v structure is a low-lying isomer. 201 Figure 6.22 The low-lying structures of VB10–. Their electronic states, point group symmetries, and relative energies at BP86 and PBEPBE DFT/B/6-311+G(d)/V/Stuttgart’97 levels of theory. All relative energies, given in kcal/mol, have been corrected for ZPEs. The relative ordering, electronic states, and geometries are based on the BP86 calculations. Figure 6.23 Comparison of the VB10– structures of (a) the global minimum isomer I (1A C2) and (b) the low-lying isomer II (3A2, C2v) with that of their optimized neutral (2A1, C2v) (c). Selected V-B distances are given in Å. Only distances below 2.24 Å are shown. All structures are from the BP86/6- 311+G(d)/V/Stuttgart’97 level of theory. 202 Figure 6.24 Simulated spectra of VB10– based on (a) isomer I and (b) isomer II, compared with (c) experimental spectrum at 193 nm. The calculations are performed at the BP86/B/6- 311+G(2df)/V/Stuttgart’97 level of theory. The simulated spectra were generated by fitting the calculated VDEs given in Table 6.8 with Gaussian functions of 0.08 eV half width. 203 Table 6.8 Observed VDEs of VB10– and comparion with theoretical values. The calculated values are based on the global minium isomer I (C2, 1A) and isomer II of VB10– (C2v, 3A2). VDE (theo.) Observed VDE Final State Electronic Configuration BP8 PBEPB Feature (exp.)a 6 E 1 Isomer I (C2, A) b 2 X 2.47 (5) A …5b26a26b27a27b28b28a29a210a1 2.37 2.28 2 2 2 2 2 2 2 2 1 2 A 2.91 (4) A …5b 6a 6b 7a 7b 8b 8a 9a 10a 2.90 2.80 2 2 2 2 2 2 2 1 2 2 B 3.27 (5) A …5b 6a 6b 7a 7b 8b 8a 9a 10a 3.24 3.15 2 2 2 2 2 2 1 2 2 2 C 4.16 (3) B …5b 6a 6b 7a 7b 8b 8a 9a 10a 4.06 3.94 2 2 2 2 2 1 2 2 2 2 B …5b 6a 6b 7a 7b 8b 8a 9a 10a 4.74 4.64 D 4.96 (6) 2 2 2 2 1 2 2 2 2 2 A …5b 6a 6b 7a 7b 8b 8a 9a 10a 4.80 4.70 2 2 2 1 2 2 2 2 2 2 B …5b 6a 6b 7a 7b 8b 8a 9a 10a 5.24 5.14 2 2 1 2 2 2 2 2 2 2 E 5.62 (6) A …5b 6a 6b 7a 7b 8b 8a 9a 10a 5.33 5.21 2 1 2 2 2 2 2 2 2 2 B …5b 6a 6b 7a 7b 8b 8a 9a 10a 5.41 5.33 3 Isomer II (C2v, A2) 2 A2 … 2b1 3b123b222a225a124b224b126a123a227a114a20 2 2.27 2.19 2 2 2 2 2 2 2 2 2 2 0 1 A1 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 2.80 2.71 4 2 2 2 2 2 2 2 2 1 1 1 A2 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 2.93 2.75 2 2 2 2 2 2 2 2 2 1 1 1 A2 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 3.02 2.95 4 2 2 2 2 2 2 2 2 2 1 1 A1 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 3.08 2.91 2 2 2 2 2 2 2 2 1 2 1 1 A1 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 3.22 3.14 4 2 2 2 2 2 2 1 2 2 1 1 * 3.77 (3) B1 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 4.15 3.97 2 2 2 2 2 2 2 1 2 2 1 1 ** ~ 4.4 B1 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 4.29 4.23 4 2 2 2 2 2 1 2 2 2 1 1 B2 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 4.81 4.65 2 2 2 2 2 2 1 2 2 2 1 1 B2 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 4.91 4.76 2 2 2 2 2 1 2 2 2 2 1 1 A1 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 4.94 4.76 4 2 2 2 2 1 2 2 2 2 1 1 A1 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 5.05 4.9 2 2 2 2 1 2 2 2 2 2 1 1 A2 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 5.18 4.98 4 2 2 2 1 2 2 2 2 2 1 1 A2 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 5.29 5.09 2 2 2 1 2 2 2 2 2 2 1 1 B2 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 5.33 5.34 4 2 2 1 2 2 2 2 2 2 1 1 B2 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 5.36 5.15 4 2 1 2 2 2 2 2 2 2 1 1 B1 … 2b1 3b1 3b2 2a2 5a1 4b2 4b1 6a1 3a2 7a1 4a2 5.48 5.17 a The numbers in the parentheses represents the uncertainty in the last digit. b The ADE of the ground state transition is measured to be 2.24 ± 0.08 eV. 204 6.7.3 Discussion The global minimum of VB10− (1A, C2) can be viewed as a V atom coordinated by a B10 unit. The B10 moiety has the same atomic connectivity of the quasi-planar bare B10− cluster,133 but is bent and distorted due to the interaction with the V atom. Figure 6.23 compares the structures of isomers I and II with that of the neutral. In the global minimum isomer I, the V atom is bonded with six boron atoms with V-B distances less than 2.2 Å, whereas isomer II only features four such V-B bonds. The stronger interaction between V and the B10 moiety in isomer I is the origin of its higher stability. The neutral VB10 cluster has nearly identical structures as isomer II with very slight changes of the four V-B bond lengths. On the other hand, there are substantial structural changes between the global minimum isomer I and the neutral cluster, consistent with the broad PES transitions. 6.8 On the Way to the Highest Coordination Number in the Planar Metal‐ Centered Aromatic Ta©B10− Cluster: Evolution of the Structures of TaBn−(n = 3 – 8) 6.8.1 Introduction A series of molecular wheel structures have been characterized experimentally and theoretically in this chapter. It would be interesting to understand atom-by-atom how these remarkable structures are formed. Theoretical calculations on TiBn (n = 1–10) clusters showed that planar 2D fan- and wheel-type structures are more stable than three-dimensional pyramidal structures.313 However, the calculations were done at relatively low level of theory and whether these structures are true global minima on their potential energy surfaces was 205 not addressed. Furthermore, the viability of Ti-containing molecular wheels of any size has not been examined experimentally. An interesting question arises, concerning the structures of these precursors to the decacoordinated Ta©B10−: do the boron atoms nucleate around the Ta atom in fan-like structures on the way to the highest coordinate Ta or are there non-planar structures and structural transitions? In this section we provide an extensive and systematic experimental and theoretical studies on a series of Ta©Bn− (n = 3 – 8) clusters to examine how boron atoms nucleate around the Ta atom to form the highest coordination molecular wheel in Ta©B10−. We found that in the small Ta©Bn− (n = 3 – 5) clusters the B atoms form a fan structure around the Ta atom, as expected. However, the cluster structure takes a different turn at TaB6−, which has a B-centred hexagonal structure with Ta on the periphery, whereas TaB7− has a 3D structure. Only at TaB8− is a complete B8 ring formed with a pyramidal structure. From then on, the boron ring enlarges with each additional B atom until the perfect decagonal wheel-type structure is achieved at the Ta©B10− (D10h) cluster. 6.8.2 Experimental Results The photoelectron spectra of TaBn− (n = 3 – 8) at 193 and 266 nm are shown in Figure 6.25. For the smaller clusters, we have also obtained spectra at 355 nm (n = 3 – 7) and 532 nm (n = 3),118 which are not shown here. The VDEs for the observed PES bands are compared with the theoretical data in Table 6.9 and Table 6.10 for n = 3 – 8, respectively. TaBn− (n = 3 – 8): The small clusters TaBn− (n = 3 – 6) shows broad and congested spectral features and low electron affinities. The congested features suggest large density of states in near the HOMO. The weak tails (X') and features labeled as X" are observed in these small clusters, which are possibly due to the existence low-lying isomers. The larger 206 clusters TaBn− (n = 7 – 8) show relatively simple and well-resolved bands. Large HOMO−LUMO gap was observed for TaB7−, which imply a stable neutral TaB7. The TaB8− spectrum is similar to the spectra of CoB8− and FeB8−, suggesting the similarity of their structures. Overall, the binding energy increases from TaB3− to TaB5− and then drops at TaB6− and reaches a minimum at TaB7− before increasing again at TaB8−. This observation may suggest a structural change at TaB6− and TaB7−. The spectra of TaB8− exhibit some similarity to those of TaB9− and TaB10− with systematic increasing VDEs,115,117 suggesting that TaB8− may show structural similarities to the larger Ta©B9− and Ta©B10− molecular wheels. 207 Figure 6.25 Photoelectron spectra of TaBn− (n = 3–8) at 193 nm. 208 6.8.3 Theoretical Results The unbiased global minimum searches results for TaBn− (n = 3 – 8) are shown in Figure 6.26 and Figure 6.27 and the relative energies are calculated at CCSD(T) level of theory. TaBn− (n = 3 – 5): The TaBn− (n = 3 – 5) cluster have fan-type global minimum structures. The TaB3− global minimum is C2v (4B1) symmetric with three boron atoms nucleate around the Ta atom (Figure 6.28a). The isomers I.2 and I.3 can be viewed as Ta interacts with a bare B3 unit, which are only 0.2 and 1.6 kcal/mol higher than the global minimum. The Ta-B bond lengths are 2.08 Å and 2.32 Å in the C2v (4B1) minima (Figure 6.28b). The TaB4− cluster has a singlet global minimum structure (C2v, 1A1), the Ta-B bond lengths of which are similar to those in TaB3−. Its triplet isomer (II.2) has a slightly distorted molecular plane and is 2.7 kcal/mol above the global minimum. The global minimum of TaB5− is also a planar fan-like structure (III.1 in Figure 6.28c). The second lowest isomer (III.2 in Figure 6.28c) which is similar to isomer II.3 of TaB4− is only 1.4 kcal/mol higher in energy. Thus, TaB5− continues the fan-growth mode, which is now half way on to the Ta©B10− molecular wheel. However, some subtle structural trends can be seen from TaB3− to TaB5−: the B−B bond lengths seem to decrease, whereas the Ta−B bond lengths increase. This trend suggests that the interaction between Ta and individual B atoms decreases, while the boron ring motif is taking shape. TaB6−: The fan-growth mode is disrupted at TaB6−. Our global search showed that the most stable structure of TaB6− (IV.1 in Figure 6.28d) is planar with a hexagonal shape, but with a B atom in the center. We also found two boat-like 3D isomers (IV.2 and IV.3 in Figure 6.28d), which are competitive, lying within 3 kcal/mol of isomer IV.1. The expected 209 fan-shaped structure (IV.5)118 is only the fifth lowest isomer of TaB6−, being 9.8 kcal/mol above IV.1. It seems that the B−B interactions prevail over Ta-B bonding in TaB6−. TaB7−: We found that the global minimum of TaB7− is a very stable boat-like 3D structure (Figure 6.29a), which can be viewed as being formed from the IV.3 isomer of TaB6−. The fan-like structure (V.9)118 is now a much higher isomer by 20.2 kcal/mol above the global minimum. Interestingly, the second lowest isomer of TaB7− is heptagonal pyramidal structure (V.2)118, which is higher than the global minimum by 4.9 kcal/mol. This isomer can be viewed as Ta atom interacting with a B7 ring. Thus, starting from n = 7, a boron-ring based isomer becomes energetically favorable, even though the global minimum of TaB7− is 3D. TaB8−: According to our CK search, the global minimum of TaB8− is a pyramidal structure with a triplet spin state (Figure 6.29b), in which the Ta atom is interacting with a B8 ring. Ta atom is obviously too large to fit in the center of the B8 ring to form the planar octacoordinated Ta. Our calculations at the PBE0 level of theory showed that the global minimum VI.1 represents only a low-symmetry Cs structure. However, optimization with follow-up frequency calculations using the exchange-correlation potential PW91PW91 and the hybrid meta-exchange-correlation functional M06-2X confirmed the C8v structure VI.1 to be the global minimum. The distortion in the Cs structures relative to the C8v symmetry is small and our chemical bonding analyses yielded very similar results for either Cs or C8v symmetry. 210 Figure 6.26 The global minimum structures and low-lying isomers of (a) TaB3−, (b) TaB4−, (c) TaB5−, and (d) TaB6−. Also given are the point group symmetries, spectroscopic states, and relative energies at the CCSD(T)/Ta/Stuttgart/B/aug-cc-pVTZ level with ZPE corrections at the PBE0/Ta/Stuttgart/B/aug-cc-pVTZ level. Bond lengths for the global minimum structures are given in Å at the PBE0/Ta/Stuttgart/B/aug-cc-pVTZ level. Figure 6.27 The global minimum structures of (a) TaB7−, (b) TaB8−, (c) TaB9−, and (d) TaB10−. Bond lengths in Å at PBE0/Ta/Stuttgart/B/aug-cc-pVTZ level. Point group symmetries, and spectroscopic states are also shown. The structures of TaB9− and TaB10−, which were reported previously,39,40 are given for comparison. 211 Table 6.9 Experimental VDEs compared with calculated VDEs for the global minimum structure and low-lying isomers of TaB3−, TaB4− and TaB5−.All energies are in eV. VDE (theoretical) Featur VDE Final State and electronic configuration ROCCSD(T) e (exp)a ROPBE0b c TaB3−, I.1. C2v (4B1) 3 X 1.87(3) A2, 1a1(2)1b2(2)2a1(2)1b1(2)3a1(2)2b2(2)1a2(1)3b2(0)4a1(1) 1.93 1.82 3 (2) (2) (2) (2) (2) (2) (1) (1) (0) A 2.03(4) B1, 1a1 1b2 2a1 1b1 3a1 2b2 1a2 3b2 4a1 2.30 2.24 3 (2) (2) (2) (2) (2) (2) (0) (1) (1) B 2.22(3) B2, 1a1 1b2 2a1 1b1 3a1 2b2 1a2 3b2 4a1 2.38 2.24 5 (2) (2) (2) (2) (2) (1) (1) (1) (1) C 2.78(5) A2, 1a1 1b2 2a1 1b1 3a1 2b2 1a2 3b2 4a1 2.55 2.51 5 (2) (2) (2) (2) (1) (2) (1) (1) (1) D 3.04(5) B1, 1a1 1b2 2a1 1b1 3a1 2b2 1a2 3b2 4a1 2.71 3.00 5 (2) (2) (2) (1) (2) (2) (1) (1) (1) E 3.56(6) A1, 1a1 1b2 2a1 1b1 3a1 2b2 1a2 3b2 4a1 3.26 3.42 5 (2) (2) (1) (2) (2) (2) (1) (1) (1) F 3.95(6) B1, 1a1 1b2 2a1 1b1 3a1 2b2 1a2 3b2 4a1 4.07 4.06 5 (2) (1) (2) (2) (2) (2) (1) (1) (1) d G 4.67(8) A2, 1a1 1b2 2a1 1b1 3a1 2b2 1a2 3b2 4a1 4.64 − 1 TaB4 , II.1. C2v ( A1) 2 B2, …3a1 2b2(2)1b1(2)4a1(2)1a2(2)3b2(1) (2) X 2.78(3) 2.67 2.66 2 (2) (2) (2) (2) (1) (2) A 3.14(3) A2, …3a1 2b2 1b1 4a1 1a2 3b2 3.01 3.09 2 (2) (2) (2) (1) (2) (2) B 3.46(3) A1, …3a1 2b2 1b1 4a1 1a2 3b2 3.53 3.49 2 (2) (2) (1) (2) (2) (2) C 4.07(3) B1, …3a1 2b2 1b1 4a1 1a2 3b2 4.09 4.21 − 3 TaB4 , II.2. Cs ( A’’) 2 (2) (2) X’ ~ 2.5 A’’, …3a’ 4a’ 5a’ (2)2a’’(2)3a’’(2)4a’’(1)6a’(0) 2.53 2.50 4 (2) (2) (2) (2) (1) (1) (1) A’, …3a’ 4a’ 5a’ 2a’’ 3a’’ 4a’’ 6a’ 2.71 2.80 A’ 2.91(4) 2 (2) (2) (2) (2) (2) (0) (1) A’, …3a’ 4a’ 5a’ 2a’’ 3a’’ 4a’’ 6a’ 3.00 2.82 4 (2) (2) (2) (1) (2) (1) (1) d A’, …3a’ 4a’ 5a’ 2a’’ 3a’’ 4a’’ 6a’ 3.25 4 A’’, …3a’(2)4a’ (2)5a’ (1)2a’’(2)3a’’(2)4a’’(1)6a’(1) d 3.55 B’ 3.71(4) 4 A’’, …3a’(2)4a’ (1)5a’ (2)2a’’(2)3a’’(2)4a’’(1)6a’(1) 3.87 4.09 − 2 TaB5 , III.1. C2v ( A1) 3 B2, …2b2 3a1 1b1(2)4a1(2)3b2(1)1a2(2)4b2(2)5a1(1) (2) (2) d X 2.81(3) 2.81 3 (2) (2) (2) (2) (2) (2) (1) (1) d B2, …2b2 3a1 1b1 4a1 3b2 1a2 4b2 5a1 2.86 A 3.09(5) 1 (2) (2) (2) (2) (2) (2) (2) (0) A1, …2b2 3a1 1b1 4a1 3b2 1a2 4b2 5a1 2.84 2.89 3 (2) (2) (2) (2) (2) (1) (2) (1) d B 3.89(8) A2, …2b2 3a1 1b1 4a1 3b2 1a2 4b2 5a1 3.69 3 (2) (2) (2) (1) (2) (2) (2) (1) d C 4.09(8) A1, …2b2 3a1 1b1 4a1 3b2 1a2 4b2 5a1 4.12 3 (2) (2) (1) (2) (2) (2) (2) (1) d D 4.65(5) B1, …2b2 3a1 1b1 4a1 3b2 1a2 4b2 5a1 4.49 − 2 TaB5 , III.2. C1 ( A) 1 A, …3a 4a 5a 6a(2)7a(2)8a(2)9a(2)10a(2)11a(0) (2) (2) (2) X’ ~ 2.4 2.20 2.35 3 (2) (2) (2) (2) (2) (2) (2) (1) (1) d A, …3a 4a 5a 6a 7a 8a 9a 10a 11a 2.82 a Numbers in parentheses represent the uncertainty in the last digit. b VDEs were calculated at ROPBE0/Ta/Stuttgart/B/aug-cc-pVTZ//PBE0/Ta/Stuttgart/B/aug-cc-pVTZ. c VDEs were calculated at ROCCSD(T)/Ta/Stuttgart/B/aug-cc-pVTZ//PBE0/Ta/Stuttgart/B/aug-cc-pVTZ. d VDE could not be calculated at this level of theory. 212 Table 6.10 Experimental VDEs compared with calculated VDEs for the global minimum structure and low-lying isomers of TaB6−, TaB7− and TaB8−.All energies are in eV. VDE (theoretical) Feature VDE (exp)a Final State and electronic configuration ROPBE0b ROCCSD(T)c TaB6−, IV.1. C2v (3A2) 2 B1, ...1b1(2)3b2(2)5a1(2)4b2(2)1a2(2)2b1(1)5b2(0) d X 2.49(3) 2.43 2 (2) (2) (2) (2) (2) (0) (1) A 2.75(5) B2, ...1b1 3b2 5a1 4b2 1a2 2b1 5b2 2.86 2.81 4 (2) (2) (2) (2) (1) (1) (1) B 3.07(4) A1, ...1b1 3b2 5a1 4b2 1a2 2b1 5b2 2.80 2.99 4 (2) (2) (2) (1) (2) (1) (1) C 3.58(3) B1, ...1b1 3b2 5a1 4b2 1a2 2b1 5b2 3.55 3.56 4 (2) (2) (1) (2) (2) (1) (1) D 3.77(5) A2, ...1b1 3b2 5a1 4b2 1a2 2b1 5b2 3.71 3.76 4 (2) (1) (2) (2) (2) (1) (1) d E 4.36(5) B1, ...1b1 3b2 5a1 4b2 1a2 2b1 5b2 4.44 d d F 5.08(8) − 1 TaB6 , IV.2. C2v ( A1) 2 X’ ~ 2.3 B2, …2b2(2)4a1(2)1a2(2)2b1(2)5a1(2)6a1(2)3b2(1) 2.21 2.32 2 (2) (2) (2) (2) (2) (1) (2) A1, …2b2 4a1 1a2 2b1 5a1 6a1 3b2 2.62 2.73 2 (2) (2) (2) (2) (1) (2) (2) A1, …2b2 4a1 1a2 2b1 5a1 6a1 3b2 3.20 3.23 2 (2) (2) (2) (1) (2) (2) (2) B1, …2b2 4a1 1a2 2b1 5a1 6a1 3b2 4.66 4.68 2 (2) (2) (1) (2) (2) (2) (2) A2, …2b2 4a1 1a2 2b1 5a1 6a1 3b2 4.72 4.73 2 (2) (1) (2) (2) (2) (2) (2) A1, …2b2 4a1 1a2 2b1 5a1 6a1 3b2 4.83 4.85 − 1 TaB6 , IV.3. C2v ( A1) 2 B1, ...4a1 2b1(2)2b2(2)5a1(2)3b2(2)3b1(1) (2) X” 2.64(3) 2.50 2.56 2 (2) (2) (2) (2) (1) (2) A” 2.85(3) B2, ...4a1 2b1 2b2 5a1 3b2 3b1 2.86 2.84 2 (2) (2) (2) (1) (2) (2) B” 3.28(4) A1, ...4a1 2b1 2b2 5a1 3b2 3b1 3.13 3.28 2 (2) (2) (1) (2) (2) (2) B2, ...4a1 2b1 2b2 5a1 3b2 3b1 3.70 3.72 2 (2) (1) (2) (2) (2) (2) C” 4.00(5) B1, ...4a1 2b1 2b2 5a1 3b2 3b1 3.99 3.90 2 (1) (2) (2) (2) (2) (2) A1, ...4a1 2b1 2b2 5a1 3b2 3b1 4.90 4.86 − 2 TaB7 , V.1. Cs ( A’) 1 A’, …5a’ 6a’ 4a’’(2)5a’’(2)7a’(2)8a’(2)9a’(0) (2) (2) X 2.05(4) 2.09 2.18 3 (2) (2) (2) (2) (2) (1) (1) d A 3.43(8) A’, …5a’ 6a’ 4a’’ 5a’’ 7a’ 8a’ 9a’ 3.32 3 (2) (2) (2) (2) (1) (2) (1) d B 3.80(8) A’’, …5a’ 6a’ 4a’’ 7a’ 5a’’ 8a’ 9a’ 3.91 d d C 4.9(1) TaB8−, VI.1. Cs (3A’’) 4 A’, …6a’(2)7a’(2)8a’(2)4a’’(2)9a’(2)5a’’(1)6a’’(1)10a’(1) 3.17 3.32 X 3.35 (4) 4 (2) (2) (2) (2) (1) (2) (1) (1) A’’, …6a’ 7a’ 8a’ 4a’’ 9a’ 5a’’ 6a’’ 10a’ 3.17 3.32 2 (2) (2) (2) (2) (2) (2) (1) (0) A’’, …6a’ 7a’ 8a’ 4a’’ 9a’ 5a’’ 6a’’ 10a’ 3.52 3.42 A 3.52 (3) 2 (2) (2) (2) (2) (2) (2) (0) (1) A’, …6a’ 7a’ 8a’ 4a’’ 9a’ 5a’’ 6a’’ 10a’ 3.52 3.43 2 (2) (2) (2) (2) (2) (1) (2) (0)e B 3.98 (8) A’’, …6a’ 7a’ 8a’ 4a’’ 9a’ 5a’’ 6a’’ 10a’ 3.84 3.78 4 (2) (2) (1) (2) (2) (2) (1) (1) f C 4.42 (5) A’’, …6a’ 7a’ 8a’ 4a’’ 9a’ 5a’’ 6a’’ 10a’ 4.23 4.48f d d D 5.0 (1) 213 TaB8−, VI.2. C4v (1A1) 2 B2, …1b2(2)2e(4)2a1(2)1a2(2)3a1(2)3e(4)4e(4)2b2(1) 3.29 3.23 2 (2) (4) (2) (2) (2) (4) (3) (2) E, …1b2 2e 2a1 1a2 3a1 3e 4e 2b2 3.43 3.52 2 (2) (4) (2) (2) (2) (3) (4) (2) d E, …1b2 2e 2a1 1a2 3a1 3e 4e 2b2 4.41 2 A1, …1b2(2)2e(4)2a1(2)1a2(2)3a1(1)3e(4)4e(4)2b2(2) 5.02 5.06 2 (2) (4) (2) (1) (2) (4) (4) (2) A2, …1b2 2e 2a1 1a2 3a1 3e 4e 2b2 5.59 5.38 2 (2) (4) (1) (2) (2) (4) (4) (2) d A1, …1b2 2e 2a1 1a2 3a1 3e 4e 2b2 6.09 a Numbers in parentheses represent the uncertainty in the last digit. b VDEs were calculated at ROPBE0/Ta/Stuttgart/B/aug-cc-pVTZ//PBE0/Ta/Stuttgart/B/aug-cc-pVTZ. c VDEs were calculated at ROCCSD(T)/Ta/Stuttgart/B/aug-cc-pVTZ//PBE0/Ta/Stuttgart/B/aug-cc-pVTZ. d VDE could not be calculated at this level of theory. e Peak B can only be explained by the shake-up. f VDEs were calculated at UPBE0/Ta/Stuttgart/B/aug-cc-pVTZ and at UCCSD(T)/Ta/Stuttgart/B/aug-cc-pVTZ. The values of 〈 2 S 〉 are 3.79 (UPBE0) and 4.11 (UCCSD(T)). 6.8.4 Comparison between Experimental and Theoretical Results TaB3−: According to the relative energies calculated at the CCSD(T) level, isomer I.1 is the global minimum and should be responsible for the observed PES spectra of TaB3−. Isomers I.2 and I.3 are quite low-lying (Figure 6.26a) and may be present in the cluster beam and make contributions to the PES spectra. Isomer I.1 is open shell with a quartet ground state (4B1). The calculated VDEs for TaB3− are compared with the experimental data in Table 6.9. Three CMOs are singly occupied in isomers I.1, yielding triplet or quintet neutral final states upon electron detachment. The first VDE is calculated VDE at 1.82 eV (all the calculated values discussed in this section are at ROCCSD(T) level of theory), in excellent agreement with the experimental value of 1.87 ± 0.03 eV. All the other calculated VDEs agree well with the observed major PES bands. There is a small tail in front of peak X at ~1.6 – 1.7 eV, which might come from I.2 and I.3. The calculated first VDEs for I.2 and I.3 are 1.64 eV and 1.60 eV, respectively, at the CCSD(T) level of theory. The almost negligible signals in the low 214 binding energy tail in the experimental spectra suggest that the populations of isomers I.2 and I.3 are minor, if at all. Thus, their relative energies may be even higher than the CCSD(T) results indicate. TaB4−: The global minimum (II.1) of TaB4− is closed shell with a singlet ground state (Figure 6.26b). The triplet isomer II.2 is only 2.7 kcal/mol higher in energy and may be present in the cluster beam and contribute to the PES spectra. The calculated VDE from the 3b2 HOMO of II.1 is 2.66 eV (Table 6.9) is assigned to band X at 2.78 eV. The VDEs from HOMO−1, HOMO−2 and HOMO−3 are consistent with the observed bands A, B and C, respectively. The weak features X′, A′, and B′ cannot be explained by the global minimum and they may come from the low-lying isomer II.2. As shown in Table 6.9, the calculated VDEs are in agreement with features X' and A'. Thus, the observed PES spectra can be explained well by isomers II.1 and II.2. Isomer II.2 is a triplet state, which is metastable and cannot relax readily to the singlet ground state in the cluster beam, which is why it was populated even though its energy is relatively high (by 2.7 kcal/mol) above isomer II.1. TaB5−: The global minimum isomer III.1 of TaB5− (Figure 6.26c) is open shell with a doublet ground electronic state. The first detachment channel is from the fully occupied 3b2 MO producing a 3B2 final state (Table 6.9). The calculated first VDE of 2.81 eV is in perfect agreement with the experimental result. The detachment channels from the 4b2 and 5a1 orbitals yielded similar VDEs of 2.86 and 2.89 eV, which should correspond to the broad A band. Following an energy gap, the next three detachment channels yielded VDEs in good agreement with bands B, C, and D in the experiment. The isomer III.2 is only 1.4 kcal/mol above III.1 and is expected to be present in the experiment. Indeed, the calculated first VDE 215 from III.2 of 2.35 eV agrees well with the weak X′ band in the low binding energy side. Higher energy detachment channels are likely buried in the broad features of isomer III.1. TaB6−: The global minimum isomer IV.1 of TaB6− has a triplet ground state (Figure 6.26d), which can lead to both doublet and quartet final states in PES. The calculated first VDE of 2.43 eV from the 5b2 MO is in excellent agreement with band X at 2.49 eV (Table 6.10). The calculated VDEs for the next four detachment channels at the CCSD(T) level are in excellent agreement with the observed bands A, B, C, and D, respectively. However, higher energy channels corresponding to bands E and F were unfortunately unable to be calculated at CCSD(T). The VDE from PBE at 4.44 eV is in good agreement with band E. These assignments leave several weaker features unaccounted for in the experimental spectra, which must come from low-lying isomers. Our calculations suggested two 3D isomers (IV.2 and IV.3), which are within 3 kcal/mol of the global minimum (Figure 6.26d). They can be populated experimentally, even though their energies are relatively high. The calculate VDEs are in excellent agreement with feature X′ and may have contribution to band A and B". The calculated VDEs from isomer IV.3 are in excellent agreement with the remaining weak features (X″, A″, B″, C″), as shown in Table 6.10. The fourth detachment channel of IV.3 at 3.72 eV is likely buried in the intense C band. Overall, the complicated PES spectra of TaB6− are well explained by the global minimum and the two 3D low-lying isomers. TaB7−: The global minimum 3D structure of TaB7− is very stable (Figure 6.29a) and the nearest low-lying isomer is at least 4.9 kcal/mol higher in energy118, thus unlikely to be present in the experiment. Indeed, the PES spectra of TaB7− are relatively simple with no hint of major low-lying isomer contributions. The first detachment channel from the global minimum V.1 isomer of TaB7− is from the 9a′ singlet occupied MO, producing the neutral 216 singlet ground state. The calculated VDE of 2.18 eV is in good agreement with band X at 2.05 eV (Table 6.10). The second detachment channel is from the fully occupied 8a′ orbital with a calculated VDE of 3.32 eV, in excellent agreement with band A at 3.43 eV. The large X-A separation defines a large HOMO−LUMO gap (∼1.4 eV) for the neutral TaB7, suggesting it is a relatively stable cluster. The third detachment is from the 5a″ MO with a calculated VDE of 3.91 eV, in good agreement with the observed band B at 3.80 eV. Even though the VDEs for deeper MOs could not be calculated at these levels of theory, the good agreement between experiment and theory for the first three detachment channels provides strong support for the global minimum of TaB7−. TaB8−: The global minimum of TaB8− has a triplet electronic state (either C8v or Cs symmetry). The first and second detachment channels are from the fully occupied 5a″ and 9a′ MOs, producing two quartet final states. The calculated VDEs of 3.32 eV for these detachment channels are the same, in good agreement with band X at 3.35 eV (Table 6.10). Detachment from the two singly occupied 10a′ and 6a″ MOs, resulting in two doublet final states, also with very similar calculated VDEs, 3.42 and 3.43 eV, respectively, is in good agreement with band A at 3.52 eV. The fifth detachment channel is from the 8a′ MO, producing a quartet final state, with a calculated VDE of 4.48 eV in good agreement with the observed band C at 4.42 eV. The VDEs for higher binding energy MOs could not be calculated at the current level of theory. However, the above assignment still leaves the lower binding energy B band at 3.98 eV unaccounted for. This feature could be due to contributions from a low lying isomer. The second isomer TaB8− is a singlet state, 4.1 kcal/cal above the triplet global minimum.118 The first calculated VDE for isomer VI.2 is 3.23 eV (Table 6.10), which is consistent with the 217 very weak tail around 3.2 eV (Figure 6.25l). However, this tail is almost negligible, suggesting that contributions from isomer VI.2 is negligible. Furthermore, there is no detachment channel from isomer VI.2 that agrees with the observed band B. We found that a two-electron detachment channel produced a VDE of 3.78 eV, in good agreement with the observed VDE of band B at 3.98 eV (Table 6.10). Overall, the computational results and the experimental data are in good agreement, lending considerable credence to the global minima and the low-lying isomers obtained for all the TaBn− (n = 3 – 8) clusters. 6.8.5 Structural Evolution and Chemical Bonding in TaBn– To understand the structural evolution and how boron atoms nucleate around the central Ta atom to form the highest coordination Ta©B10− molecular wheel, we analyzed the chemical bonding in TaBn− (n = 3 – 8) using the AdNDP, as shown in Figure 6.28, Figure 6.29 and Figure 6.30. TaBn− (n = 3 – 5): Nucleation of B around Ta: The AdNDP analyses for the global minimum TaB3− (C2v, 4B1) cluster (Figure 6.28, I.1) revealed four 2c-2e peripheral σ bonds (two B-B bonds and two Ta-B bonds) with occupation numbers ranging from 1.95 |e| to 1.98 |e|, one delocalized 4c-2e σ bond and one delocalized 4c-2e π bond (ON = 2.00 |e|). Since TaB3− has three unpaired electrons, the AdNDP analyses also showed one delocalized 4c-1e σ bond (ON = 1.00 |e|), one delocalized 4c-1e π bond (ON = 1.00 |e|), and one 1c-1e 6s lone- pair on Ta (ON = 1.00 |e|). The single electron delocalized σ and π bonds both describe Ta 5d bonding with the two terminal B atoms, rendering partial multiple bond characters for the two Ta-B bonds. This bonding picture is consistent with the short terminal Ta-B bond lengths 218 (2.08 Å) and the relatively long bond length between Ta and the central B atom (2.32 Å). The latter is characterized by multicenter delocalized bonding only. The bonding in the global minimum TaB4− (C2v, 1A1) consists of five localized 2c-2e σ peripheral bonds (three B-B bonds and two Ta-B bonds), two delocalized 3c-2e σ and π bonds (Figure 6.28 , II.1). The two 3c-2e delocalized σ bonds describe bonding of Ta with two terminal B-B units, while the two delocalized π bonds mainly describe bonding between Ta and the terminal B atoms. Thus, the Ta-Bterminal bonds can be viewed as Ta=B double bonds, consistent with the very short Ta-B bond lengths (2.07 Å). From TaB3− to TaB4−, the bonding between Ta and the terminal B atoms is strengthened slightly. Again, the Ta bonding with the two middle B atoms is through multicenter delocalized bonding only. The chemical bonding picture in the TaB5− global minimum fan structure is similar to that in TaB4−. The AdNDP analyses recovered six localized 2c-2e peripheral σ bonds (four B-B bonds and two Ta-B bonds), two delocalized 4c-2e σ and π bonds, and one 6c-1e σ bond (ON = 1.00 |e|) (Figure 6.28, III.1). Thus, the bonds between Ta and the two terminal B atoms contain multiple bond characters, whereas the bonding between Ta and the middle three B atoms is entirely via multicenter delocalized bonding. TaB6− and TaB7−: Structural excursions: The Ta atom in the global minimum of TaB6− (C2v, 3B1) is part of a hexagonal ring with a central B atom. Our AdNDP analyses revealed six localized 2c-2e σ peripheral bonds for the hexagonal ring, three delocalized 7c- 2e σ bonds (ON = 2.00 |e|), two 7c-2e π bonds (ON = 2.00 |e|), one 1c-1e 5 d lone-pair (ON = 1.00 |e|), and one delocalized 7c-1e π bond (ON = 1.00 |e|) (Figure 6.29, IV.1). The three delocalized 7c-2e σ bonds make TaB6− σ aromatic. The structure and bonding in TaB6− are reminiscent of those in AlB6−, 30 which has a similar structure with Al being part of the 219 peripheral hexagonal ring and a central B atom. However, the Al atom is slightly out of plane due to π antiaromaticity because AlB6− only has four delocalized π electrons. Clearly, the additional delocalized π bond in TaB6− is sufficient for a perfect planar structure, even though it only has a single electron. Thus, TaB7− can be considered to be doubly aromatic. The AlB6− cluster was related to the pyramidal B7− cluster and the Al atom was considered as an isoelectronic substitute of a peripheral B atom. 30 The large size of the Al atom enlarges the hexagonal ring and planarizes the central B atom. However, because of the π antiaromaticity the Al atom is slightly bent out of plane in AlB6−. Thus, Ta can be considered as a better substitute of the peripheral B atom in the B7− cluster to yield the doubly aromatic and perfectly planar TaB6− cluster. This favorable bonding situation is why the fan structure of TaB6− is not competitive. The 3D global minimum structure of TaB7− has seven localized 2c-2e σ bonds (ON = 1.77-1.94 |e|), two delocalized 3c-2e σ bonds (ON = 1.85 |e|), one delocalized 8c-2e σ bond (ON = 1.99 |e|), three delocalized 8c-2e π bonds (ON = 2.00 |e|), and one completely delocalized 8c-1e σ bond (ON = 1.00 |e|) (Figure 6.29, V.1). The bonding pattern in this case is complicated and cannot be expressed in a simple manner. The term σ and π bonds are used loosely here. Clearly, the interactions between Ta and the boron atoms are optimized in the TaB7− global minimum structure. TaB8−: On the way to Ta©B10−: Our calculations at different levels of theory found the pyramidal structure VI.1 to be the global minimum for TaB8− (Figure 6.29b). As mentioned above, the structure VI.1 has Cs point group symmetry at PBE0 level of theory and C8v symmetry at the PW91PW91 and M06-2x levels of theory. However, regardless of Cs or C8v symmetry, our AdNDP analyses recovered similar chemical bonding patterns for 220 both structures (Figure 6.30), because the structural distortion in the Cs symmetry is very small. While the TaB8− cluster is not planar, the deviation from planarity is not that large in order to interpret its bonding approximately in terms of σ and π bonds. The AdNDP analyses showed eight localized 2c-2e σ bonds (ON = 1.88-1.93 |e|) for the B8 ring, three delocalized 9c-2e σ bonds (ON = 2.00 |e|), three delocalized 9c-2e π bonds (ON = 2.00 |e|), and two delocalized 9c-1e σ bonds (ON = 1.00 |e|) (Figure 6.30, VI.1). The delocalized bonds closely resemble the CMOs. Thus, TaB8− is π aromatic with 6 π electrons. Because the ground state of TaB8− is open shell, the eight totally delocalized σ electrons occupy five MOs, rendering it σ-aromatic. Thus, TaB8− is doubly aromatic. The bonding of the triply TaB8− is consistent with the design principle for metal-centred aromatic wheel-type clusters.113,114,120,294,298,299,314 Clearly the B8 ring is too small to fit the Ta atom, resulting in the pyramidal structure. We showed recently even the B9 ring is not large enough to host a Ta atom, resulting a slight pyramidal distortion in TaB9−.115 Only the B10 ring is large enough for the Ta atom, resulting in the perfectly planar Ta©B10− highest coordination borometallic molecular wheel. Thus, TaB8− is on the way to the Ta©B10− cluster by successive additions of two boron atoms. 221 Figure 6.28 Results of AdNDP analyses for the global minimum structures of TaB3− (I.1), TaB4− (II.1), and TaB5− (III.1). 222 Figure 6.29 Results of AdNDP analyses for the global minimum structures of TaB6− (IV.1) and TaB7− (V.1). 223 Figure 6.30 Results of AdNDP analyses for the C8v and Cs TaB8−. 6.8.6 Conclusions A comprehensive experimental and theoretical study is reported on the structures and bonding in a series of TaBn− (n = 3 – 8) clusters to elucidate the steps necessary to form the highest coordination Ta©B10− molecular wheel. Photoelectron spectroscopy is combined with extensive global minimum searches to locate the most stable structures and low-lying isomers for each cluster. TaB3−, TaB4−, and TaB5− are found to have fan-like global minimum structures, in which the Ta atom interacts with the terminal boron atoms strongly with multiple Ta-B bond characters, whereas Ta interacts with the middle boron atom(s) via delocalized bonding. Thus, these clusters can also be viewed as ring structures with Ta being 224 part of the ring. The fan growth mode is interrupted at TaB6−, which is found to have a planar hexagonal wheel-type structure with Ta being on the periphery of the wheel and a central B atom. The chemical bonding in the TaB6− cluster is found to be reminiscent of the AlB6− cluster and TaB6− can be viewed to be doubly aromatic. The TaB7− cluster is a three- dimensional boat-like global minimum structure, which seems to maximize Ta-B interactions. The global minimum of the TaB8− cluster is found to be an octagonal pyramidal structure with Ta being out of the cyclic octagonal ring by about 1.1 Å. The B8 ring is apparently too small to host a Ta atom, but the TaB8− cluster can be viewed as the precursor to the Ta©B10− molecular wheel. Addition of one B atom will form the pyramidal TaB9− cluster, in which the Ta atom is only slightly above the B9 ring. 115 And finally the B10 ring is perfect to host a Ta atom to form the doubly aromatic Ta©B10− molecular wheel.117 The current study shows that the competition between B−B interactions and Ta−B interactions determines the most stable structures of the TaBn− clusters. The structural evolution of the TaBn− clusters is not only important to understand the formation mechanisms for the highest known coordination number in planar species (Ta©B10−)315 but also provides insights into the interactions between early transition metals with boron. 6.9 Geometric Requirements Geometrical factors in determining the structures of M©B92− (M = V, Nb, Ta): The M©B92− dianions are all closed-shell species and obey the electronic design principle ( 16). However, only V©B92− is a perfect planar molecular wheel according to our calculations, whereas both Nb©B92− and Ta©B92− have C9v symmetry (Figure 6.15). The out-of-plane distortion is about 0.45 Å for both Nb©B92− and Ta©B92−. These species 225 provide another example of the interplay between electronic and geometrical factors in determining the structures of the M©Bnq− type molecular wheels. The covalent radii of V, Nb, and Ta are 1.53, 1.64, and 1.79 Å, respectively.316 Clearly, the V atom fits perfectly inside a B9 ring in V©B92−, but the B9 ring is too small to accommodate Ta and Nb, so that they are squeezed out of the ring center slightly to give the C9v Nb©B92− and Ta©B92−, as well as in the singly charged or neutral species of these clusters. Geometrical factors in determining the structures of M©B10− (M = V, Nb, Ta): The M©B10− clusters are all closed-shell species and obey the electronic design principle (x + q + n = 16). Both TaB10− and NbB10− have perfect D10h wheel structures as the global minimum and a boat-like 3D low-lying isomer. The boat-like isomer is 8.6 kcal mol−1 higher in energy than the global minimum Ta©B10− molecular wheel, whereas in NbB10− the boat- like 3D isomer is only 5.4 kcal mol−1 higher and became accessible experimentally in NbB10− (Figure 6.31). However, the boat-like structure becomes the global minimum and the V©B10− molecular wheel becomes significantly unstable, even though it fits with our electronic design principle for forming the doubly aromatic molecular wheel. We see a systematic destabilization of the M©B10−molecular wheel going up the periodic table from Ta to V due to the decreasing atomic size (Figure 6.32). The smaller atomic size and its more contracted 3d orbitals make V energetically unfavorable to fit inside a B10 ring. Thus, both the electronic design principle and the atomic sizes must both be taken into account when designing metal-centered boron wheels. The larger early 5d elements should be more favorable to stabilize larger boron rings, whereas the late 3d transition metals are expected to be better suited to form smaller metal-doped boron wheels. 226 Thus, we show that both electronic and geometric factors are important to form perfectly planar M©Bnq− type molecular wheels. The Ta©B10− and Nb©B10− systems may be the largest metal-doped boron wheels to be expected for transition metals. Even larger metal- doped boron wheels may require consideration of lanthanide or actinide elements. Figure 6.31 Comparison of the photoelectron spectrum of VB10– with those of NbB10– and TaB10– at 193 nm. 227 Figure 6.32 The relative energies of MB10− (M = V, Nb, Ta) between the wheel-type structures and the boat-like structures. 6.10 Conclusions and Perspectives We have discussed recent experimental and theoretical discoveries of a new class of aromatic borometallic compounds, containing a highly coordinated central transition metal atom inside a monocyclic boron ring. Electronic design principle has been advanced that allow both rationalization of the stability of the Dnh-M©Bnk– type molecular wheels and the prediction of new stable clusters. Research so far has focused on n = 8 – 10, which are the most promising size range. As concluded in a recent Perspective article by Heine and Merino,315 “Are Ta©B10– and Nb©B10– the planar systems with the highest coordination number? We don’t know.” Indeed, we have not considered experimentally all the metal 228 elements in the periodic table. The augmented design principle for 6 delocalized π and 10 delocalized σ electrons predicts electronically stable M©B11– systems for valence IV metals. A more important and pertinent question is: can these molecular wheels be synthesized in bulk quantities and crystallized? Interestingly, planar monocyclic B6 rings have been discovered recently as key structural building blocks in a multimetallic compound, Ti7Rh4Ir2B8.317 A relevant question would be: what about transition metal doped boron rings in the bulk? On the other hand, because of the central position of the transition-metal atom in the M©Bnk– molecular wheels, appropriate ligands may be conceived for coordination above and below the molecular plane, rendering chemical protection and allowing syntheses of this new class of novel borometallic complexes. The examples discussed in this chapter demonstrate that atomic clusters remain a fertile field to discover new structures, new chemical bonding, and maybe new nanostructures with tailored properties. 229 Chapter 7 Boron Clusters as the Foundation of New Boron Nanostructures It has been a long-sought goal in cluster science to discover stable atomic clusters as building blocks for cluster-assembled nanomaterials, as exemplified by the fullerenes and their subsequent bulk syntheses.5,6 Clusters have also been considered as models to understand bulk properties, providing a bridge between molecular and solid-state chemistry.7 Because of its electron deficiency, boron clusters tend to form planar structure. The unusual planar boron clusters have been suggested as potential new bulking blocks or ligands in chemistry.215 In a joint PES and ab initio study of LiB6− and LiB8− clusters,134,136 the lithium atom was found to form charge-transfer complexes, Li+[B62−] or Li+[B82−], in which the geometries or electronic structures of the boron clusters130,132 were not changed significantly. Theoretically, the NaB3 cluster was found to be a C3v Na+[B3−] ionic species.318 Complexes of the planar B5 and B6 clusters with alkali (M+B5−) and alkali-earth (M2+B6−) elements were also calculated, where the B5 and B6 units were found to similar to the bare clusters, respectively.319,320 Most recently, our studies have shown that single transition-metal atom prefers occupying the central position of a boron ring to form molecular wheels (M©Bn−) with octa-, hepta-, and deca-coordination numbers.113,114,117,120,121 Because of the central metal atom with available electron lone pairs, appropriate ligands may be conceived for coordination above and below the molecular plane, allowing syntheses of this new class of novel boron-based metal complexes. 230 The first synthesized and structurally characterized compounds containing planar boron clusters as ligands were the triple-decker [(Cp*Re)2BnXn] (n = 5, 6; X = H or Cl, Cp* = Me5C5), in which the BnXn unit was found to be perfectly planar pentagonal or hexagonal motif.321,322 The electronic structures of these two complexes are interesting, where the Re atoms can be viewed to donate six electrons to the planar BnXn units as hexa-charged species.322 Similar hexa-charged B5H56− and B6H66− units have been predicted theoretically in Li6B5H5 and Li6B6H6.323,324 A number of planar cyclic B5- or B6- containing compounds have been synthesized with either different metal atoms or different ligands.325-336 However, all the planar boron rings in the above mentioned compounds were actually B5X5 or B6X6 species. 322-336 The only bare planar B6 ring as a structural motif was discovered recently in the solid compound Ti7Rh4Ir2B8,317 in which the B6 ring is sandwiched between two metal atoms in a bipyramidal fashion. This chapter presents three types of interesting boron clusters: 1) the hydrogen or boronyl terminated ladder like molecular wires. They have alternating σ and π bonding pattern similar to the polyenes and a name of polyboroene was proposed to designate such molecular wires; 2) the bipyramidal di-tantalum boron cluster. Boron atoms was found the nucleate around a Ta-Ta axis and the B-B ring closes at the number of six to from a D6h- TaB6Ta bipyramid, similar to the core structure of the synthesized triple-decker [(Cp*Re)2BnXn]321,322 and the structural motif in Ti7Rh4Ir2B8,317 providing the connection between the gas-phase cluster and solid-state materials. 3) the half sandwich metal doped boron clusters. The cobalt and rhodium atom were found to form half-sandwich-type structures with the quasi-planar B12 moiety coordinating to the metal atom. The B12 ligand is found to have similar structure as the bare B12 cluster with C3v symmetry. The exposed metal 231 sites in these complexes can be further coordinated by other ligands or become reaction centers as model catalysts. 7.1 Elongation of Planar Boron Clusters by Hydrogenation: Boron Analogues of Polyenes 7.1.1 Introduction Hydrogenation of the planar boron clusters is expected to break the peripheral B-B σ bonds, leading to structural transformation. Partially hydrogenated boron clusters (BnHm, n > m) are expected to evolve into 3D borane-like structures as a function of m. This 2D-to-3D structural transition for B12Hm+ clusters has been suggested to occur at B12H6+.337,338 An early theoretical study reported monohydrogenated boron cluster cations (BnH+, n = 1 – 13) to have structures similar to the bare Bn+ clusters.339 The first dihydrogenated boron cluster studied computationally was H2B7–,340 which was found to have a two-row elongated structure with two terminal H atoms, quite different from the B7– global-minimum structure.131 Its Au2B7– auroanalogue was experimentally characterized and found to have the same structure as H2B7–.341 Recently, a number of computational studies on hydrogenated boron clusters have been reported.151,257,342-347 In addition to having interesting structures and bonding properties, partially hydrogenated boron clusters play important roles during dehydrogenation of boron hydride hydrogen-storage materials.344,347,348 Here we report the first experimental observation and characterization of a series of dihydride boron clusters, H2Bn–/D2Bn– (n = 7 – 12), which were found to possess ladder-like elongated structures with two terminal H atoms. Chemical bonding analyses showed that the π bonding patterns in the boron cluster 232 dihydrides are similar to those in conjugated alkenes, and thus, they can be viewed as hydrocarbon analogues, or “polyboroenes”. The polyboroenes and their auro-analogues (Au2Bn) with conjugated π bonding form a new class of molecular wires. 7.1.2 Experimental Results The boron hydride cluster anions were produced by laser vaporization of an isotopically enriched 11B target with helium containing 5% deuterium (D2) as the carrier gas. D2 gas is instead of H2 for better mass separation. We found that the photoelectron spectra of D2Bn– were special, all with vibrational resolution, as shown in Figure 7.1. Spectra at higher photon energy (193 nm) are shown in Figure 7.2, where comparisons with theoretical calculations are also shown. The vibrational resolution suggests that all of the D2Bn– clusters have relatively high symmetries and that there are no significant differences in geometry between the ground states of the anions and those of the neutrals. In particular, the photoelectron spectrum of D2B7– (Figure 7.1) is almost identical to that of Au2B7–,341 indicating their similar structures and confirming the previously reported global-minimum structure of H2B7–.340 233 Figure 7.1 Photoelectron spectra of D2Bn– (n = 7–12). (A) D2B7– at 266 nm. (B) D2B8– at 355 nm. (C) D2B9– at 355 nm. (D) D2B10– at 266 nm. (E) D2B11– at 266 nm. (F) D2B12– at 355 nm. 234 Figure 7.2 Photoelectron spectra of D2Bn– (n = 7–12) at 193 nm compared with simulated spectra for the optimized global minimum ladder structures. The features labelled with “*” in the experimental spectra of D2B9– and D2B12– are from low-lying isomers. The vertical bars in the simulated spectra of D2B9– and D2B12– represent the VDEs from low-lying isomers. D2B9–: the blue bar is from isomer 9.II and the red bar is from isomer 9.III. D2B12–: the blue bars are from isomer 12.II and the red bars are from isomer 12.III. 235 7.1.3 Theoretical Results and Comparison with Experimental Results We carried out theoretical calculations and found that the global minima of the H2Bn– /0 clusters for n = 8 – 12 (Figure 7.3) have ladder structures similar to that of H2B7–.340 Calculations for D2Bn– were also performed. Except the vibrational frequencies, the structures and electron binding energies for the hydrogenated and deuterated species were identical. For odd n, the two H atoms are in the cis position, whereas for even n, the two H atoms are in the trans position. No low-lying isomers within 5 kcal/mol of the global- minimum ladder structures were found for n = 7,340 8, 10, and 11. One or more low-lying isomers were found for n = 9 and 12, consistent with the experimental observation that isomers were present in these cluster beams (Figure 7.2). The calculated ADEs and VDEs for the global-minimum ladder structures are compared with the experimental data in Table 7.1. Good agreement between the calculated ADE/VDE and the experimental data is observed. The ADEs of D2B8– and D2B12– are low because their neutrals are closed-shell species with large energy gaps between their LUMOs and HOMOs, which were observed to be 1.63 and 1.47 eV for D2B8 and D2B12, respectively (Figure 7.2), suggesting that they are highly stable neutral species. The neutral D2B10 ladder structure has a nearly degenerate closed-shell singlet state and a triplet state with two unpaired electrons, in agreement with the observed high ADE of D2B10–and the small energy gap between the first and second detachment transitions (Figure 7.1d). This observation suggests that D2B102– should be a stable closed- shell species, which will be used in the chemical bonding analyses below. All of the odd- sized D2Bn– clusters have closed-shell electronic structures, giving rise to high ADEs, except for D2B9–. The relatively low ADE of D2B9– suggests that its HOMO is unstable, in agreement with the large observed energy gap between the first and second detachment 236 transitions (Figure 7.2). In fact, the global-minimum structure of D2B9– is not perfectly planar, and the B9 ladder framework has a slight out-of-plane twist, giving rise to C2 symmetry (Figure 7.3). The broader vibrational line width in the photoelectron spectrum of D2B9– (Figure 7.1C) is consistent with the excitation of a low-frequency vibrational mode, because neutral D2B9 is planar with C2v symmetry262 and has a very low frequency bending mode. These observations suggest that D2B9+ should be a more stable closed-shell planar species, which was confirmed by our calculations. The simulated spectra using the calculated VDEs for the global-minimum ladder structures are compared with the 193 nm photoelectron spectra in Figure 7.2 for all of the dihydrides. The overall agreement between the theoretical and experimental data is excellent, lending considerable credence to the identified ladder-like structures for the boron cluster dihydride anions. The resolved vibrational information for the ground-state transition provides additional support for the ladder structures of the dihydride clusters. The observed vibrational frequencies are compared with the calculated frequencies for the D2Bn ground states in Table 7.1. 237 Figure 7.3 Optimized global minimum structures for H2Bn–/0 (n = 7–12). The bond lengths are in Å. 238 Table 7.1 Observed ADEs, VDEs and vibrational frequencies for the ground state photodetachment transitions of D2Bn– (n = 7–12), compared with calculations. Experimenta Calculation -1 Vib. freq. (cm ) Vib. freq. (cm-1) ADE (eV) VDE (eV) ADE (eV) VDE (eV) ν1 ν2 ν1 ν2 − 1 b D2B7 ( A1, C2v) 3.49 (3) 3.49 (3) 1250 (40) 620 (40) 3.35 3.47 1323 609 − 2 D2B8 ( Bu, C2h) 2.49 (3) 2.56 (3) 1230 (50) 550 (40) 2.60 2.75 1232 516 − 1 D2B9 ( A, C2) 3.07 (3) 3.15 (3) 630 (40) 2.92 3.04 636 − 2 D2B10 ( Au, C2h) 3.24 (3) 3.35 (4) 3.44 3.57 − 1 D2B11 ( A1, C2v) 3.89 (3) 3.89 (3) 550 (40) 3.79 3.91 581 D2B12 (2Ag, C2h) − 2.87 (3) 2.87 (3) 680 (40) 2.98 3.04 680 a The numbers in the parentheses are the uncertainties in the last digits. b − The measured and calculated ADE and VDE are the same as those of D2B7 . The corresponding measured vibrational -1 frequencies for the ground state of H2B7 are ν1 = 1350 (40) cm , ν2 = 720 (40) cm-1, while the calculated values are ν1 = 1335 −1 −1 cm , ν2 = 681 cm . 7.1.4 Chemical Bonding Analyses and Discussion We performed chemical bonding analyses of the boron cluster dihydrides using the AdNDP method. Figure 7.4 shows the AdNDP results for H2B7–, H2B8, H2B9–, H2B102–, H2B11–, and H2B12. These charge states were chosen because the AdNDP method can handle only closed-shell systems.107,239 The B–H bonds and the peripheral B–B bonds are described mainly as 2c-2e localized σ bonds, except for a few cases where some 3c-2e bonding character is also seen. The peripheral B–B bonding is similar to that observed in all of the planar boron clusters. The two rows of boron atoms in the ladder structures are bonded via multicenter σ and π bonds. H2B7–, H2B8, and H2B9–, each with two 4c-2e π bonds (four π electrons), can be considered to be anti-aromatic according to the Hückel 4n rule. This bonding property in H2B7– (or its auro-analogue, Au2B7–) has been compared with that in the prototypical anti-aromatic cyclobutadiene.340,341 H2B102–, H2B11–, and H2B12, each with three delocalized π bonds (six π electrons), can be considered to be aromatic according to the 239 Hückel 4n + 2 rule. However, the elongated shapes of H2B102–, H2B11–, and H2B12 are not consistent with π aromaticity, which usually leads to circular structures in boron clusters and the recently discovered transition-metal-centered boron clusters. We noticed that the π bonds in the dihydrides are delocalized only over parts of the boron ladder frameworks, and they can be viewed as π bonds between two pairs of boron atoms, reminiscent of the π bonds in conjugated alkenes. The two π orbitals in H2B7–, H2B8, and H2B9–are similar to those of butadiene in Figure 7.5A, and the three π orbitals of H2B102–, H2B11–, and H2B12 are similar to those of 1,3,5-hexatriene in Figure 7.5B. This similarity in π bonding suggests that the boron cluster dihydrides should be considered more appropriately as analogues of polyenes and thus may be called “polyboroenes”. In particular, each pair of boron atoms in H2B8 and H2B12 can be viewed as contributing one π electron to form a 4c-2e π bond with the adjacent B2 pair in each B4 unit, while there is a delocalized 4c-2e σ bond between two B4 units in H2B8 and H2B12. We think that it is this perfect alternating 4c-2e π and 4c-2e σ bonding pattern in H2B8 and H2B12 that contributes to their high electronic stability and the large HOMO−LUMO gap in these two dihydrides. Similar π and σ bonding patterns are expected to exist in all of the H(B4)xH dihydrides (x = 1, 2, 3, ...), which should form a series similar to polyacetylenes, H(CH═CH)xH. On the bases of the stable closed-shell H2B7–, H2B102–, and H2B9+ species, there should also exist three similar series of charged dihydride polyboroenes, [H2(B4)xB3]−, [H2(B4)xB2]2–, and [H2(B4)xB]+. Since Au has been found to behave like a hydrogen atom to form covalent bonds,349,350 such as those found in Au2B7–,341 it is expected that the auroanalogues (or auropolyboroenes) Au2(B4)x, [Au2(B4)xB3]−, [Au2(B4)xB2]2–, and [Au2(B4)xB]+ should also be highly stable molecular species. The polyboroenes or 240 auropolyboroenes may be synthesized in the bulk or deposited on surfaces to give a new family of molecular wires. Figure 7.4 Chemical bonding analyses using the AdNDP method. (A) H2B7–. (B) H2B8. (C) H2B9–. (D) H2B102–. (E) H2B11–. (F) H2B12. 241 Figure 7.5 Comparison of the π CMOs of the boron cluster dihydrides with those of conjugated alkenes. (A) The π orbitals of H2B7–, H2B8, H2B9–, and butadiene (C4H6). (B) The π orbitals of H2B102–, H2B11–, H2B12, and 1,3,5-hexatriene (C6H8). 242 7.2 π and σ Double Conjugations in Boronyl Polyboroene Nanoribbons: Bn(BO)2− and Bn (BO)2 (n = 5 − 12) 7.2.1 Introduction Boron dihydride clusters were found to form planar, elongated, ladder-like double- chain structures terminated by a hydrogen atom on each end.262,263 It was shown that in these dihydride species a rhombic B4 unit, which effectively contributes two delocalized π electrons, appears to be equivalent to a C=C unit in polyenes. This establishes an interesting analogy between boron dihydride clusters and the conjugated polyenes, and polyboroene was coined to designate this new class of boron compounds.262 Boronyl (BO) has a strong B≡O triple bond351-353 comparable to that in CN. Recent studies have shown that BO group dominates the electronic and structural properties of boron-rich oxide clusters.245,354,355 BO as a monovalent σ radical is analogous to H, suggesting a new route to design novel boron oxide clusters. In particular, the boron dioxide clusters, Bn+2O2− or Bn+2O2, are expected to be isolobal to the BnH2− or BnH2 clusters.262,263 Here we report the observation and characterization of a series of boron dioxide clusters, BxO2− ( x = 7 − 14), using PES and theoretical calculations. These dioxide clusters and their corresponding neutrals are shown to possess elongated double-chain structures with two boronyl groups attached terminally and can be formulated as Bn(BO)2− and Bn(BO)2 ( n = 5 − 12). Theoretical calculations further suggest that even larger elongated boron dioxide clusters are possible, such as B16(BO)2 and B20(BO)2. The EA of Bn(BO)2 are found to follow a 4n periodic pattern, indicating the rhombic B4 unit as the building block in the boron nanoribbons. Both π and σ conjugations are found in these nanoribbon clusters, which is not known in hydrocarbon molecules. It is noted that the double-chain boron nanoribbons are the 243 favored structural features in a variety of proposed low-dimensional boron nanostructures, such as the tubular boron clusters,135,139 the B80 fullerene,142 and the most stable form of monolayer boron sheet.147,148,152,163,258 7.2.2 Experimental Results The PES spectra of BxO2− ( x = 7 − 14) are shown in Figure 7.6. The ground state ADE and VDE are given in Table 7.2. Higher VDEs are given in the supplementary material of Ref. 264, where they are compared with the theoretical data.264 All PES spectral features observed for BxO2− ( x = 9 − 14) are remarkably similar to those reported previously for the corresponding dihydrides,262 H2Bn− ( n = 7 − 12) ( Figure 7.2), respectively, except that the electron binding energies of the dihydrides are lower by ∼1 eV. The spectral similarities suggest that the BxO2− clusters should have similar structures as the dihydrides and should be formulated as Bn(BO)2− with two boronyl groups as σ radicals. The EA of BO is much higher than that of the H atom.353,356 Hence, the BO σ radical should be much more electron-withdrawing relative to the H atom, resulting in much higher electron binding energies observed for the oxides. Vibrationally resolved PES bands are observed for a number of species, that is, the X band for B8O2− and B9O2− and the A band for B12O2− and B13O2−, yielding symmetric vibrational frequencies for their corresponding neutrals. Weakly populated isomers are clearly observed in the cases of B12O2− (the X′ feature in Figure 7.6f) and B14O2− (the X′ feature in Figure 7.6h). As will be shown below, the intense A and B bands observed for B11O2− (Figure 7.6e) are also due to a nearly degenerate isomer. Interestingly, even the spectral features from the isomers are similar to those observed for the corresponding H2Bn− species,262 suggesting that the diboronyl and dihydride boron clusters have similar potential landscapes. 244 Figure 7.6 Photoelectron spectra of BxO2– (x = 7  14) at 193 nm. Vertical lines represent vibrational structures. The inset in (b) shows the spectrum at 266 nm. 245 Table 7.2 Experimental Ground State ADEs and VDEs from the Photoelectron Spectra of BxO2– (x = 714), compared to theoretical calculations. All energies are in eV. ADE (exp.)a,b VDE (exp.)a transition ADE (theo.)c VDE (theo.)c B7O2– 3.90 (3) 4.01 (3) 2 A1  1A 3.69/3.61 3.89/3.82 – 1 2 B8O2 4.07 (2) 4.07 (2) Ag  Bg 4.12/3.87 4.21/3.99 – 2 B9O2 4.61 (3) 4.61 (3) A2  1A1 4.50/4.42 4.60/4.57 B10O2– 3.50 (5) 3.62 (5) 1 2 Ag  Bu 3.56/3.31 3.71/3.42 B11O2– 3.98 (5) 4.06 (5) 2 1 B2  A 3.86/3.80 3.98/3.90 d d d 4.45 (5) 4.81 (5) 2 1 A A 4.22/4.22 4.59/4.58d B12O2– 4.33 (3) 4.33 (3) 1 Ag  2Au 4.28/4.07 4.39/4.23 B13O2– 4.80 (3) 4.80 (3) 2 1 B1  A1 4.65/4.60 4.74/4.76 B14O2– 3.67 (5) 3.72 (5) 1 2 Ag  Ag 3.68/3.47 3.78/3.53 a Numbers in the parentheses represent experimental uncertainties in the last digit. b EA of the neutral species. c Calculated at the B3LYP/TDDFT level. Shown in bold italic are values calculated at the single-point CCSD(T) level. d Coexisting isomer. 7.2.3 Theoretical Results As already hinted by the PES spectra, we initially only optimized a set of structures at the B3LYP/6-311++G(d,p) level for the boron dioxide anion clusters with two boronyls, Bn(BO)2− ( n = 5 − 12), as shown in Figure 7.7, which are analogous to the ladder-like BnH2− clusters. The B4(BO)2− cluster was studied previously357 and is included here for comparison. Similar structures for the Bn(BO)2 neutral species were also. The diboronyl type of structures for the boron dioxide clusters were also reported for n = 5 − 8 in a previous computational study.358 For B9(BO)2−, we considered a variety of structures based on two BO units bonded to different positions on the B9 molecular wheel.132 One structure based on a distorted B9 wheel with C1 symmetry was found to be competitive with the double- chain C2 structure, within ∼1 kcal/mol at the single-point CCSD(T)//B3LYP/6-311++G(d,p) level. Nonetheless, their calculated first VDE values are very different from each other, 4.59 246 eV for C1 versus 3.98 eV for C2 at the B3LYP level,264 which ensure that such isomeric structures can be easily identified without ambiguity in the PES spectrum. All double-chain ladder-like Bn(BO)2− and Bn(BO)2 clusters adopt planar structures with D2h, C2h, or C2v symmetries, except for B5(BO)2− and B9(BO)2−, which undergo slight out-of-plane distortion, resulting in C2 symmetry. The out-of-plane distortion of B9(BO)2− is exactly the same as that found in B9H2−.262 For even n clusters, the two BO groups are in trans positions, whereas for odd n clusters they are in cis positions, similar to the dihydrides. Several alternative anion and neutral structures (not shown) were also considered for all Bn(BO)2− and Bn(BO)2 ( n = 5 − 12) clusters. As mentioned above, the isolable analogy between the diboronyls and dihydrides and the similarity between the PES spectra of the dioxides and the dihydrides allowed us to bypass extensive structural searches usually necessary to find the global minima for such complicated systems. Figure 7.7 Optimized double-chain nanoribbon global-minimum structures for Bn(BO)2– (n = 412). 247 Figure 7.8 The experimental EAs of Bn(BO)2 (n = 412; solid dots) as a function of n, compared to theoretical values at the single-point CCSD(T) level (empty dots). The EA of B4(BO)2 is taken from 357 ref. . Computational ground-state VDEs of BnH2– at the B3LYP level (empty squares, ref. 263 ) and experimental values (solid squares, ref. 262) are also shown for comparison. 7.2.4 Comparison between Experimental and Theoretical Results The calculated ground state ADEs and VDEs for Bn(BO)2− ( n = 5 − 12), at both the B3LYP/6-311++G(d,p) and single-point CCSD(T)//B3LYP/6-311++G(d,p) levels, are compared with the experimental data in Table 7.2. The B3LYP results are in good agreement with the experimental data, with errors of less than ∼0.2 eV. Indeed, for the majority of these values, the B3LYP results are within ∼0.1 eV of the experimental data. The single-point CCSD(T) values are slightly lower than those at B3LYP in most cases, which are also in 248 overall good agreement with experiment within ~0.1 eV. It may be stated that the B3LYP and single-point CCSD(T) methods perform equally well for the current system. The experimental VDEs can be viewed as the electronic fingerprint of a cluster. The double-chain nanoribbon structures shown in Figure 7.7 reproduce well the experimental PES patterns for all the Bn(BO)2− ( n = 5 − 12) clusters, confirming these structures as their global minima. The VDEs for the first and second detachment channels from the second isomer of B9(BO)2 – are also in excellent agreement with the observed A and B bands (Figure 7.6e), whereas the VDEs for the C2 ribbon structure are in good agreement with the remaining spectral features. The second detachment channel of the C2-B9(BO)2− corresponds to band C, giving rise to a large energy gap between the first and second detachment channels, resembling exactly the spectral features for B9H2−.262 As discussed for the B9H2− case, the large gap for B9(BO)2− suggests that its HOMO is relatively unstable, which causes the out of plane distortion. Removing the two electrons should result in a much more stable and perfectly planar B9(BO)2 +species, similar to B9H2 +.262 The much weakly populated isomers for B10(BO)2− and B12(BO)2− are also similar to those of the corresponding dihydrides. The overall excellent agreement between the calculated and experimental data lends strong support for the nanoladder structures of the boron dioxide clusters, which provide new examples for the BO/H isolobal analogy. 7.2.5 Discussion Chemical bonding in boron nanoribbons: π conjugation in Bn(BO)2− and Bn(BO)2 and analogy to polyenes. The experimental and theoretical EAs of Bn(BO)2 and H2Bn ( n = 4−12) are displayed in Figure 7.8, revealing a regular 4n periodicity. This observation suggests that the rhombic B4 unit plays an essential role in the double-chain 249 nanoribbon structures. In particular, the low EAs for B4X2, B8X2, and B12X2 (X = H and BO) concur with their large HOMO−LUMO gaps, indicating highly stable neutral species. The chemical bonding in the Bn(BO)2− and Bn(BO)2 nanoribbons can be elucidated through MO analyses (Figure 7.9) and AdNDP analyses (Figure 7.10). We found that, similar to the corresponding dihydrides, the B4(BO)2, B8(BO)2, and B12(BO)2 nanoribbons possess one, two, and three delocalized π MOs, respectively, which resemble those in ethylene, 1,3-butadiene, and 1,3,5-hexatriene (Figure 7.9). Therefore, these boron dioxide clusters can be considered as boronyl analogues of the conjugated polyenes, similar to the bonding revealed recently in the H2Bn−/ H2Bn clusters.262,263 Polyboroenes have been coined for the boron dihydride nanoribbons.262 Hence, the dioxides are boronyl polyboroenes, where the rhombic B4 unit is equivalent to a C=C unit in the polyenes. Figure 7.9 Comparison of the delocalized  CMOs of C2H4 (a) and B4(BO)2 (b), C4H6 (c) and B8(BO)2 (d), and C6H8 (e) and B12(BO)2 (f). Figure 7.10 presents the AdNDP analyses for all the closed-shell neutral and anionic species of the boron dioxide nanoribbons for n = 4 − 12. As in pure boron clusters, the B−B bonds in the periphery in the nanoribbons are described by 2c-2e bonds, whereas the bonding between the two boron rows in the nanoribbons is via delocalized σ and π bonds. As shown in Figure 7.10, the delocalized π bonds are over B4 rhombus units in B4(BO)2, B8(BO)2, and 250 B12(BO)2. Other nanoribbons at different charge states exhibit similar π bonding patterns as these three prototypical polyboroenes. σ conjugation in polyboroenes. The delocalized σ bonds in the Bn(BO)2− clusters (Figure 7.10) are similar to the delocalized π bonds, suggesting σ conjugation in the boronyl polyboroenes, in addition to the π conjugation. There are no known cases of σ conjugation in hydrocarbon molecules. Thus, the σ conjugation in the polyboroenes is quite unique as a new bonding feature. As shown in Figure 7.10, the partition of the π or σ bonds alternates, depending on the size and the charge state of the boronyl polyboroenes. In the ideal cases when the number of π bonds differs from that of σ bonds, such as in B8(BO)2 and B12(BO)2, the π and σ bonds are delocalized over alternating B4 units in the boron ribbon framework, giving rise to a more balanced bonding pattern throughout the nanoribbons. This bonding pattern results in the highly stable B8(BO)2 and B12(BO)2 boronyl polyboroenes. In cases when the number of π bonds is equal to that of the σ bonds, the π and σ bonds are delocalized over the same B4 unit, as seen in B6(BO)2and B10(BO)2 (Figure 7.10). This bonding pattern gives rise to more strongly bonded versus less bonded B4 units and can result in structural distortions along the nanoribbon. 251 Figure 7.10 AdNDP analyses for closed-shell Bn(BO)2, Bn(BO)2–, and Bn(BO)22– (n = 412). For odd n species, monoanions are considered, whereas for even n species both neutrals and dianions are analyzed. Only the bonds within the Bn nanoribbon frameworks are shown; the localized bonding elements within the BO groups are not shown. 252 Figure 7.11 AdNDP analyses for the boronyl polyboroenes, B16(BO)2 and B20(BO)2. The localized bonding elements within the BO groups are not shown. Possibility for larger polyboroenes. We note that the double-chain nanoribbon structures are also the key structural elements in the proposed B80 cage142 and the 2D boron sheets.147 Therefore, much longer polyboroenes terminated by BO may be possible. In the boronyl polyboroenes, the intramolecular Coulomb repulsion between two BO groups offers a driving force to elongate the clusters to the nanoribbon shapes. Furthermore, the π orbitals in the terminal BO groups can also participate in the π conjugation in the nanoribbon clusters, thus providing additional stabilization to the nanoribbon system. As suggested by the 4n periodicity (Figure 7.8), the next expected stable boronyl polyboroenes should be B16(BO)2 and B20(BO)2. We thus carried out preliminary calculations at the B3LYP level and found that these two nanoribbons are indeed highly stable among the alternative structures located in our structural searches. The B20(BO)2 boronyl polyboroene is about ∼1.5 nm in length. The AdNDP bonding patterns are shown in Figure 7.11. Thus, B16(BO)2 and B20(BO)2 are boronyl analogues of the larger polyenes, H(CH=CH)nH ( n = 4, 5), respectively. 7.2.6 Conclusions A series of boron dioxide clusters, Bn(BO)2− and Bn(BO)2 ( n = 5 − 12), are produced and characterized via photoelectron spectroscopy and quantum chemical calculations. The 253 electron affinities of Bn(BO)2 display a 4n periodicity, implying that the rhombic B4 unit is the natural structural building block in the boron dioxide clusters. These clusters are shown to possess double-chain nanoribbon structures with lengths ranging from 2.7 to 8.9 Å, with the two boronyl groups bonded at each end. The π bonding in these nanoribbons is analogous to polyenes and they thus belong to a new class of boronyl polyboroenes. Preliminary theoretical calculations suggest that even larger boronyl polyboroenes, B16(BO)2 and B20(BO)2, are viable, extending the nanoribbon length to ∼1.5 nm. These clusters may be viewed as molecular zippers, in which two boron atomic-chains are bonded together via π and σ double conjugations, a unique bonding feature unknown in hydrocarbons. The new boron nanoribbons may serve as novel molecular wires, as well as precursors for low- dimensional boron nanostructures. 7.3 Structural Revaluation of Di‐Tantalum Boride Clusters: Ta2Bx− (x = 2 – 5) 7.3.1 Introduction Di-metal doped boron clusters (M2Bn) are relatively unexplored in comparison to the mono-metal doped boron clusters. Calculations of Li2B− and Au2B2− were reported.359-361 A joint PES and theoretical study found that two Au atoms covalently bond to the planar B7 in the Au2B7− cluster,341 similar to the structural pattern of H2B7−.262,340 In the current work, we investigate the structural and electronic properties for the di-tantalum doped boron clusters Ta2Bx– (x = 2 – 5). Photoelectron spectra for these four clusters have been obtained at several detachment laser energies. DFT calculations at the BP86 level are performed to search for the global minima for Ta2Bx– (x = 2 – 5) and their neutral counterparts. Theoretical results are 254 compared with the experimental results to confirm the identified global minima and low- lying isomers. The boron atoms are found to form an equatorial fan around the Ta–Ta axis, giving rise to quasi-bipyramidal geometries for the lowest-energy structures of these di- tantalum boron clusters. Strong Ta–Ta bonding is observed for species with x = 2 – 4, whereas for x = 5 a significant increase of the Ta–Ta distance is observed. The current study provides important information about the competition among metal-metal, B–B, and metal-B bonding in boride clusters and sets the stage for us to study more complex MxBy– type metal boride clusters. 7.3.2 Experimental Results The photoelectron spectra of Ta2Bx− (x = 2 – 5) are shown in Figure 7.12, Figure 7.13, Figure 7.14, and Figure 7.15, respectively, at three detachment energies (355, 266, and 193 nm). We also performed experiment at 532 nm. But the 532 nm spectra did not reveal additional electronic or vibrational features and are not shown. All the measured VDEs are summarized in Table 7.3 and Table 7.4. Ta2B2−: The 355 nm spectrum of Ta2B2− (Figure 7.12a) shows four detachment bands. Band X is relatively sharp with a VDE of 1.39 ± 0.04 eV. Even at 532 nm, no vibrational fine features were resolved for band X, suggesting a possible low frequency vibrational progression. The ADE is measured 1.31 ± 0.04 eV, which also represents the EA of neutral Ta2B2. Following a relatively large energy gap, three broad and congested bands (A, B, C) are observed. Band A has a VDE of 2.28 eV and its relative intensity increases with photon energies. The large X-A gap suggests that neutral Ta2B2 is likely a closed shell species with a HOMO−LUMO gap represented by the X-A gap. Band B (VDE: 2.78 eV) is relatively weak and is better resolved in the 266 and 193 nm spectra. The congested tail (labeled Band C) 255 near the threshold of the 355 nm spectrum is likely due to thermionic emission,49,362 as can be seen clearly in the 266 and 193 nm spectra, which show an energy gap after band B. The spectral features in the higher binding energy side are quite congested and three bands are tentatively labeled: C (VDE: 3.35 eV), D (VDE: 3.66 eV) and E (VDE: 3.98 eV). Ta2B3−: The 355 nm spectrum of Ta2B3− (Figure 7.13a) reveals two well resolved bands, X and A, with VDEs of 2.00 eV and 2.16 eV, respectively. The ADE of the X band is measured to be 1.93 ± 0.03 eV, which also represents the EA of neutral Ta2B3. These two bands are relatively sharp, indicating a small geometry change between the ground state of Ta2B3− and the ground and first excited state of Ta2B3. Two relatively weak and broad bands, B (VDE: 2.75 eV) and C (VDE: 3.17 eV), are observed in the 355 nm, but they are better defined in the 266 and 193 nm spectra. At the higher binding energy side, more congested spectral features are observed at 266 and 193 nm. Two bands, D (VDE: 3.96 eV) and E (VDE: 4.69 eV), are labeled. A relatively weak feature at ∼3.5 eV is observed in the 193 nm spectrum (Figure 7.13c), but are not labeled. Ta2B4−: The 355 nm spectrum of Ta2B4− (Figure 7.14a) shows three broad bands: X (VDE: ∼1.9 eV), A (VDE: 2.43 eV), and B (VDE: 2.88 eV). The ADE of the X band is estimated to be 1.70 ± 0.07 eV, which represents the EA of Ta2B4. The broad widths of these three bands indicate that there are multiple transitions in each band and/or a very large geometry change upon detachment. Following a large energy gap, the 266 and 193 nm spectra reveal a band C (VDE: 3.81 eV) and a broad band D (VDE: ~4.42 eV), which may also contain multiple transitions. Ta2B5−: The 355 nm spectrum of Ta2B5− (Figure 7.15a) exhibits five detachment transitions and a low energy tail labeled as “*.” Band X with a VDE of 1.93 eV is relatively 256 broad, suggesting a significant geometry change between the ground states of Ta2B5− and Ta2B5. The ADE of band X is estimated to be 1.83 ± 0.04 eV, which represents the EA of Ta2B5. The band A with a VDE of 2.23 eV is relatively sharp. Band B with a VDE of 2.70 eV is not well resolved at 355 nm, but better defined in the 266 and 193 nm spectra. VDEs of bands C and D are measured to be 2.87 and 3.10 eV, respectively. At 266 nm (Figure 7.15b), a band E with a VDE of 3.54 eV is well resolved. However, both the 266 and 193 nm spectra show that the higher binding energy side is very congested. Two bands, F (VDE: 4.01 eV) and G (VDE ∼4.7 eV), are labeled for the sake of discussion. The low energy tail “*” is likely due to contributions of a low-lying isomer. 257 Figure 7.12 Photoelectron spectra of Ta2B2− at (a) 355 nm, (b) 266 nm, (c) 193 nm. 258 Figure 7.13 Photoelectron spectra of Ta2B3− at (a) 355 nm, (b) 266 nm, (c) 193 nm. 259 Figure 7.14 Photoelectron spectra of Ta2B4− at (a) 355 nm, (b) 266 nm, (c) 193 nm. 260 Figure 7.15 Photoelectron spectra of Ta2B5− at (a) 355 nm, (b) 266 nm, (c) 193 nm. 261 Table 7.3 Experimental VDEs for Ta2Bx− (x = 2 − 3) compared to the calculated VDEs from the anion ground-state. Feature VDE (exp.)a VDE (theo.)b MO − Ta2B2 X 1.39 (4) 1.45(S) 9a1 (α) 1.95(T) 2a2 (β) 2.02(S) 2a2 (α) A 2.28(5) 2.17(T) 8a1(β) 2.18(T) 4b1(β) 2.27(S) 4b1 (α) 2.34(S) 8a1(α) B 2.78(5) 3.19(T) 4b2(β) 3.20(T) 7a1(β) 3.33(S) 4b2 (α) C 3.35(3) 3.37(S) 7a1(α) D 3.66(4) 3.67(T) 6a1(β) E 3.98(4) 3.77(S) 6a1(α) − Ta2B3 X 2.00(3) 2.00(Q) 5b1(β) 2.23(D) 5b2(α) 2.27(Q) 2a2(β) A 2.16(3) 2.28(D) 10a1(α) 2.36(D) 5b1(α) 2.72(Q) 9a1(β) B 2.75(3) 2.74(D) 2a2(α) 3.33(D) 9a1(α) C 3.17(3) 3.35(Q) 4b1(β) 3.79(D) 4b1(α) D 3.96(6) 4.07(Q) 8a1(β) 4.16(Q) 4b2(β) E 4.69(6) 4.57(D) 8a1(α) a Numbers in parentheses represent the uncertainty in the last digit. b VDEs were calculated at BP86 level. 262 Table 7.4 Experimental VDEs for Ta2Bx− (x = 4 − 5) compared to the calculated VDEs from the anion ground state. Feature VDE (exp.)a VDE (theo.)b MO − Ta2B4 2.05(S) 11a1 (α) X ~1.9 2.12(T) 5b1(β) 2.23(S) 5b1(α) 2.37(T) 10a1(β) A 2.43 (4) 2.39(S) 10a1(α) 2.65(S) 2a2(α) 2.67(T) 2a2(β) B 2.88(6) 2.94(S) 6b2(α) 3.00(T) 6b2(β) 3.89(T) 9a1(β) C 3.81(3) 4.04(S) 9a1(α) 4.29(T) 5b2(β) 4.30(S) 5b2(α) D 4.42(6) 4.54(T) 8a1(β) 4.54(S) 8a1(α) − Ta2B5 X 1.93(4) 2.02(D) 3a2(α) A 2.23(3) 2.38(D) 11a1(α) B 2.70(4) 2.71(D) 5b1(α) C 2.87(4) 2.74(D) 7b2(α) D 3.10(4) 2.93(D) 6b2(α) E 3.54(4) 3.30(D) 10a1(α) F 4.01(4) 4.44(D) 9a1(α) G 4.7(1) 4.87(D) 4b1(α) a Numbers in parentheses represent the uncertainty in the last digit. b VDEs were calculated at BP86 level. 263 7.3.3 Theoretical Results The optimized anion (Ta2Bx−) and neutral (Ta2Bx) ground states and low-lying isomers (within ~0.50 eV) at the BP86 level are presented in Figure 7.16 for x = 2 – 5, respectively. Ta2B2− and Ta2B2: The structures for Ta2B2− and Ta2B2 are extensively searched and optimized at the BP86 level with different spin states. The ground state of Ta2B2− has a C2v (2A1) geometry (Figure 7.16a-I), in which the Ta–Ta bond is perpendicular to the B–B bond in a distorted tetrahedral shape. Isomer II (Figure 7.16b) (C2v, 2B1) with a much longer B–B bond is only 0.04 eV higher in energy, essentially degenerate with the ground state within the accuracy of our calculations. To resolve the true ground state of Ta2B2−, we performed optimizations for these two isomers in CCSD(T) calculations with the Ta/Stuttgart+2f1g/B/aug-cc-pVTZ basis sets. The results show that the isomer I is the ground state, but isomer II is still very close only 0.05 eV higher using the CCSD(T) optimized structures (Table 7.5). Thus, isomer II may also contribute to the experimental observation. Other selected low-lying isomers are at least 0.20 eV higher in energy, which are not competitive for the global minimum. The global minimum of Ta2B2 (1A1, C2v) has a slightly longer Ta–Ta bond (0.05 Å) compared to that of the anion. The second low-lying isomer is 0.29 eV higher in energy with a remarkably shorter B–B bond (1.681 Å) as shown in Figure 7.16b-II. Ta2B3− and Ta2B3: The ground state of Ta2B3− is open-shell with a triplet electronic state (3B2) and C2v symmetry (Figure 7.16c-I). It can be viewed as a quasi-bipyramidal structure with the Ta–Ta dimer interacting perpendicularly with a bent B3 chain. The corresponding closed-shell state (Figure 7.16c-IV) is 0.17 eV higher in energy. A low 264 symmetry Cs (1A′) structure (Figure 7.16c-II) with a shorter Ta–Ta bond is 0.12 eV above the ground state. A very low symmetry C1(1A) structure (Figure 7.16c-III) is 0.17 eV above the ground state, featuring a boron atom interacting with only one other B and Ta atom on a quasi-tetrahedral Ta2B2 core. For the neutral Ta2B3 cluster, six low-lying isomers are found within 0.10 eV at the BP86 level. The ground state is a C2v (4A2) structure (Figure 7.16d-I), similar to the global minimum of Ta2B3−. Further theoretical calculations at the CCSD(T) level are performed for these low-lying isomers to resolve the true ground state, as reported in Table 7.5. The CCSD(T) results show that the C2 (2B) structure (Figure 7.16d-VI), which is also similar to the anion ground state, but 0.08 eV above the C2v (4A2) structure at the BP86 level, is the global minimum, whereas the C2v (4A2) structure is 0.17 eV higher than the C2 (2B) state at the higher level of calculation. Ta2B4− and Ta2B4: The ground state of Ta2B4− (2A1, C2v) (Figure 7.16e-I) can be viewed as extending the B3 chain in the Ta2B3− global minimum structure to form a bent B4 chain. Interestingly, while the Ta–Ta distance is similar in the two clusters, the B–B bond lengths seem to be shortened significantly in Ta2B4− relative to those in Ta2B3−. The next isomers are at least 0.4 eV higher in energy (Figure 7.16e-II). The low-lying isomers of the neutral Ta2B4 are depicted in Figure 7.16f. The global minimum (Figure 7.16f-I) resembles that of Ta2B4−, except a slightly lengthened Ta–Ta bond (by 0.06 Å) and the middle B–B bond (by 0.05 Å). The low-lying isomer (Figure 7.16f-II) with Cs symmetry is a triplet state (3A′), only 0.14 eV above the ground state. Ta2B5− and Ta2B5: The low-lying isomers for Ta2B5− are given in Figure 7.16g. The ground state (Figure 7.16g-I) has a five-member bent boron chain with C2v (1A1) symmetry. 265 A very competitive isomer (Figure 7.16g-II) with a shorter Ta–Ta bond is only 0.06 eV higher in energy. Single-point CCSD(T) calculations are performed using the BP86 geometries, showing isomer (Figure 7.16g-II) is 0.21 eV higher than isomer (Figure 7.16g-I) at the higher level of theory (Table 7.5). The third isomer (Figure 7.16g-III) is a triplet state (3B2) also with C2v symmetry and is 0.25 eV above the singlet ground state. The other structures in Figure 7.16g are at least 0.35 eV above the global minimum. For the neutral Ta2B5, two competitive low-lying isomers are found at the BP86 level, which are similar to the two low-lying isomers of the anion. Single-point CCSD(T) calculations are performed for the neutral Ta2B5 low-lying isomers, revealing that isomer 8b- II is 0.23 eV higher than 8b-I (Table 7.5). The third low-lying isomer C2v (2A1) (Figure 7.16h-III) is 0.28 eV higher in energy at the BP86 level. 266 Figure 7.16 Low-lying isomers for (a) Ta2B2−, (b)Ta2B2, (c) Ta2B3−, (d)Ta2B3, (e) Ta2B4−, (f)Ta2B4, (g) Ta2B5−, and (h)Ta2B5 at the BP86 level of theory. The bond lengths are in Å. 267 Table 7.5 Relative energies of the low-lying states of the Ta2Bx−/0 (x = 2-5) clusters at the BP86 level (within 0.10 eV), and comparisons with those from the CCSD(T) single-point calculations electronic state BP86 a, b CCSD(T) a, c CCSD(T) a, d (C2v 2A1) 0.00 0.004 0.00 − Ta2B2 (C2v 2B1) 0.04 0.00 0.05 4 (C2v A2) 0.00 0.16 0.17 2 (Cs A' ) 0.02 0.19 0.20 (C2v 2B1) 0.05 0.07 0.07 Ta2B3 (Cs 2A") 0.08 0.15 0.16 2 (C1 A) 0.08 0.22 0.06 2 (C2 B) 0.08 0.00 0.00 (C2v 1A1) 0.00 0.00 --- Ta2B5− (C2v 1A1) 0.06 0.21 --- 2 (C2v A2) 0.00 0.00 --- Ta2B5 (C2v 2A1) 0.09 0.23 --- a All energies are in eV. b BP86/Ta/Stuggart+2f1g/B/aug-cc-pvtz. c CCSD(T) single-point calculations at the BP86/Ta/Stuggart+2f1g/B/aug-cc-pvtz geometries. d CCSD(T) optimization calculations. 7.3.4 Comparison between Experimental and Theoretical Results In order to verify the global minimum and low-lying structures of Ta2Bx− (x = 2−5), we have calculated the VDEs on the basis of the identified anionic structures with the generalized Koopmans’ theorem. The calculated VDEs and simulated PES spectra for the ground state structures are compared with the experiment data in Table 7.3 and Figure 7.17. The simulated PES spectra for all the low-lying structures of the anions are compared with the experimental spectra in Figure 7.17 for Ta2Bx− (x = 2−5), respectively. In the single- particle picture, photodetachment involves removal of electrons from occupied MOs of an anion. The final states are the ground and excited states of the corresponding neutral. 268 Considering the complicated nature of the electronic structures of these systems, we can only make qualitative comparisons between experiment and theory in some cases. Ta2B2−: The ground state of Ta2B2− (Figure 7.16a-I) is open-shell. As shown in Figure 7.17a, the simulated PES spectrum from the global minimum of Ta2B2− agrees well with the experimental spectrum. The 9a1 SOMO of Ta2B2− (Figure 7.18a) is primarily a Ta– Ta nonbonding σ orbital. The Mülliken spin density (Figure 7.18a) shows that the unpaired spin is equally shared by the two Ta atoms. On removal of an electron, the HOMO (4b1) of the neutral (Figure 7.18a) is shown to be a δ bonding orbital and the neutral Ta2B2 remains the C2v structure with a shorter Ta–Ta bond by about 0.06 Å. The first calculated VDE (1.45 eV), corresponding to the electron detachment from the 9a1SOMO is in good agreement with the experimental VDE of band X (1.39 eV, Table 7.3). Detachment from the fully occupied MOs below the 9a1 SOMO can lead to both singlet (S) and triplet (T) final states. At the BP86 level, the calculated VDEs from the 2a2 (T, S), 8a1(T), and 4b1 (T, S) orbitals are very close to each other ranging from 1.95 to 2.27 eV, consistent with the intense and broad A band. The calculated VDEs for the higher binding energy features are also in qualitative agreement with the observed spectral pattern, as shown in Table 7.3 and and Figure 7.17. Ta2B3−: The simulated spectrum for the global minimum of Ta2B3− is found to agree well with the experimental spectrum (Figure 7.17b). The ground state of Ta2B3− (Figure 7.17b-I) is a triplet state. The first detachment channel corresponds to electron removal from the HOMO (5b1), which is basically a δ-bonding orbital (Figure 7.18b). The calculated VDE of 2.00 eV at the BP86 level is in excellent agreement with the experimental observation at 2.00 eV. There are four close-lying detachment channels with calculated VDEs ranging from 2.23 to 2.36 eV (Table 7.3), which are tentatively assigned to the A band. This assignment is 269 tentative because the A band is relatively sharp and is inconsistent with so many detachment channels. However, the calculated VDEs for the higher binding energy channels seem to be in good agreement with the experiment, as can be seen from Table 7.3 and Figure 7.17b. The second isomer of Ta2B3− (Figure 7.16c-II) is closed shell with Cs symmetry (1A′), which is 0.12 eV higher in energy at BP86 level. The simulated spectrum of this isomer119 also seems to be consistent with the experimental spectrum. Thus, at the current level of theory, we cannot assign definitively which isomer is responsible for the observed spectra. Both structures are similar, except that the Cs isomer features a slightly stronger and shorter Ta–Ta bond. Ta2B4−: The C2v (2A1) structure (Figure 7.16e-I) is clearly the ground state for Ta2B4−. The X band in the experimental spectra is broad and congested, suggesting that it may contain multiple detachment channels. Indeed, the calculated VDEs for the first three detachment channels, from the SOMO 11a1 and the 5b1 orbital (T and S), are very close to each other (Table 7.4), consistent with the broad X band. The 11a1SOMO is mainly a Ta–Ta σ bonding orbital, as shown in Figure 7.18c and Figure 7.18c for the spin density. Detachment of the electron in the SOMO leads to a slightly increased Ta–Ta bond length in the neutral ground state of Ta2B4 (Figure 7.16f-I). The calculated VDEs from the 10a1 orbital, 2.37 eV (T) and 2.39 eV (S), corresponding to the removal of the spin-down and spin-up electrons, are in good agreement the observed VDE of the A band (2.43 eV). The 10a1 orbital, which is primarily a σd-d bonding orbital (Figure 7.18c), becomes the HOMO of the closed- shell neutral Ta2B4 cluster. Each of the subsequent experimental spectral features also corresponds to multiple detachment channels. Overall, the calculated spectral pattern from the global minimum of Ta2B4− is in good agreement with the experimental observation 270 (Table 7.4 and Figure 7.17c), lending considerable credence to the global minimum identified. Ta2B5−: The comparisons between experiment and theory for the ground state of Ta2B5− are presented in Table 7.4 and Figure 7.17d. The ground state of Ta2B5− is closed shell (1A1). The first calculated VDE corresponds to electron detachment from the 3a2 HOMO, which is an antibonding δ orbital (Figure 7.18d). The SOMO (3a2) of the neutral cluster upon removing an electron from the anion HOMO is shown in Figure 7.18d and its spin density (Figure 7.18d) is seen to concentrate on the two Ta atoms. The calculated VDE of 2.02 eV is in good agreement with the experimental value of 1.93 eV (Table 7.4). The next two calculated VDEs correspond to electron detachments from HOMO−1 (11a1) and HOMO−2 (5b1), which are in good agreement with the experimental bands A and B, respectively. The next three detachment channels are derived from the 7b2, 2a2, and 6b2, which correspond to the bands C, D, and E at VDEs of 2.87, 3.10, and 3.54 eV in the experimental spectra, respectively. The higher detachment channels are also in good agreement with the experiment. The weak feature on the low binding energy side of the experimental spectra of Ta2B5− (Figure 7.15) suggests possible contributions from low-lying isomers. The second low-lying isomer Figure 7.16g-II is 0.06 eV and 0.23 eV higher in energy at BP86 and CCSD(T) level of theory, respectively. The simulated spectrum for this isome119 shows that its binding energies are similar to those of the global minimum. Thus, this isomer can be ruled out to be the contributor to the low binding energy feature, in agreement with its relatively high energy at the CCSD(T) level. The third isomer (Figure 7.16g-III) is open-shell (3B2), which is 0.25 eV above the global minimum at BP86. However, the VDE of its 271 detachment channel119 is at a lower binding energy and this isomer is a possible contributor to the observed low binding energy feature. Thus, at higher level of theory, we expect that the relatively energy of this isomer should be lower than the BP86 calculation suggests. Therefore, overall the theoretical results are in good agreement with the experimental data, confirming the ground state and low-lying isomers for the Ta2B5− cluster. Figure 7.17 Comparison of the experimental spectra of Ta2Bx− (x = 2−5) with the simulated spectra from the lowest energy structures. The simulated spectra were made by fitting the calculated VDEs with unit-area Gaussian functions of 0.10 eV half width. 272 Figure 7.18 The highest occupied orbitals and the Mülliken spin density for (a) Ta2B2−, (b) Ta2B3− (C2v, 3B2), (c) Ta2B4− (C2v, 2A1), and (d) Ta2B5− (C2v, 1A1). 7.3.5 Structural Evolution The current study shows that the structures of the Ta2Bx − (x = 2 − 5) clusters are all related and can be viewed as forming an equatorial boron belt around a Ta–Ta dimer with increasing x, as shown in Figure 7.19. Starting from the C2v Ta2B2−, each additional B atom is added to the boron moiety to extend the boron chain around the Ta–Ta bond (Figure 7.19). Even though in a couple of cases the global minimum structures cannot be definitively assigned, this basic structural evolution holds true because all the low-lying isomers of Ta2Bx− display similar structures with the same B-B connectivity. The structural evolution is due to the strong B–B bonding, which leads to the formation of monotantalum metal- centered B10 ring in Ta©B10−.118 Thus, we expect that with additional B atoms one may also achieve a closed equatorial boron ring around the Ta–Ta bond. In fact, we already see that the Ta–Ta bond length in Ta2B5− (Figure 7.16g-I) is significantly longer than that in Ta2B4− (Figure 7.16e-I), en route to a closed boron ring with a bipyramidal structure with a 273 much longer Ta–Ta distance. Further studies of larger dinuclear boron clusters to observe such structures would be interesting and are forthcoming. Figure 7.19 Structure evolution of Ta2Bx− (x = 2 − 5). Geometries of the second row are projections viewing along the Ta-Ta axis. 7.3.6 Conclusions We present a systematic study of the Ta2Bx−/0 (x = 2 − 5) clusters using photoelectron spectroscopy and DFT calculations. Photoelectron spectra were obtained for the size-selected anionic clusters, revealing congested electronic transitions for all systems. Extensive DFT calculations were performed at the BP86 level to locate the ground states and low-lying isomers for the Ta2Bx−/0 (x = 2−5) clusters. Qualitative agreement between the experimental data and theoretical calculations was obtained, lending support for the global minimum structures from the DFT calculations. The ground states of Ta2Bx− (x = 2 − 5) are shown to possess C2v (2A1), C2v (3B2), C2v (2A1), and C2v (1A1) structures, respectively, which can all be viewed as a partial equatorial boron ring around a Ta–Ta bond. The global minima of the 274 neutral clusters follow the same pattern and are similar to the respective anions. The current results reveal that the strong boron–boron bonding dominates the structures of the di- tantalum clusters. 7.4 Hexagonal Bipyramidal Ta2B6−/0 Clusters: B6 Rings as Structural Motifs 7.4.1 Introduction A combined experimental and theoretical study on di-tantalum doped boron clusters (Ta2Bn−) were carried out, showing that boron atoms build around a Ta–Ta dimer equatorially from Ta2B2− to Ta2B5−,119 in which strong Ta–Ta bonding still exists. The equatorial ring is expected to close as the number of boron atoms increases. Herein we report a joint experimental and theoretical study on the Ta2B6− and Ta2B6 clusters. We found that the most stable structures of both the neutral and anion are D6h bipyramidal, similar to the recently discovered MB6M structural motif in the Ti7Rh4Ir2B8 solid compound.317 7.4.2 Experimental Results The photoelectron spectra of Ta2B6− are shown in Figure 7.20 at four photon energies. The 532 nm spectrum (Figure 7.20a) displays one strong feature X (1.59 ±0.03 eV) and a weak feature labeled with ‘*’ (1.88 eV). Since no clear vibrational progression was resolved for band X, the ADE was evaluated by drawing a straight line along the leading edge of the X band in the 532 nm spectrum and then adding the experimental resolution to the intersection with the binding energy axis. The ADE so measured is 1.51 ± 0.03 eV, which also represents the EA of neutral Ta2B6. The next major detachment band, labeled as A in Figure 7.20, has a VDE of 2.74 eV. The energy separation of 1.15 eV between bands X and 275 A represents a large gap between the HOMO and LUMO of Ta2B6, indicating its high electronic stability with a closed-shell electron configuration. Three more well-resolved bands (B, C, and D) are observed in the 266 nm spectrum (Figure 7.20c). The intense band C at 3.61 eV is quite broad and it may contain multiple detachment transitions. More detachment transitions were observed in the 193 nm spectrum (Figure 7.20d), band E at a VDE of 4.57 eV and band F at 5.11 eV. There are more congested features at higher binding energies beyond 5.5 eV, where the signal-to-noise ratios were poor. The label G is only for the sake of discussion. All the VDEs are summarized in Table 7.6, where they are compared with the calculated VDEs of the global minimum of Ta2B6−. The weak signal labeled as “*” at 1.88 eV is probably due to contributions of a low- lying isomer. This feature is resolved into a well-defined peak in the 355 nm spectrum (Figure 7.20b). Weak signals were also present at approximately 2.5 eV as a tail to the A band. These signals seemed to be enhanced in the 355 nm spectrum and may have the common origin as the 1.88 eV feature. 7.4.3 Theoretical Results and Comparison with Experimental Results Global minimum searches for Ta2B6− and Ta2B6 were performed using DFT with analytical gradients. Candidate structures with a variety of initial geometries and spin multiplicities were taken into consideration (see the Experimental Section). The D6h- bipyramid structure (2A1g; Figure 7.21) with a B6 ring turned out to be the global minimum for Ta2B6−. The B-B bond length is 1.607 Å and the Ta-B bond length is 2.222 Å. The neutral Ta2B6 was found to have a very similar D6h bipyramidal structure (1A1g) with the same B-B bond length as that in the anion except that the Ta–B distance is shortened by about 0.02 Å. The nearly identical structures of the anion and neutral suggest the first electron detachment 276 is likely from a non-bonding orbital, confirming the electronic and structural stability of Ta2B6. The similar structures of the anion and neutral species are also consistent with the sharp ground-state PES band (X). Figure 7.20 Photoelectron spectra of Ta2B6− at (a) 532 nm, (b) 355 nm, (c) 266 nm and (d) 193 nm. 277 Figure 7.21 Optimized structures of Ta2B6− and Ta2B6 at the BP86/Ta/ Stuttgart+2f1g/B/aug-cc-pVTZ level of theory. The bond lengths are in Å. To further confirm the bipyramidal global minimum structure for Ta2B6−, we computed the VDEs at BP86/Ta/Stuttgart+2f1g/B/aug-cc-pVTZ level of theory, which was found previously to give superior results for energetic properties for clusters involving early transition metals.116,363,364 The calculated VDEs are compared with the experimental data in Table 7.6. The first VDE corresponds to electron detachment from the 3a1g HOMO to yield the 1A1g neutral ground state. The calculated VDE of 1.67 eV agrees well with the experimental value of 1.59 eV. The calculated ADE of 1.63 eV is also in good agreement with the experimental ADE of 1.51 eV. The next detachment channel is from the 1e2u HOMO−1 to produce a3E2u final state. The calculated VDE of 2.77 eV is in excellent agreement with the VDE of the A band at 2.74 eV. The calculated VDE for the corresponding singlet state is 2.97 eV, which is assigned to the observed PES band B at 3.08 eV. The calculated higher binding energy detachment channels are all in good agreement with the experimental observations (Table 7.6). Indeed, a number of detachment channels contribute to the congested features above 5.5 eV (bands G). The excellent overall agreement 278 between the calculated VDEs and the experimental data lends considerable credence to the D6h global minimum found for Ta2B6−. The second low-lying isomer (D6h, 2A2u) of Ta2B6− is 0.19 eV and 0.31 eV above the global minimum at the BP86 and CCSD(T) levels of theory, respectively.365 The structure of this isomer is similar to the global minimum, corresponding to electron occupation of the LUMO+1 of the D6h neutral Ta2B6. Its first calculated VDE of 1.46 eV is lower than that of the global minimum by about 0.2 eV. The lower binding-energy side of band X in the experimental spectra (Figure 7.20) was pretty clean, indicating that the population of this isomer in our experiment was negligible. The next low-lying isomer at the CCSD(T) level is 0.76 eV above the global minimum. This isomer has a quartet electronic state (4A2u) with D2h symmetry. Even though it is energetically unfavorable, it might be a long-lived state because the relaxation to the ground state is spin-forbidden. Interestingly, its first VDE is calculated to be 1.94 eV,365 in good agreement with the “*” feature at 1.88 eV (Figure 7.20). Its second VDE was calculated to be 2.18 eV, consistent with the low-binding-energy tail off band A. Thus, we conclude that this isomer was weakly populated in our experiment and it might also contribute to the congestion of the higher binding energy side of the observed spectra. Such “spin-protected” high-lying isomers have been observed in a number of clusters previously.131,133,366 279 Table 7.6 Observed VDEs for Ta2B6− compared with theoretical values. All energies are in eV. Band VDE(exp)a Final States and electronic Configuration BP86b 1 X 1.59(3) A1g … 1e2g41a2u22a1g21b2u21e1g42e1u41e2u43a1g0 1.67 3 A 2.74(5) E2u … 1e2g41a2u22a1g21b2u21e1g42e1u41e2u33a1g1 2.77 1 B 3.08(5) E2u … 1e2g41a2u22a1g21b2u21e1g42e1u41e2u33a1g1 2.97 3 E1u … 1e2g41a2u22a1g21b2u21e1g42e1u31e2u43a1g1 3.37 C 3.61(5) 1 E1u … 1e2g41a2u22a1g21b2u21e1g42e1u31e2u43a1g1 3.66 3 D 4.21(5) E1g … 1e2g41a2u22a1g21b2u21e1g32e1u41e2u43a1g1 4.18 1 E 4.57(5) E1g … 1e2g41a2u22a1g21b2u21e1g32e1u41e2u43a1g1 4.26 3 B2u … 1e2g41a2u22a1g21b2u11e1g42e1u41e2u43a1g1 4.90 F 5.11(5) 1 B2u … 1e2g41a2u22a1g21b2u11e1g42e1u41e2u43a1g1 4.99 3 A1g … 1e2g41a2u22a1g11b2u21e1g42e1u41e2u43a1g1 5.69 1 A1g … 1e2g41a2u22a1g11b2u21e1g42e1u41e2u43a1g1 5.80 G ~5.8 3 A2u … 1e2g41a2u12a1g21b2u21e1g42e1u41e2u43a1g1 6.04 1 A2u … 1e2g41a2u12a1g21b2u21e1g42e1u41e2u43a1g1 6.14 a Numbers in the parentheses are the uncertainty in the last digit. b The VDEs were calculated at BP86/Ta/Stuttgart+2f1g/B/aug-cc-pVTZ level of theory. 7.4.4 Chemical Bonding Analyses Figure 7.22 displays the valence conical MOs for the global minimum of Ta2B6−. The HOMO (a1g) is a non-bonding orbital composed mainly of the Ta 6s and 6p atomic orbitals. Electron detachment from this orbital is not expected to change the symmetry or structure of the resulting neutral cluster much, in agreement with the nearly identical structures of the D6h Ta2B6− and Ta2B6 and the sharp ground state PES band (X). The HOMO−1 (e2u) is doubly degenerate, consisting mainly of two Ta 5d δ-type orbitals with antibonding characters. The HOMO−2 (e1u) and HOMO−5 (a1g) are three σ-type orbitals delocalized mainly over the B6 ring, whereas the HOMO−3 (e1g) and HOMO−6 (a2u) are three π type orbitals delocalized over the B6 ring. All these six boron-based orbitals interact with the Ta 5d orbitals along the Ta–Ta axis. 280 Figure 7.22 Valence conical orbitals of Ta2B6− at the BP86/Ta/Stuttgart+2f1g /B/aug-cc-pVTZ level of theory. We analyzed the chemical bonding of the closed-shell D6h Ta2B6 using the AdNDP method. The AdNDP analyses (Figure 7.23) provide a relatively simple bonding picture for the Ta-B6-Ta inverse-sandwich structure. There are six 4c-2e σ-type bonds, each of which involves one B-B bond and the two Ta atoms. These six bonds are essentially the six B-B bonds, forming the B6 ring. The interactions between the B6 ring and the apex Ta atoms are through the six 4c-2e π bonds and, interestingly, two totally delocalized 8c-2c bonds. Hence, the AdNDP analyses reveal that all 28 valence electrons in Ta2B6 are participating in the chemical bonding, underlying the electronic and geometrical stability of the bipyramidal Ta2B6. The chemical bonding analyses show that there is no significant direct Ta–Ta interaction, consistent with the relatively long Ta–Ta distance (3.01 Å) in Ta2B6. Interestingly, in [(Cp*Re)2B6H4Cl2], the Re–Re distance is much shorter (2.689 281 Å),322 indicating significant Re–Re bonding, probably due to the larger B6 ring in the B6H4Cl2 moiety. Figure 7.23 Chemical bonding analyses of Ta2B6 using the AdNDP method. 7.4.5 Conclusions In conclusion, we report the first gas-phase cluster containing a planar B6 ring coordinated by two Ta atoms in a bipyramidal structure. Photoelectron spectroscopy revealed that neutral Ta2B6 is an electronically highly stable system with a closed-shell electron configuration and a large HOMO−LUMO gap. Global minimum searches found a bipyramidal Ta2B6 to be the most stable structure. AdNDP analyses revealed the nature of the B6 and Ta interactions and uncovered strong covalent bonding between B6 and Ta. The D6h- TaB6Ta gaseous cluster is reminiscent of the structural pattern in the ReB6X6Re core in the [(Cp*Re)2B6H4Cl2]322 and the TiB6Ti motif in the newly synthesized Ti7Rh4Ir2B8 solid-state compound.317 The current work provides an intrinsic link between a gaseous cluster and motifs for solid materials. Continued investigations of the transition-metal boron clusters may lead to the discovery of new structural motifs involving pure boron clusters for the design of novel boride materials. 282 7.5 Complexes between Planar Boron Clusters and Transition Metals: the Case of CoB12– and RhB12– 7.5.1 Introduction In the studies of the M©Bn– molecular wheels, the position of the metal atom has been found to depend on two factors: the electronic requirement to fulfill double aromaticity and the geometrical factor depending on the size of the metal atom.116,120 The geometrical factor requires that the central atom fit into the cavity of a monocyclic ring. The electronic factor requires the right number of valence electrons to achieve electronic stability of the high-symmetry structure. It was shown that a systematic destabilization of the M©B10– molecular wheel going up the periodic table from Ta to V is due to the decreasing metal atom size.116 The smaller atomic size and the more contracted 3d orbitals make the V atom energetically unfavorable to fit inside a B10 ring to form a stable V©B10– molecular wheel. Hence, VB10– has a boat-like structure with the V bonded above a B10 unit, which resembles the structure of the bare B10 cluster. This is the largest boron cluster, observed thus far to act as a ligand. On the basis of these ideas, one would expect to find similar clusters with a transition metal atom coordinated in the same manner with respect to a quasiplanar boron framework. The boron cluster should maintain a similar planar geometry to that of the undoped boron cluster of the same stoichiometry. Then, the question is: what is the largest planar boron ligand that will maintain its structure in a half-sandwich-type complex with a metal atom? A good candidate is the highly stable quasiplanar B12, an aromatic cluster with a large HOMO−LUMO gap, as revealed from the photoelectron spectra of B12–.133 It has a very interesting bowl structure: a nine-membered outer ring and an inner B3 triangle that is 283 slightly out of plane. Theoretical calculations suggested that monometal doped B12 clusters could form the half-sandwich clusters.367,368 The B12 fragment in such doped clusters has the C3v symmetry as the bare B12 cluster, but is more curved. However, there has been no experimental evidence of such structures. In the current study, we report two transition-metal-doped B12 clusters, i.e., RhB12– and CoB12–, which are characterized by photoelectron spectroscopy and ab initio calculations. The photoelectron spectra of both clusters show relatively simple spectral patterns, suggesting they may have similar high symmetry structures. Extensive structural searches found that the half sandwich structures are indeed the global minima for both clusters. Chemical bonding analyses showed that the B12 motif maintains similar structures as the bare cluster, but becomes slightly more curved toward to the metal atoms. Both σ and π bonds are found between the B12 motif and the metal atom. 7.5.2 Experimental Results The photoelectron spectra of CoB12– and RhB12– at two different photon energies are shown in Figure 7.24. The spectra measured at 193 nm reveal more detachment features, while those obtained at 266 nm provide slightly better spectral resolution. The VDEs for all observed bands are given in Table 7.7, where they are compared with the calculated VDEs. CoB12–: The 193 nm spectrum (Figure 7.24a) exhibits a relatively simple spectral pattern with five resolved bands, labeled as X and A–D. All the PES bands are quite broad, suggesting significant geometry changes between the anion and the neutral states or overlapping of multiple detachment transitions. The X band represents the detachment transition from the ground state of CoB12– to that of neutral CoB12. The VDE and ADE of the X band are measured as 3.37 eV, 3.23 eV, respectively. The VDE of band A is measured as 284 4.20 eV from the 266 nm spectrum, whereas the VDEs of band B, C, and D are obtained from the 193 nm spectrum as 4.58 eV, 5.55 eV, and 6.1 eV, respectively. The band D is tentatively assigned due to the low signal-to-noise ratio in the high binding energy side of the 193 spectrum. RhB12–: The spectra of RhB12– are similar to those of CoB12– except the relative intensities and splitting of certain spectral bands. For example, the lowest binding energy band of RhB12– at 193 nm (Figure 7.24c) is the most intense band and it is resolved into two relatively sharp features (X and A) in the 266 nm spectrum (Figure 7.24d). This splitting could be due to either the Jahn–Teller or spin–orbit effect. The VDE of the lowest binding energy band X is measured to be 3.49 eV and its ADE is measured to be 3.45 eV from the 266 nm spectrum. Feature A is split from band X by 0.16 eV with a VDE of 3.65 eV. The VDEs of the next two bands B and C are measured to be 4.39 and 4.64 eV, respectively. Band D at ~5.5 eV is fairly broad and likely consists of several overlapping detachment channels. Similar to the 193 nm spectrum of CoB12–, the signal-to-noise ratio of the high binding energy side of the 193 nm spectrum of RhB12– is also poor and the sharp peak at 6.13 eV cannot be assigned as a single vibronic transition. A VDE of ~6.2 eV is tentatively identified for the band E, similar to the band D in the CoB12– case. 285 Figure 7.24 Photoelectron spectra of CoB12− (a,b) and RhB12− (c,d) at 193 nm and 266 nm. The 266 nm spectra offer better spectral resolution than the 193 nm spectra. 7.5.3 Theoretical Results The global minimum structures of CoB12– and RhB12– are similar, as shown in Figure 7.25. Both anions possess C3v symmetry with a half sandwich structure, in which the B12 moiety is similar to the bare B12 cluster. The B12 framework is slightly puckered to achieve optimal interactions with the metal atoms. In RhB12–, the distance between Rh and the three inner boron atoms is slightly larger (2.09 Å) than for Co (1.97 Å), consistent with the atomic radii of the two metal atoms. All B–B bond distances in RhB12– and CoB12– are similar to those in the bare B12 cluster (Figure 7.26a). The only significant difference comes from the curvature of the B12 framework: the peripheral atoms bend out of the plane of the inner triangle by 0.70 Å and 0.88 Å in RhB12–, by 0.74 Å and 0.94 Å in CoB12–, whereas in pure B12 these distances are 0.22 Å and 0.35 Å, respectively. 286 The inner atoms in the planar B13+ cluster with a 9-atom periphery213,216 have been shown previously to be fluxional with an internal rotation barrier of only 0.1 kcal/mol,219 similar to that in the planar B19– cluster.104,218 The facile internal rotation in B13+ and B19– is akin to “molecular Wankel motors”.218,219 Figure 7.26 shows results of the internal rotation in the pure B12 cluster, compared with that in MB12–. In both cases, the 60° rotation of the inner B3 triangle results in a transition state, corresponding to a saddle point with an imaginary frequency. It seems that complexion of B12 with a metal atom significantly reduces the barrier of the internal rotation. Figure 7.25 Two views of the global minimum structures of (a) RhB12− and (b) CoB12−. Their point group symmetries and spectroscopic states are shown in parenthesis. Bond lengths are given in Å. 287 Figure 7.26 Rotational barriers of the inner boron triangle with respect to the outer ring for B12 and MB12−. They results are obtained at the PBE0/aug-cc-pVTZ and PBE0/M/Stuttgart/B/aug-cc-pVTZ (M=Rh, Co) levels of theory, respectively. NIF denotes number of imaginary frequencies. Table 7.7 Observed VDEs of CoB12− and RhB12− compared with the calculated values. All energies are in eV. Feature VDE (exp)a Final State and Electronic Configuration VDE CoB12− (C3v, 1A1)b TD(BP86) 2 2 2 2 4 4 2 4 2 4 4 3 X 3.37(4) E … 1a2 3a1 4a1 3e 4e 5a1 5e 6a1 6e 7e 8e 3.39 2 2 2 2 4 4 2 4 2 4 3 4 A 4.20(4) E … 1a2 3a1 4a1 3e 4e 5a1 5e 6a1 6e 7e 8e 4.28 2 2 2 2 4 4 2 4 2 3 4 4 E … 1a2 3a1 4a1 3e 4e 5a1 5e 6a1 6e 7e 8e 4.52 B 4.58(5) 2 2 2 2 4 4 2 4 1 4 4 4 A1 … 1a2 3a1 4a1 3e 4e 5a1 5e 6a1 6e 7e 8e 4.88 2 2 2 2 4 4 2 3 2 4 4 4 E … 1a2 3a1 4a1 3e 4e 5a1 5e 6a1 6e 7e 8e 5.72 C 5.55(4) 2 2 2 2 4 4 1 4 2 4 4 4 A1 … 1a2 3a1 4a1 3e 4e 5a1 5e 6a1 6e 7e 8e 5.88 2 2 2 2 4 3 2 4 4 2 4 4 D ~6.1 E … 1a2 3a1 4a1 3e 4e 5a1 5e 6e 6a1 7e 8e 6.21 − 1 c RhB12 (C3v, A1) TD(PBE0) X 3.49(4) 2 E … 3e44e45e45a126e46a127e48e3 3.42 A 3.65(4)d B 4.39(4) 2 E … 3e44e45e45a126e46a127e38e4 4.59 C 4.64(5)e 2 E … 3e44e45e45a126e36a127e48e4 5.26 D ~5.5 2 4 4 4 2 4 1 4 4 A1 … 3e 4e 5e 5a1 6e 6a1 7e 8e 5.41 2 4 4 3 2 4 2 4 4 E ~6.2 E … 3e 4e 5e 5a1 6e 6a1 7e 8e 6.34 a Numbers in parentheses represent the uncertainty in the last digit. b The VDEs were calculated at TD-BP86/Co/Stuttgart/B/aug-cc-pVTZ// BP86/Co/Stuttgart/B/aug-cc-pVTZ. c The VDEs were calculated at TD-PBE0/Rh/Stuttgart/B/aug-cc-pVTZ// PBE0/Rh/Stuttgart/B/aug-cc-pVTZ. d 2 This feature is assigned to the second spin–orbit component of the E ground state. e 2 This is assigned to the Jahn-Teller or spin-orbit splitting of the E excited state. 288 7.5.4 Comparison between Experimental and Theoretical Results CoB12–: The global minimum of CoB12– is closed shell with a 1A1 ground state and thus only doublet final states are expected upon one electron detachment. The HOMO (8e) of CoB12– is doubly degenerate, resulting in a 2E final state upon one electron detachment (Table 7.7). This doubly degenerate final state is unstable against Jahn–Teller distortion and it can also be split by spin–orbit effects, consistent with the broad width of the X band (Figure 7.24b). The calculated first VDE of 3.39 eV agrees well with the 3.37 eV VDE measured for the X band (Table 7.7). The calculated ADE of 3.22 eV is also in good agreement with the measured value of 3.23 eV. The next three detachment channels from HOMO−1 (7e), HOMO−2 (6e), and HOMO−3 (6a1) give rise to calculated VDEs of 4.28, 4.52, and 4.88 eV, respectively, which are fairly close to each other and are in good agreement with the VDEs for the broad and overlapping bands (4 to 5 eV) labeled A and B (Figure 7.24a). Following a large energy gap, the next two detachment channels from the 5e and 5a1orbitals yield VDEs very close to each other and are assigned to band C. The detachment from the 4e orbital has a calculated VDE of 6.21 eV, in good agreement with that of band D at 6.1 eV. Overall, the calculated VDEs and spectral pattern are in excellent agreement with the experimental PES data, lending considerable credence to the C3v global minimum of CoB12–. RhB12–: The electronic structure and MO configuration of RhB12– (Table 7.7) are similar to those of CoB12–. Electron detachment from the doubly degenerate HOMO (8e) produces the 2E neutral ground state with a calculated VDE of 3.42 eV, which agrees well with that of band X at 3.49 eV. However, the second detachment channel from HOMO−1 (7e) yielded a calculated VDE of 4.59 eV and cannot be responsible for band A. Comparison of 289 the spectra of RhB12– with that of CoB12– suggests that band A in RhB12– must come from the SO splitting of the 2E neutral ground state. Spin–orbit calculations show a SO splitting of 0.1 eV, consistent with the energy difference of bands X and A (0.16 eV). The VDE of electron detachment from HOMO−2 (7e) is calculated at 4.59 eV with negligible SO splitting (<0.01 eV). This VDE agrees well with the VDEs of bands B (4.39 eV) and C (4.64 eV), which are tentatively assigned to the Jahn–Teller splitting of the excited 2E final state (Table 7.7). Similar Jahn–Teller splitting from detachment of an electron from the 7e orbital was expected to occur in the CoB12– case. However, as shown above, the 6e and 5a1 detachment channels have very close VDEs, overlapping with that of the 7e orbital and preventing a clear observation of the Jahn–Teller splitting in the CoB12– spectrum. In the case of RhB12–, detachments from the 6e and 5a1 orbitals yield much higher VDEs (5.26 and 5.41 eV, respectively), compared with those in the CoB12– case, corresponding to the broad D band at 5.5 eV (Figure 7.24c and Table 7.7). Finally, detachment from the 5e orbital results in a calculated VDE of 6.34 eV, consistent with band D at 6.2 eV. Even though the Jahn–Teller splitting cannot be treated in the current calculations, the overall agreement between the theoretical results and the experimental data is quite good, in particular, by comparing the results between RhB12– and CoB12–, confirming the C3v global minimum of RhB12–. 7.5.5 Chemical Bonding Analyses The chemical bonding of RhB12– was analyzed using the AdNDP method, as shown in Figure 7.27. The AdNDP analyses for CoB12– are almost identical and thus are not shown. As given in Figure 7.27, the occupation numbers of all the identified bonds range from 1.83 to 2.00 |e|. 290 The chemical bonding of the B12 moiety is reminiscent of the bare quasi-planar B12 cluster,133 including nine 2c–2e B–B σ bonds on the outer ring and four 3c–2e σ bonds delocalized over the surface of the B12 moiety. All the π bonds in the B12 moiety are used to form bonds with the metal atom. The metal–B12 interactions are described by three types of bonds. First, there is one clear 4c–2e π bond between the metal and the B3 fragment. Second, there are four totally delocalized 13c–2e bonds with ON = 2.00 |e|. These four bonding elements are very interesting and they can be viewed as consisting of both σ and π interactions between the metal and the entire B12moiety. Finally, there are three localized 2c– 2e σ bonds between Rh and the three nearest boron atoms (ON = 1.83 |e|). These three metal– boron covalent bonds are unique, quite different from the primarily ionic interactions observed previously in the C7v AlB7−, C8v AlB8–, or C8v LiB8– half-sandwich complexes between the metal atom and the quasi-planar B7 or B8 motif.134,292 The presented inclination to form localized bonds between metals and boron might be explained by the difference in the electronegativity values, which is almost negligible for Co and Rh atoms: 0.16 and 0.24, respectively. Significantly larger difference is seen for Al and Li atoms (0.43 and 1.06, respectively), which is responsible for the ionic interaction. We believe that electronegativity difference could be one of the useful design tools for such systems. The Co–B and Rh–B bond lengths are found to be 2.25 Å and 2.35 Å at the PBE0 level of theory in the CoB12– and RhB12– clusters, respectively. It should also be pointed out that these bonds were also revealed using the NBO analysis, which showed that the contributions of B to the metal– boron bonds are 12% and 14% for Rh and Co, respectively. It is interesting to point out that there are only two lone pairs on the metal atom with ON = 1.92 |e|. The common oxidation states of Co and Rh are II (d7) and III (d6).4,369 The 291 current bonding analyses suggest that the metal atom has a rare oxidation state of M0 (d9) in the MB12–complexes, even though six electrons participate in the formation of M–B bonds. Since the contribution of B to the M–B bonds is quite low, these six electrons might be considered primarily as lone pairs on the atom of metal. Furthermore, these two lone pairs provide possible sites for additional coordination by suitable ligands, which may allow the MB12 complexes to be synthesized in bulk. Recently, a planar B6 cluster has been found to be sandwiched by two Ta atoms in the D6h Ta2B6 cluster,365 similar to the B6 building blocks observed in a solid metal boride compound.317 The current study demonstrates that larger planar boron clusters may also be possible as ligands or solid building blocks. Figure 7.27 AdNDP analyses for RhB12−. 292 7.5.6 Conclusions We have carried out a combined experimental and theoretical study on two transition metal and B12 complexes, CoB12– and RhB12–. These two valence isoelectronic clusters have similar photoelectron spectral patterns, suggesting similarity of their structures. Extensive computational searches established that both CoB12– and RhB12– have C3v half-sandwich global minimum structures with the B12 cluster coordinating to the metal atom. The B12 moiety in the MB12– complexes maintains a similar geometry as the bare quasiplanar B12 cluster, except a slightly larger out-of-planar distortion to optimize bonding with the metal atom. Chemical bonding analyses revealed strong interactions between the metal atom and the B12 moiety via both σ and π bonds. More significantly, the Co and Rh atoms assume a rare oxidation state of M0(d9) in the MB12– complexes. The two d-electron lone pairs on the metal atom provide possible sites for appropriate ligands for further coordination to the metal, suggesting novel compounds with planar boron clusters as building blocks may be viable. 293 Chapter 8 Gaseous Uranium Compounds Actinide chemistry has attracted extensive research attention in recent years because of its increasing importance in nuclear industry and environmental science.370 The electronic structures of actinide compounds are extremely complicated due to strong electron correlation and relativistic effects. While electronic spectroscopy is critical for characterizing the electronic structure of molecules, interpretation and assignment of such spectra for actinides are challenging because of experimental difficulties and the lack of accurate theoretical data on the electronic excited states. Application of standard electronic structure methods developed for weakly correlated systems to actinides with an open 5f-shell is either inappropriate or inefficient. Therefore, high resolution electronic spectra are keenly needed, in order to develop and calibrate electronic structure models suitable for actinide systems, in which electron-electron correlations are strong. In this chapter, we present combined PES and quantum chemistry studies of four uranium molecules: UO2−, UFx− (x = 2 – 4). Strong electron-electron correlations are observed between the 7s electrons, resulting in numerous unexpected electronic transitions based on Koopmans’ Theorem for both UO2− and UF2−. The UF3− and UF4− do not have s electron pair and thus no correlation induced extra features are observed. These experimental observations provide new features for the calibration of theoretical methods for actinide systems. 294 8.1 Strong Electron Correlation in UO2 − 8.1.1 Introduction The UO2 molecule has been an important model system for actinide chemistry and has been extensively studied both experimentally and theoretically.371-385 UO2 is known to be a linear molecule with a 32u ground state and a (7sg)1(5fu)1 electron configuration. 373-383 371-373 The ground-state vibrational frequencies of UO2 were measured in rare gas matrices. An interesting matrix effect, that leads to the so-called ground-state reversal, was observed, where the ground state of UO2 in the Ar matrix was shown to have changed to a 3Hg state with a (5fu)1(5fu)1 configuration owing to strong Ar-UO2 interactions,379,385 although such a state switching was not observed in fluorescence spectroscopy of UO2 in an Ar matrix.378 The electronic spectroscopy of gaseous UO2 has also been studied, confirming its 32u ground state and its first excited state of 33u with an excitation energy of only 360 cm−1.377 A number of excited states of UO2 have also been observed and compared with theoretical results.374-378,381-383 The linear UO2 molecule is relevant to the uranium oxide solids used as nuclear fuels and it can also be viewed as the two-electron reduced version of the ubiquitous uranyl dication (UO22+).386 Despite the large number of studies on the UO2 molecule and its excited states, relatively little is known about UO2−, in which the U atom is in an oxidation state of III. The UO2− anion was observed in a Ne matrix4 and in the gas phase by mass spectrometry.387,388 Its ground state was calculated to be 2u with a (7sg)2(5fu)1 electron configuration.373 295 In this contribution, we report the first study of the UO2− anion using PES. PES is a powerful experimental technique to probe the electronic structure of molecules, providing direct information about electronic states or approximately the one-electron energy levels as predicted by the MO theory. As a cornerstone of modern chemical bonding models, the MO theory is a triumph for quantum mechanics. The validity of the MO theory was confirmed by PES since the 1960’s. The Koopmans’ theorem, which states that the ionization energy is directly related to the MO energies (IEi = -ɛi), is the bridge between PES and the MO theory. Despite its approximate nature, the Koopmans’ theorem works surprisingly well for organic compounds, but breaks down frequently in inorganic compounds. In heavy-element systems, the failure of this theorem is expected, but it is difficult to be probed experimentally. Here we show that the Koopmans’ theorem breaks down severely for the electron detachment from UO2−, as a result of significant electron correlations. We report the first well-resolved PES spectra of UO2−, providing a wealth of experimental information on the excited states of the neutral UO2 molecule, many of which are due to multi-electron transitions. We have performed highly accurate ab initio wave function theory (WFT) calculations using multi-configurational and the coupled cluster [CCSD(T)] approaches with corrections of scalar and spin-orbit coupling (SOC) relativistic effects to interpret the anion PES spectra. We show that the correlations are extremely strong between the U7s electrons in UO2−. Both the initial states (IS) and final states (FS) of the electron detachment from UO2−  e− + UO2 have to be accurately calculated to understand the complicated PES spectra. The highly resolved PES spectra of UO2− thus provide a prototype for calibrating and benchmarking various relativistic quantum chemistry methods, especially those developed for systems with strong electron correlations. 296 8.1.2 Experimental Results The PES spectra of UO2− at four photon energies from 532 to 193 nm are shown in Figure 8.1. At 193 nm (Figure 8.1d), three strong PES bands are observed. The broad low binding energy band labeled as A should be due to electron detachments from the U-based non-bonding 7s5f orbitals, whereas the much higher binding energy bands D and E and the broad signals around 6 eV should be due to electron detachment from the deeper O2p-based bonding orbitals. Weak electron signals are also observed in the energy gap region between 1.5 and 5 eV in the 193 nm spectrum, but not well resolved. At 266 nm (Figure 8.1c) and 355 nm (Figure 8.1b), however, numerous sharp peaks are resolved for the weak signals above 1.5 eV in the energy gap region. The band A is also resolved in the 355 nm spectrum into a short vibrational progression (~890 cm−1), which should be due to the symmetric stretching of UO2. At 532 nm (Figure 8.1a), band A is further resolved into numerous fine features, which should be due to the overlap of several electronic states. The peak X resolved at the lowest binding energy of 1.159 eV should correspond to the ground-state transition, which defines the ADE of UO2− or the EA of neutral UO2. The separation of peak X and the onset of band A at 1.202 eV, which should correspond to the first excited state of UO2, is only 0.043 eV (350 cm−1). This quantity is in excellent agreement with the excitation energy of the first excited state of gaseous UO2 reported previously,377 as compared in Table 8.1. In addition to the stretching progression, which is measured more accurately at 532 nm as 870 ± 50 cm−1, a lower frequency progression of 250 ± 30 cm−1 was also resolved for band A. As will be shown below, this progression is due to excitation of the even vibrational quanta of the bending mode in band A. Another well-resolved feature B at 1.339 eV is observed, which 297 is assigned as a new detachment channel and contains a possible vibrational progression of 810 ± 50 cm−1. One weaker feature C is observed with a VDE value of 1.384 eV and is assigned as another detachment channel. Feature a at 1.282 eV is observed and assigned as a new detachment transition. The features a, B, and C are assigned tentatively as distinct detachment channels because they cannot be assigned as any vibrational excitations for band A. These assignments are compared with the calculated results in Table 8.1. The most significant and surprising observation is the nearly continuous weak photodetachment signals observed between 1.5 and 5 eV in the 193 nm spectrum, which give rise to a set of congested but well-resolved peaks in the lower photon energy spectra (Figure 8.1a-c). Eighteen such peaks are tentatively identified up to 3.9 eV and labeled as b, c, … to s. No features are identified in the 4 to 5 eV range because of the low signal-to-noise ratios. The shapes and relative intensities of some of these weak features seem to vary with the detachment photon energies, suggesting that either there is more than one transition in these features or they are wavelength-dependent. Because UO2− contains only three quasi-atomic U-based valence electrons (7s25f1), such a high density of detachment channels is not expected on the basis of the Koopmans’ theorem. As shown below, these weak peaks are due to extensive two-electron detachment transitions, which are direct manifestation of the strong electron correlation effects in UO2− and the breakdown of the Koopmans’ theorem. The VDEs of all the observed detachment transitions are summarized and compared with the theoretical data in Table 8.1 and Table 8.2. 298 Figure 8.1 Photoelectron spectra of UO2− at (a) 532 nm, (b) 355 nm, (c) 266 nm and (d) 193 nm. 299 8.1.3 Theoretical Results and Comparison with Experiment Theoretical studies were carried out using both DFT and WFT methods. DFT calculations were performed on UO2− and UO2 using the GGA with the PBE exchange- correlation functional225 as implemented in the Amsterdam Density Functional (ADF 2010.02) program.389-391 The Slater basis sets with the quality of triple- plus two polarization functions (TZ2P)392 were used, with the frozen core approximation applied to the inner shells [1s2-5d10] for U and [1s2] for O. The scalar relativistic (SR) effects were taken into account by the zero-order-regular approximation (ZORA).393 Geometries were fully optimized at the SR-ZORA level. We further carried out WFT calculations using advanced ab initio electron correlation methods implemented in the MOLPRO 2012.1 program.394 The CCSD(T)179 and complete- active-space second order perturbation theory (CASPT2)395 were used. The structures of UO2– and UO2 were optimized at the level of CCSD(T) with the SR effects included (Figure 8.2). Single-point CCSD(T) energies of the ground state of UO2 were calculated at the optimized geometry of UO2–, which accurately generated the first VDE, indicating that the theoretical methods used are adequate. To obtain the higher VDEs, we used the CASPT2 method to calculate the ground and excited states of UO2 at the CCSD(T) ground-state geometry of the anion. The active spaces for the ground- and excited-state CASSCF calculations of UO2 include 13 orbitals from the U 5f, 6d, 7s, and 7p shells, i.e. 2g, 1u, 1u, 1g, 2u, 3u, 2u and 3u (Figure 8.3 and Figure 8.4) with 2 valence electrons designated as CAS(2,13). This relatively small active space is only suitable for electron detachments involving intra-atomic electronic states, which are the focus of this work. SO-averaged CASPT2 calculations were performed on all the triplet and singlet states produced by this 300 active space. Individually optimized state-averaged (SA) CASSCF orbitals were used for gerade(g)- and ungerade(u)-symmetry triplet and singlet states, respectively. In the CASPT2 calculations, the ionization potential EA (IPEA)-corrected zeroth-order Hamiltonian396 was used with an IPEA shift of 0.25 a.u.. To avoid intruder states and improve CASPT2 convergence, a level shift of 0.2 a.u. was applied. The U 6s6p and O 2s2p shells were correlated in the CASPT2 calculations. The SO coupling was treated by a state-interacting method397,398 with SO pseudopotentials on the basis of SA-CASSCF wave functions of g and u symmetries, respectively. This is justified because g and u states do not mix under the influence of SO coupling. In the MOLPRO calculations, we used the Stuttgart energy- consistent relativistic 32-valence-electron pseudopotentials, ECP60MWB (U), and the corresponding ECP60MWB-SEG basis set for U399-401 and the augmented polarized valence triple- basis sets aug-cc-pVTZ for O.402 To evaluate the error of the truncated atomic basis sets on ground-state geometrical structures of UO2– and UO2, we also performed CCSD(T) geometry optimization by employing a more accurate pseudopotential ECP60MDF and the corresponding basis sets of polarized valence quadruple- quality for U403 and the augmented polarized valence quadruple- basis sets aug-cc-pVQZ for O.402 The U-O bond length of UO2– and UO2 increases by only 0.0076 Å and 0.0066 Å, respectively, showing that the atomic basis sets used are nearly converged toward the basis sets limit. The influence on geometrical structures from further basis set improvement can be neglected in this work. 301 Figure 8.2 Optimized structures of UO2− and UO2. Their point group symmetries, spectroscopic states and electronic configurations are given. Bond lengths are given in Å. Figure 8.3 Qualitative scalar-relativistic valence MO energy-level scheme for UO2−. 302 Figure 8.4 Contour plots of the valence MOs of UO2− at the DFT/PBE level (iso = 0.038 a.u.) with a (2u)2(1u)1 electron configuration. The 1u orbital is the singly occupied MO, the 2u orbital is the highest doubly occupied MO. The optimized structures of UO2– and UO2 at the level of CCSD(T) with the SR effects included are shown in Figure 8.2. The U-O bond length in the anion is 1.823 Å, which is comparable to the previously reported value of 1.828 Å at DFT/B3LYP level.373 Neutral UO2 has an optimized U-O bond length of 1.793 Å at the SR level, which is close to the reported 1.806 Å at the SR-CASPT2 level.5 Previous calculations show that inclusion of spin-orbit coupling does not change the U-O distance significantly. The U-O bond length is 1.80 Å at the SO-CI level375, 1.770 Å at the DC-FSCC level383 and 1.766 Å at the SO- CASPT2 level374. While in general bond length depends on the atomic basis sets, electron correlation level, and spin-orbit coupling effect,374,383 our calculations using a more accurate pseudopotential and larger basis set for U and O indicate that the U-O bond lengths in UO2– and UO2 do not change substantially, showing the influence on geometrical structures from further basis set improvement can be neglected at this level of theory. 303 To understand and to interpret the PES spectra of UO2−, we performed extensive calculations of the ground and excited states of UO2− and neutral UO2 at the optimized geometry of UO2−. Figure 8.3 shows the qualitative SR energy levels of the Kohn-Sham valence orbitals of UO2−, and the corresponding MO contours are shown in Figure 8.4. The U5f orbitals transform as fumfumfumfum in the D∞h symmetry, where 5fu forms the 1u nonbonding MO and 5fu forms the 1u nonbonding MO in UO2−. The 1u and 1u MOs are almost degenerate in UO2− and UO2 due to lack of orbital interaction with the ligands. The doubly occupied 2g MO mainly consists of the U7s orbital. The unoccupied 5fu (2u) and 6dg (1g) MOs are only slightly higher in energy, whereas even higher lie the U7p-based orbitals (3u and 3u) of Rydberg character and the 5fu (2u) MO of anti-bonding character. Without SO coupling the UO2− anion has a 2u ground state with a (2g)2(1u)1 electron configuration.373 The first excited state 2Δu with a (2g)2(1u)1 electron configuration lies 0.11 eV above the ground state. All the oxygen valence electrons participate in the two U≡O triple bonds, forming the four deeper and fully occupied MOs (1u, 1u, 1g, and 1g), which are similar to those in uranyl (UO22+).370,386,404- 408 These ligand-based MOs are well separated from the U(7s5f)-based MOs and are primarily composed of O(2p) atomic orbitals with some mixing of the U(5f6d) orbitals as a result of U-O orbital interactions. According to group theory, the 2u (2g21u1) and 2Δu (2g21u1) states will mix under SO coupling, yielding four new SOC states: 25/2u, 2Δ3/2u, 27/2u and 2Δ5/2u. Their wavefunctions and relative energies from our SO-CASPT2 calculations are shown in Table 8.3. The wavefunction of the ground state 25/2u is (88% 2u + 12% 2Δu) with the SR ground 304 state 2u dominant. The first excited state 23/2u (2g21u1) is 0.26 eV higher at the SO- CASPT2 level (Table 8.3). Such a high anionic excited state is unlikely to be populated at room temperature, thus ruling out its presence in the experiment. Inasmuch as the ground state 25/2u [88% 2u (2g21u1) + 12% 2Δu (2g21u1)] of UO2− mainly involves the 2g21u1 electron configuration, UO2− should produce three major detachment channels on the basis of Koopmans’ theorem: UO2 : 2g21u1 25/2u  UO2: 2g11u1 32u, 3u, 4u Eq. 16  2g11u1 13u Eq. 17  2g21u0 10g Eq. 18 Detachment from the deeper O2p-based MOs would produce energetically much higher excited states of UO2. This picture qualitatively agrees with the 193 nm PES spectrum (Figure 8.1d). In particular, the features D and E should be due to detachment from the 1u MO, corresponding to the triplet 3g (1u12g21u1) and singlet 1g (1u12g21u1) final UO2 states, respectively. Thus, the X-D separation of 4.326 eV (34890 cm−1) should correspond to the lowest ligand-to-metal electronic excitation energy in UO2 (X3u  3g). Our calculated VDE for the triplet final state is 5.587 eV, in excellent agreement with the experimental value of 5.485 eV (Table 8.1). However, the one-electron MO picture at the Hartree-Fock or approximate Kohn- Sham levels and the Koopmans’ theorem, involving only the initial state of the electron detachment, break down severely and cannot interpret the numerous fine PES features observed for UO2−, suggesting strong electron correlation effects. These multi-electron processes are called shakeup in PES.409 Thus, the UO2 final states with the inclusion of multi- 305 reference configuration mixing and relativistic effects including SO coupling have to be considered, in order to understand the PES spectra. At the SR level, the CASPT2 calculations of UO2 show that the 3Φu state is the ground state with a 2g11u1 electron configuration. Three low-lying states (3Δu, 1Φu, and 1Δu) derived from the 2g1(1u,1u)1 electron configuration are shown in Table 8.4, along with their relative energies to the ground state. The 3Hg state with a (1u)1(1u)1 (5f5f) electron configuration, which was suggested to be the matrix-induced ground state in the Ar matrix study of UO2,379,385 lies 2449 cm−1 above the ground state. DFT calculations without SO coupling show that the 3Hg state is 1920 cm−1 (Ref. 373 ) above the 3Φu ground state. At the SR-CASPT2 level, this energy difference is calculated to be 5954 cm−1 (Ref. 381 ). At the spin-free DC-IHFSCC level of theory, the 3Hg state is found to be 12863 cm−1 above the 3Φu ground state.383 Upon including SO coupling, the ground state 3Φu and excited states 3Δu, 1Φu, 1Δu split into states with  values of 4, 3, 2 (3Φu), 3, 2, 1 (3Δu), 3 (1Φu), and 2 (1Δu). Our calculations show that the 2u state, whose wavefunction is (89%3Φu+8%3Δu), is the SO- coupled ground state (Table 8.2). The first VDE corresponding to UO2− (X2Φ5/2u)  UO2 (X3Φ2u) is calculated to be 1.097 eV at the CASSCF/CCSD(T)/SO level of theory,410 only 0.062 eV smaller than the experimental VDE (1.159 eV) measured for the ground-state detachment band X. To simplify the comparison between the experimental and calculated values, all the calculated VDEs are offset by 0.062 eV in Table 8.1 and Table 8.2. The calculated VDEs for the 3u, 1u and 2u states after the 0.062 eV offset are 1.204, 1.367, and 1.417 eV, in excellent agreement with the measured VDEs for bands A (1.202 eV), B (1.339 eV), and C (1.384 eV), respectively (Table 8.1). The excitation energy of the 3u state (350 306 cm−1) obtained from the current PES work agrees well with the previous value (360 cm−1) measured by the Heaven group for gaseous UO2.377 As compared in Table 8.1, the excitation energies obtained for the 1u and 2u states in the current study seem to be slightly higher than those obtained by the Heaven group for UO2 isolated in an Ar matrix,378 probably due to the approximation in CASPT2 and/or the non-negligible matrix effects. The calculated excitation energies for the 3u, 1u, and 2u states from several recent theoretical studies12-14 are also given in Table 8.1 for comparison. The weak feature a observed at 1.282 eV (Figure 8.1a and Table 8.1) is tentatively assigned to the lowest 4g state with a calculated VDE of 1.283 eV. There is no other low- lying state below the 4g state, in addition to the 3u state. Hence, the two peaks between the origin of the A band and the feature a are assigned to the even quanta of the bending mode for the 3u state of UO2. The average measured spacing is 250 ± 30 cm−1, which gives a bending frequency of ~125 cm−1, in agreement with the 129 cm−1 bending frequency measured for the 3u state by the Heaven group.377 The ground-state detachment band X may also contain vibrational excitations. However, the relatively weaker intensity of the X band suggests that any vibrational peaks in the X band are likely to be buried under the features of the A band. As mentioned above, the lowest 4g state was suggested previously to be the ground state of UO2 due to weak Ar-UO2 bonding in an Ar matrix.379,385 In our SO-CASPT2 calculation, the 4g state relative to the 2u ground state is 1001 cm1 higher in energy. The SOCI calculations show that the 4g state is 1642 cm−1 above the ground state.6 However, the previous calculations listed in Table 8.1 tend to give larger excitation energy of this state. The SO-CASPT2 calculations give the excitation energy to be 3330 cm1 (ref. 381 ), which 307 383 used a different active space from this work. The DC-IHFSCC method in ref. has given the 4g state 10914 cm−1 above the 2u ground state, while the DC-CCSD(T) calculations give a result of 6991 cm−1. One possible reason for the different calculated energies of the 4g state is the use of different bond lengths. In our study, the single-point calculation of neutral UO2 is performed using the anionic geometry (U-O distance: 1.823 Å) for vertical transitions, as measured in PES. However, calculations in the literature used the neutral optimized geometry with the U-O bond length varying from 1.770 Å to 1.827 Å.375,381,383 Recalculating the vertical excitation of UO2 at 1.770 Å gives the excitation energy of 4g as 2942 cm−1, which is in much better agreement with the SO-CASPT2 (ref. 12) and DC-CCSD(T) results (ref. 383 ), but is still different substantially from the DC-IHFSCC results of ref. 14. The relatively smaller effect of bond length on the 4g state has also been noted in ref. 14, and the electron correlation is suggested to be more responsible for the discrepancy. As found in a previous SR-CASPT2 calculation,12 in general different active spaces give different energy orderings and energy gaps among electronic states. Larger active spaces with accounting for more non- dynamic and dynamic electron correlations give more accurate results, but are often computationally impractical. Besides, the DC-CCSD(T) calculation of the excitation energy of the 4g state gives an energy 1464 cm1 higher than the DC-CCSD result in ref. 383, showing the effect of dynamic electron correlations. It is worth mentioning that in ref. 383 the lowest 4u state from the 5f6d configuration was found at 5047 cm−1 above the ground state, which is 5867 cm−1 lower than the 4g state above. It was proposed to likely play an important role in the UO2 chemistry in the Ar matrix. However, our SO-CASPT2 calculations show this 4u state to be 4821 cm−1 higher than the 4g 308 state at the U-O bong length of 1.823 Å (3288 cm−1 at 1.770 Å ), not supporting the proposition above. Because of the complicated nature of the PES spectra of UO2–, the above assignment is only semi-quantitative due to the approximation of the SO-CASPT2 approach and the relatively small CAS(2,13) active space used. Clearly the calculated excited-state energies significantly depend on the level of electron correlation and relativistic effects, in addition to the quality of the atomic basis sets. Evaluation of more accurate excited state energies would require much larger active space involving even higher-energy U orbitals and ligand-based orbitals and higher-level dynamic electron correlation than the PT2 level, especially when involving electron detachments from the oxygen atoms.411 Quantitative assignments of the PES spectra of UO2– demand a thorough investigation of the convergence of the calculations with respect to active space and dynamic electron correlations. Such calculations are beyond the computing capability and the scope of the current work. 8.1.4 Extensive two‐electron Transitions and Strong Electron Correlation Effects Table 8.2 shows that the main electron configuration for the 1u and 2u states is 2g11u1 (3u), which cannot be accessed from the ground-state configuration (2g21u1) via one-electron transitions, as shown in Eqs. 16 – 18. However, they can be accessed through two-electron transitions, i.e., the detachment of a 2g electron and at the same time the 1u electron is excited to the 1u orbital. These so-called shakeup processes are direct reflections of strong electron correlation effects. The observation of shakeup processes is a direct result of the multi-configurational nature and SO coupling in the ground state of UO2–, which contains a mixing of 12% 2u (2g21u1) character (Table 8.4). In fact, except for the bands X and A, which correspond to 32u,3u derived by one-electron transitions (Eq. 16), all the other 309 weak features observed between 1.5 and 5.3 eV are due to two-electron transitions, including the low-lying band a, which is assigned to the 4g state. Our calculations reveal 62 such two- electron excited states up to a binding energy of 3.9 eV, which are compared with the experimental observation in Table 8.1. All these states can be considered to be derived from one-electron detachment from one of the 2g21u1 orbitals with another electron simultaneously excited to a higher-lying unoccupied 5f, 6d or 7p orbitals (Figure 8.3 and Table 8.2), thus making all the U(5f2), U(6d15f1) and U(7p15f1) electronic configurations accessible. The SR CASPT2 calculation results are shown in Table 8.2. The SOC calculations on the excited states including these electron configurations can qualitatively account for all the observed weak features in the PES spectra, as shown in Table 8.2. We note that the assignments of these weak features are semi-quantitative because of the extremely high density of states and the limitation of the accuracy of the approximate quantum mechanical and relativistic methods, as well as unsaturated atomic basis sets used for such a complicated system. 310 Table 8.1 Observed VDEs of UO2− and comparison with theoretical calculations at different levels of theory with inclusion of spin-orbit coupling. Current E from literature (cm−1) Final ∆E SO-CASPT2 experiment ∆E exp. IHFSCC GASCI CASPT2 State (cm−1)b VDE (eV) VDEs (eV)a (cm ) −1 b 377,378 383 382 381 X 2u 1.159 (20) 0 1.159c 0 0 0 0 0 A 3u 1.202 (20) 350 1.204 362 360 368 427 378 f a 4g 1.282 (30) 990 1.283 1001 10914 3300 e B 1u 1.339 (20) 1450 1.367 1679 1094 2231 1089 2567 C 2u 1.384 (30) 1810 1.417 2083 1401e 2588 1542 2908 3 d D g 5.485 (30) 34890 5.587 35730 E 5.604 (30) 35850 a Numbers in parentheses represent the uncertainty in the last two digits. b Excitation energies of the excited states of UO2 relative to the ground state. c Theoretical results from the current work. The calculated first VDE is 1.097 eV. All higher VDEs are offset by 0.062 eV to facilitate comparison with the experimental data. d From CCSD(T) calculations. 378 The experimental excitation energies in an Ar matrix. f −1 381 This value is 3330 cm according CASPT2 calculations in ref. . It is primarily due to the completely different approach to 383 electron correlation chosen in both methods. 311 Table 8.2 All the observed weak features from the photoelectron spectra and their comparison with the CASSCF/CASPT2/SO calculation results of UO2−. The leading configurations are shown in bold face. Featur VDE Cal. E E  Compositions of SR states e (eV) (eV) (cm−1) (cm−1) X 1.159(20) 1.159 9356 0 2u 89% 3Φu(2g1u) + 8% 3∆u(2g1u) A 1.202(20) 1.204 9718 362 3u 51% 3Φu(2g1u) + 36% 1Φu(2g1u) + 13% 3∆u(2g1u) a 1.282 (30) 1.283 10357 1001 4g 93% 3Hg(1u1u) B 1.339(20) 1.367 11035 1679 1u 98% 3∆u(2g1u) C 1.384(30) 1.417 11439 2083 2u 56% 3∆u(2g1u) + 41% 1∆u(2g1u) 57% 3Σ−g(1u2+1u2) + 28% 3Πg(1u1u) + 15% b 1.63(3) 1.571 12679 3323 0g 1 + Σ g(1u2+1u2) 48% 3Πg(1u1u) + 35% 3Σ−g(1u2+1u2) + 13% c 1.74(4) 1.741 14047 4691 1g 1 Πg(1u1u) 1.797 14504 5148 5g 99% 3Hg(1u1u) 1.799 14515 5159 4u 100% 3Φu(2g1u) d 1.85(3) 1.840 14850 5494 3u 47% 3Φu(2g1u) + 29% 3∆u(2g1u) + 24% 1Φu(2g1u) 1.878 15158 5802 3u 57% 3∆u(2g1u) + 40% 1Φu(2g1u) + 2% 3Φu(2g1u) 1.881 15176 5820 4u 92% 3Hu(1u1g) 1.916 15463 6107 2u 55% 1∆u(2g1u) + 35% 3∆u(2g1u) + 10% 3Φu(2g1u) e 1.98(4) 2.013 16247 6891 0u 67% 1Σ−u(1u1g) + 31% 3Σ+u(1u1g) f 2.10(3) 2.116 17074 7718 3u 98% 3Γu(1u1g) 61% 3Σ−g(1u2+1u2) + 21% 1Πg(1u1u) + 15% 2.167 17487 8131 1g 3 Πg(1u1u) g 2.22(4) 2.175 17552 8196 0g 100% 3Πg(1u1u) 2.214 17864 8508 6g 95% 3Hg(1u1u) 2.257 18214 8858 5u 85% 3Hu(1u1g) + 12% 3Γu(1u1g) 2.263 18259 8903 2g 93% 3Πg(1u1u) h 2.31(3) 2.277 18371 9015 1u 40% 3Πu(1u1g) + 28% 3Σ+u(1u1g) + 28% 1Πu(1u1g) 2.305 18603 9247 0g 63% 3Πg(1u1u) + 25% 1Σ+g(1u2+1u2) 2.408 19428 10072 0u 65% 3Πu(1u1g) + 24% 3Σ+u(1u1g) + 11% 1Σ−u(1u1g) 2.416 19491 10135 4g 87% 1Γg(1u2) i 2.42(4) 2.455 19809 10453 4u 88% 3Γu(1u1g) +5%a1Γu(1u1g)+5%a3Hu(1u1g) 2.473 19955 10599 3g 93% 3Γg(1u3u) 2.505 20209 10853 1u 58% 3Σ+u(1u1g) + 24% 3Σ−u(1u1g) + 10% 1Πu(1u1g) j 2.52(4) 2.509 20247 10891 0u 86% 3Πu(1u1g) + 13% 3Σ−u(1u1g) 59% 3Σ−g(1u2) + 18% 1Σ+g(1u2+1u2+1g2+2g2) + 12% 2.609 21052 11696 0g 1 + k 2.58(4) Σ g(1u2+1u2) 2.615 21097 11741 0u 66% 3Σ−u(1u1g) + 22% 1Σ+u(1u1g) + 9% 3Πu(1u1g) 312 2.747 22166 12810 6u 100% 3Hu(1u1g) 2.773 22377 13021 2g 51% 3Φg(1u3u) + 21% 1∆g(1u3u) + 21% 3∆g(1u3u) 2.807 22651 13295 5u 85% 3Γu(1u1g) + 14% 3Hu(1u1g) l 2.76(3) 2.822 22772 13416 1g 43% 3Σ−g(1u2) + 30% 1Πg(1u1u) + 22% 3Πg(1u1u) 2.826 22799 13443 2g 45% 3Φg(1u3u) + 25% 3∆g(1u3u) + 22% 1∆g(1u3u) 46% 1Σ+g(1u2+1u2) + 27% 3Σ−g(1u2+1u2) + 11% 2.829 22826 13470 0g 3 − Σ g(1u2) 2.867 23128 13772 0u 43% 3Σ+u(1u1g) + 35% 3Πu(1u1g) + 20% 1Σ−u(1u1g) m 2.88(5) 2.869 23149 13793 1u 68% 3Σ−u(1u1g) + 15% 3Πu(1u1g) + 13% 3Σ+u(1u1g) 2.881 23248 13892 2u 100% 3Πu(1u1g) n 2.95(5) 2.964 23917 14561 4g 93% 3Γg(1u3u) 3.014 24319 14963 4u 92% 1Γu(1u1g) + 4% 3Γu(1u1g) o 3.04(5) 3.035 24486 15130 1g 50% 3Σ−g(1u2) + 32% 1Πg(1u1u) 3.142 25348 15992 1g 83% 3∆g(1u3u) + 9% 3Πg(1u1u) 3.168 25558 16202 1u 53% 1Πu(1u1g) + 35% 3Πu(1u1g) 3.187 25713 16357 6g 95% 1Ig(1u2) p 3.21(3) 3.213 25919 16563 3g 92% 3Φg(1u3u) 3.214 25930 16574 0u 96% 3Πu(2g2u+2g3u) 3.224 26013 16657 0u 97% 3Πu(2g2u+2g3u) 3.283 26485 17129 3g 94% 3∆g(1u3u) 3.305 26665 17309 1u 64% 3Πu(2g2u+2g3u) + 25% 1Πu(2g2u) q 3.31 3.327 26846 17490 5g 75% 3Γg(1u3u) + 25% 1Hg(1u1u) 3.360 27110 17754 1g 64% 3Πg(1u3u) + 28% 1Πg (1u3u) 3.521 28410 19054 0u 73% 1Σ+u(1u1g) + 19% 3Σ−u(1u1g) 3.560 28723 19367 2u 98% 3Πu(2g2u+2g3u) 3.565 28759 19403 5u 96% 1Hu(1u1g) 3.624 29239 19883 0g 100% 3Πg(1u3u) r 3.53(5) 3.638 29349 19993 2g 62% 3Πg(1u3u) + 26% 3∆g (1u3u) 3.638 29350 19994 4g 90% 3Φg(1u3u) 3.644 29396 20040 1u 66% 1Πu(2g2u) + 24% 3Πu(2g2u+2g3u) 3.645 29410 20054 0g 80% 3Πg(1u3u) + 13% 3Σ−g(1u2) 3.699 29843 20487 0g 72% 1Σ+g(1u2+1u2+1g2+2g2) + 16% 3Σ−g(1u2) 3.751 30265 20909 5g 75% 1Hg(1u1u) + 24% 3Γg(1u3u) 3.785 30540 21184 2g 46% 1∆g(1u3u) + 30% 3Πg(1u3u) + 20% 3∆g(1u3u) s 3.76(4) 3.797 30632 21276 1g 95% 3∆g(1u2u+2g1g) 3.818 30799 21443 2u 99% 3Φu(1g2u+1g3u+1u2g) 3.844 31012 21656 4g 93% 1Γg(1u3u+1u2) 3.922 31642 22286 2g 88% 3∆g(1u2u+2g1g) 313 Table 8.3 The ground state and the lowest excited states of UO2−. Vertical excitation energies (E in eV) at the CASSCF/X/SO (X = CCSD(T), CASPT2) level and the SR-CCSD(T)-optimized ground- state geometry (Figure 8.2). CASSCF/CCSD(T)/SO CASSCF/CASPT2/SOa SO state Composition of SR states E Composition of SR states E 2 2 2 2 5/2u 89% u+11% u 0 88% u+12% u 0 3/2u 100%2u 0.29 100%2u 0.26 7/2u 100%2u 0.67 100%2u 0.67 2 2 2 2 5/2u 89% u+11% u 0.76 88% u+12% u 0.74 a with an active space of CAS(2,13) 314 Table 8.4 The calculated vertical excitation energies of UO2 at the SR CASPT2 level. The leading configurations are shown in bold face. E/cm State Main configurations (leading in bold) E/eV 1 a3u 2g1u (7s5f) 0.0000 0 3 a u 2g1u (7s5f) 0.0735 593 1 a u 2g1u (7s5f) 0.1135 916 1 a u 2g1u (7s5f) 0.1888 1523 3 a g 1u1u (5f5f) 0.3037 2449 a3g 1u2+1u2 (5f5f+5f5f) 0.5363 4325 3 a g 1u1u+1u2u+1u3u (5f5f+5f5f+5f7p) 0.7380 5953 1  a u 1u1g (5f6d) 0.7399 5968 3 a u 1u1g (5f6d) 0.8280 6678 1 a g 1u2 2 +1u3u+1u2u (5f +5f7p+5f5f) 0.9176 7401 3 a u 1u1g (5f6d) 0.9411 7591 3 + a u 1u1g (5f6d) 0.9882 7970 a1+g 1u2 +1u2 (5f2+5f2) 0.9904 7988 1 a g 1u1u+1u2u+1u3u (5f5f+5f5f+5f7p) 1.1101 8954 3 a u 1u1g+2g2u+2g3u (5f6d+7s5f+7s7p) 1.2090 9751 3  a u 1u1g (5f6d) 1.2772 10301 1 a u 1u1g+2g2u+1g2u (5f6d+7s5f+6d5f) 1.3429 10831 b3g 1u2+1g2+1u2 (5f5f+6d6d+5f5f) 1.4427 11636 1 a u 1u1g (5f6d) 1.4764 11908 3 a g 1u3u+1u2u (5f7p+5f5f) 1.4851 11978 1 a g 1u2 (5f2) 1.6178 13049 3 a g 1u3u+1u2u (5f7p+5f5f) 1.7112 13802 3 a g 1u3u+1u2u+2g1g (5f7p+5f5f+7s6d) 1.7188 13863 1 + a u 1u1g (5f6d) 1.8121 14616 1 a g 1u3u+1u2u+2g1g (5f7p+5f5f+7s6d) 1.8582 14987 3 b u 2g2u+2g3u (7s5f+7s7p) 1.8764 15134 b1+g 1u2+1u2+1g2+2g2 (5f2+5f2+6d2+7s2) 1.9140 15437 a1u 1u1g (5f6d) 2.0002 16133 1 b u 2g2u+2g3u+1g2u +1g3u (7s5f+7s7p+6d5f+6d7p) 2.0673 16674 1 a g 1u1u (5f5f) 2.1340 17212 3 b g 1u3u+1u1u+1u2u (5f7p+5f5f+5f5f) 2.1590 17413 1 b g 1u3u+1u2 (5f7p+5f2) 2.3748 19154 1 b g 1u3u+1u1u+1u2u (5f7p+5f5f+5f5f) 2.4876 20064 3 b g 1u2u+2g1g (5f5f+7s6d) 2.5024 20183 3 b u 1g2u+1g3u+2g1u (6d5f+6d7p+7s5f) 2.6068 21026 315 c3u 1g2u+1g3u+2g2u (6d5f+6d7p+7s5f) 2.6846 21652 1 a g 1u3u+1u2u (5f7p+5f5f) 2.8265 22798 1 b u 1g2u+1g3u+2g1u (6d5f+6d7p+7s5f) 2.8850 23269 c1+g 2g +1g +1u2 2 2 (7s 2 +6d2+5f2) 2.9083 23457 1 c u 1g2u+1g3u+2g2u+1g1u (6d5f+6d7p+7s5f+6d5f) 2.9220 23567 8.1.5 Conclusions PES is the most powerful experimental technique to probe electron correlation effects in many-electron systems via the observation of shakeup transitions.409 However, such clear and numerous shakeup peaks observed for UO2− in the valence range are unprecedented. This complexity happens because of the high density of the unoccupied and accessible valence orbitals (5f, 6d, and 7p). The strong electron correlation effects break down the one-electron MO picture and give rise to new excited states that would be difficult to be accessed in any other experiment. The strong electron correlations and spin-orbit couplings produce orders- of-magnitude more photodetachment transitions for UO2− than expected on the basis of the Koopmans’ theorem. These experimental observations provide new features for the calibration of theoretical methods for actinide systems. The current PES data for UO2− provide both a challenge and an opportunity for various WFT and DFT methods aimed at treating molecular systems with strong electron correlation. 316 8.2 Probing the Electronic Structures of low Oxidation‐State Uranium Fluoride Molecules UFx− (x = 2 – 4) 8.2.1 Introduction The most common and most important uranium fluoride is uranium hexafluoride (UF6), which is used in the nuclear industry for isotope separation to produce 235U-enriched nuclear fuels. The UF6 molecule in the gas phase has been extensively studied both experimentally and theoretically.40,412-440 It is a perfect octahedral molecule (Oh symmetry) with a U−F bond length of 1.996 ± 0.008 Å,412 in which U is in its most stable oxidation state of VI. UF5 is a photolysis product of UF6 and can be produced by reactions of uranium with fluorine.416 The UF5 molecule, which has C4v symmetry, has also been well characterized.40,415-417,441-444 Uranium tetrafluoride (UF4) is a stable compound, in which U has an oxidation of U4+(5f2). The UF4 molecule in the gas phase has T d symmetry with a bond length of 2.056 ± 0.001 Å.445,446 However, there have been suggestions that UF4 may have a distorted tetrahedral structure due to the Jahn-Teller effect.447-450 More recent infrared spectroscopy data seem to support the Td symmetry in the gas phase.83,451 Although there have been extensive investigations on the UFx ( x = 4 – 6) molecules, much less is known about the lower oxidation-state UFx species, primarily because these are all transient species and are expected to be highly reactive. UFx+ ( x = 1 – 4) cations were observed by mass spectrometry.441 UFx ( x = 1 – 3) species were proposed to exist in noble gas matrix,442 but the absorption spectra attributed to UF and UF2 were later reassigned to HF dimer and trimer, respectively.451,452 Only very recently, a spectroscopic and theoretical study is reported on the diatomic UF and UF+ species.452 Even though there have been a number of theoretical investigations on the geometries and vibration frequencies of UFx ( x = 317 1 – 6) systematically,453-457 there is little experimental information available for low oxidation-state uranium fluoride species. The low oxidation state UFx species with unpaired 5f or 7s electrons are expected to exhibit more complicated electronic structures and possess rich spectroscopic information, which will provide better systems to compare with theoretical calculations and verify new computational methods. Our recent investigation on UO2−, which has a (7s)2(5f)1 electron configuration, illustrates an example that gives extremely rich photoelectron spectra due to strong electron correlation effects.38 Accurate calculations involving both the initial and final states, with inclusion of electron correlation and spin-orbit coupling effects, are needed to interpret the observed spectra. In this section, we report the first observation of gaseous UFx− (x = 2 – 4) anionic species and their characterization using PES and quantum chemical calculations. Vibrationally resolved photoelectron spectra have been obtained for each species at several photon energies. The photoelectron spectra show all three species have much lower electron binding energies than the previously observed UF5− and UF6−.40,444 The ADEs of the anions or the electron affinities (EAs) of the corresponding neutral UFx (x = 2 – 4) species are accurately measured. The geometries, bond order indexes, and ADEs of the UFx− (x = 2 – 4) species are calculated. The experimental spectra are qualitatively understood using the calculated electron configurations of UFx− (x = 2 − 4). 8.2.2 Experimental Results The photoelectron spectra of UFx− (x = 2 – 4) at four different photon energies are shown in Figure 8.5, Figure 8.6 and Figure 8.7, respectively. The measured VDEs, ADEs, and vibrational frequencies are summarized in Table 8.5. The use of the Ar-seeded helium carrier gas (also in the current experiment) was shown previously to produce very cold gold 318 cluster anions.173 Very recently high resolution photoelectron imaging experiments showed that with the Ar-seeded helium carrier gas we could produce vibrationally cold Au4− clusters, for which vibrational hot bands were completely eliminated.458 The sharp onset in the 532 nm spectra of UF2− (Figure 8.5a) and UF3 − (Figure 8.6a) suggested that these anions were vibrationally cold. We only observed very weak vibrational hot band in the 532 nm spectrum of UF4− (Figure 8.7a). The cold anions and the vibrationally resolved photoelectron spectra at 532 nm were critical for us to evaluate the ADEs for the anions. In each spectrum, the X band represents the transition from the anionic ground electronic state to that of the neutral. The A, B, … bands denote transitions from the anionic ground electronic state to the excited states of the neutrals. The weak broad features in the energy region from 2 to 4 eV in the UF2− spectra are labeled with low-case letters a, b, c… and their peak positions are also listed in Table 8.5. UF2−: The photoelectron spectrum of UF2− at 532 nm (Figure 8.5a) shows a number of well-resolved features (X and A) in the low binding energy range and three weak peaks (B, C, D). The low binding energy features seem to consist of two vibrational progressions. The progression labeled as X has a VDE of 1.18 ± 0.03 eV with a vibrational spacing of 580 ± 30 cm−1. Each vibrational peak has a splitting of about 20 meV, indicating excitation of another vibrational mode with a low frequency of about 160 ± 30 cm−1. The ADE is defined by the 0- 0 transition to be 1.16 ± 0.03 eV (Table 8.5), which represents the EA of UF2. The progression labeled with A has an origin at 1.31 ± 0.03 eV with an average vibrational spacing of 510 ± 30 cm −1. Each vibrational peak of band A is also fairly broad, indicating unresolved low frequency vibrational features. Three weak and relatively sharp features 319 labeled as B, C, and D are observed at 1.76 ± 0.03 eV, 1.84 ± 0.03 eV, and 1.90 ± 0.03 eV, respectively. The spectra of UF2− at 355 nm (Figure 8.5b) and 266 nm (Figure 8.5c) show weak and almost continuous signals in the 2 – 4 eV region. Three broad features can be tentatively identified as a at ~2.2 eV, b at ∼2.7 eV, and c at ∼3.2 eV. Another feature E is observed at ∼4.3 eV in the 266 nm spectrum (Figure 8.5c), but it became rather weak in the 193 nm spectrum (Figure 8.5d), most likely due to the severe noise in the high binding energy range that resulted in poor signal to noise ratios after background subtraction. The continuous signals observed between 2 and 4 eV indicate a high density of electronic states in this energy region in neutral UF2. They are similar to those observed in the photoelectron spectra of UO2− observed recently, as a result of two-electron detachment transitions.38 UF3−: The 532 nm spectrum of UF3− (Figure 8.6a) displays three broad features, an intense band X and two relatively weak bands A and B. The intense band X with a VDE of 1.16 ± 0.03 eV contains congested vibrational features. The ADE of band X is evaluated by drawing a tangential line along the leading edge and then adding the instrumental resolution to the intersection with the binding energy axis. The so obtained ADE for UF3− is 1.09 ± 0.03 eV (Table 8.5), which is also the EA of neutral UF3. Band X contains two possible vibrational progressions, a long progression with a spacing of 530 ± 50 cm −1 and tentatively a short progression with spacing of 260 ± 50 cm−1. The weak band A has an estimated VDE of ∼1.8 eV. At 355 nm (Figure 8.6b), band B is observed to be quite broad, which may be due to extensive vibrational excitations or multiple detachment transitions. The VDE of band B is estimated to be ∼2.2 eV. Following a large energy gap, a broad band C is observed at a VDE of ∼4.5 eV in the 266 and 193 nm spectra. 320 UF4−: The 532 nm spectrum of UF4− shown in Figure 8.7a displays a nice vibrational progression. Each vibrational peak seems to be a doublet. Careful examination shows that there are two similar vibrational progressions, which should correspond to two nearly degenerate detachment channels. The ground state vibrational progression X has a slightly higher frequency of 620 ± 20 cm −1, whereas the slightly higher energy progression A has a frequency of 600 ± 20 cm −1. The 0–0 transition of band X defines an ADE of 1.58 ± 0.03 eV (Table 8.5), which represents the EA of UF 4. A very weak hot band was observed around 1.50 eV. The ADE of band A is measured to be 1.61 ± 0.03 eV. The VDEs of bands X and A cannot be measured from the 532 nm, because of the cutoff in the high binding side. The 355 nm spectrum (Figure 8.7b) shows that the v = 5 vibrational level defines the VDEs for bands X and A, which are measured from the 532 nm as 1.97 ± 0.03 eV and 1.98 ± 0.03 eV, respectively. The 355 nm spectrum (Figure 8.7b) reveals a new band B also with an extensive vibrational progression that overlaps with those of bands X and A. The VDE of band B is estimated to be 2.50 ± 0.03 eV. The 266 nm spectrum (Figure 8.7c) does not reveal additional bands, while the 193 nm spectrum (Figure 8.7d) shows a broad feature C at a VDE of ∼5.1 eV following a large energy gap. 321 Figure 8.5 Photoelectron spectra of UF2− at (a) 532 nm, (b) 355 nm, (c) 266 nm, and (d) 193 nm. The vertical lines in the inset indicate vibrational structures. 322 Figure 8.6 Photoelectron spectra of UF3− at (a) 532 nm, (b) 355 nm, (c) 266 nm, and (d) 193 nm. The vertical lines in the inset indicate vibrational structures. 323 Figure 8.7 Photoelectron spectra of UF4− at (a) 532 nm, (b) 355 nm, (c) 266 nm, and (d) 193 nm. The vertical lines in the inset indicate vibrational structures. 324 8.2.3 Theoretical Results The symmetries, ground-state electron configurations, and structural parameters for UFx and UFx− ( x = 1 – 6) are summarized in Table 8.6, where the calculated first ADEs for the anions are also given. The geometry optimizations were performed on UFx− ( x = 1 – 6) with various electron configurations. The most stable configurations for UFx− ( x = 1 – 6) anions are U(5f)3(7s)2(6d)1, U(5f)3(7s)2, U(5f)3(7s)1, (5f)3, U(5f)2, and U(5f)1, respectively. While these electron configurations and molecular symmetries are consistent with previous calculations on the neutral species,455 they should be considered as tentative because of the complexity arising from the strong electron correlation and configuration-mixing due to spin- orbit coupling. For instance, theoretical analyses with only SR effects cannot resolve the debate regarding the geometry of the UF4 molecule because its (t2)2 electron configuration is in principle subject to a Jahn-Teller distortion. With spin-orbit coupling the t2 MOs under Td symmetry transform into u3/2 + e5/2 spinors in double-group symmetry. Our preliminary SO-ZORA calculations with PBE functional show that the quadruply degenerate u3/2 spinor is well below the e5/2 spinor (by ∼0.63 eV), implying a (u3/2)2 ground state electron configuration, which is still Jahn-Teller active. Therefore, the geometry slightly distorts into D2d symmetry even with spin-orbit coupling, but the distortion is nearly negligible relative to Td symmetry because of the weak coupling between the 5f x states, as shown in Table 8.6. For UF4−, the most stable configuration at SR level is 5f3. However, with inclusion of SO effects, the most stable configuration is 5f27s1. It is likely that the ground state of UF4− involves a strong mixing of the 5f3 and 5f27s1 configurations. 325 8.2.4 Discussion Figure 8.8 depicts the contours of the occupied valence CMOs of UFx− ( x = 2 – 4) based on SR calculations. Quantitative assignments of the PES spectra of these open-shell species to specific electronic states of the neutrals are challenging because of the strong electron correlation and spin-orbit effects in the initial and final states involved in the electron detachment, as demonstrated in our recent detailed study of UO2−.38 Here we propose qualitative assignments of the photoelectron spectra on the basis of the MO configurations and the drastically different detachment cross sections for the 5f or 7s-based MOs. Our previous PES studies on UF5− and UCl5− show that the detachment cross sections for the 5f-based MOs are much smaller relative to those of the ligand-based MOs.40,459 UF2− and strong multi-electron transitions: The UF2− anion has an electron configurations of U(5f)3(7s)2 and neutral UF2 has a U(5f)3(7s)1 configuration, as shown in Table 8.6 and Figure 8.8a. Hence, the first detachment channel should correspond to removal of a 7s electron, resulting in both a quintet and triplet final state. At the SR level, the triplet neutral state is 0.075 eV higher than the quintet state. This energy difference is in good agreement with the experimental energy separation between the X and A bands in the photoelectron spectra of UF2− (∼0.13 eV in Table 8.5). Thus, the ground state of UF2 should correspond to the quintet state and the A band should correspond to the triplet final state. The relatively high intensities of the X and A bands are consistent with the high electron detachment cross sections expected for a 7s-based MO. Electron detachments from the three unpaired 5f-based MOs should each produce a triplet final state with close energies and should correspond to the weak and relatively sharp features B, C, and D. The very weak intensities of these peaks relative to the X and A bands are consistent with electron 326 detachment from 5f-based MOs. Electron detachment from the ligand-based F2p MOs should have high electron binding energies, corresponding to the relatively broad band E at ∼4.3 eV. As will be seen below, the binding energies for electron detachment from the F2p based MOs all have similarly high binding energies in the UF3− and UF4− cases as well. Hence, no more one-electron detachment channels are expected between 2 and 4 eV. However, almost continuous transitions are observed in this photoelectron spectral region, as seen in Figure 8.5 (bands labeled as a, b, c). These observations are reminiscent of the photoelectron spectra of the linear UO2− anion, which has a U(7s25f 1) electron configuration.38 Because of the strong correlation between the pair of 7s electrons, an unprecedented number of two-electron transitions were observed as a result of detaching one 7s electron and simultaneous excitation of the other 7s electron to higher-lying unoccupied 7f orbitals. Such strong electron correlation effects between electrons in s-type orbitals have been commonly observed in photoionization of atoms with ns2 configurations.409 The nearly continuous PES features observed from 2 to 4 eV in the spectra of UF2− are most likely due to such multi-electron transitions, further confirming the U(5f)3(7s)2 electron configuration for UF2−. Our calculated ADE for UF2− is 0.88 eV (Table 8.6), consistent with the short U–F vibrational progression observed in the X band (Figure 8.1a). The ∠FUF angle in UF2 is decreased by 3.5°, in agreement with the observed low-frequency vibrational excitation in the X band, which should be due to the bending mode. UF3−: The UF3− anion has a quintet ground state with a U(5f)3(7s)1 electronic configuration while neutral UF3 has a U(5f)3(7s)0configuration (Table 8.6 and Figure 8.8b). The first detachment channel is then from removal of the 7s-based a1 electron (Figure 8.8b), 327 resulting in the ground state band X (Figure 8.6). The strong relative intensity of this band is consistent with detachment from a 7s-based orbital. The next detachment channel should correspond to the removal of the 5f-based a1 electron, corresponding to the weak band A. Detachment from the degenerate 5f-based e1 orbital (Figure 8.8b) should correspond to the broad band B. The broad width of band B is likely a result of the Jahn-Teller effect, expected from detachment from the degenerate e1 orbital. The relative weak intensities of bands A and B are consistent with their 5f characters. The broad band C at 4.45 eV should come from detachment of F2p-based MOs. It is interesting to note that all the observed PES bands for UF3− correspond to one-electron detachment transitions. Unlike the UF2− case above, there is no evidence of multi-electron transitions. This observation provides indirect confirmation for the U(5f)3(7s)1electron configuration of UF3−. We would expect strong multi-electron transitions for a U(5f)2(7s)2 configuration because of the strong correlation effects of the 7s electrons, as observed for UF2− above and UO2− previously.38 The ADE of UF3− is calculated to be 0.89 eV, again underestimated in comparison with the experimental value of 1.09 eV (Table 8.5). Both the ground states of UF3− and UF3 have C3v symmetry, but the U–F bond length and ∠FUF bond angle decrease significantly in the neutral (Table 8.6), suggesting a long vibrational progression in the symmetric vibrational mode and also major Franck-Condon activities in the umbrella mode. These structural changes are in agreement with the broad and congested PES band observed for the ground state transition (Figure 8.6a). The frequency of the totally symmetric U−F breathing mode of UF3 was calculated to be 543 cm−1 previosuly,455 in good agreement with the main vibrational progression of 530 cm−1. The extensive Franck-Condon activities in 328 both the stretching and bending modes of UF3 would be expected to produce a very complicated and congested ground state vibrational progression, as observed experimentally. UF4−: The ground state electron configuration of the UF4− anion is more complicated. At the SR level, it has a 5f3 configuration in its ground state. However, when SO coupling is included, the configuration becomes 5f27s1. It is possible that the ground state of UF4− is multi-configurational with strong mixing of the two configurations. The relatively strong intensities of all the three observed PES bands at low binding energies are consistent with strong contributions of 7s characters in each of the detachment channel. The broad band C at ∼5.1 eV should come from detachment of F2p-based orbitals. There is a slight increase of the binding energies of this detachment feature from UF2− to UF4− (Figure 8.5, Figure 8.6 and Figure 8.7 ). The ADE of UF4− is calculated to be 1.66 eV, in good agreement with the measured value of 1.58 eV (Table 8.5). There is a large U–F bond length reduction in the neutral UF4 ground state (by 0.08 Å) and little change in the ∠FUF bond angles, in excellent agreement with the long vibrational progression (Figure 8.7a), which should be due to the totally symmetric stretching mode with no discernible activity of any bending modes. The previously calculated frequency for the U–F breathing mode was 598 cm −1,455 close to the experimentally measured frequency of 620 cm−1. Our experiment indicates that the first excited state of UF4 (band A) is nearly degenerate with the ground state (band X) and they have similar structures. In fact, the observation of a simple stretching vibrational progression for the ground state detachment transition without any hint of bending excitation suggests that both UF4− and UF4 in their ground states may possess the high symmetry Td structure, even though our current DFT calculations suggest a very slight distortion to a D2d structure for both the anion and neutral uranium tetra-fluoride. 329 The low oxidation-state UFx− species with open 5f and 7s shells are challenging electronic systems. Advanced ab initio wavefunction calculations with both dynamic and static electron correlations and relativistic effects (including spin-orbit coupling) are necessary to provide quantitative interpretations of the PES data. The rich electronic structure information would be ideal for verifying new computational methods for accurate treatments of the electronic structures of open-shell actinide compounds. Figure 8.8 Contours of the scalar-relativistic valence CMOs of (a) UF2− (C2v), (b) UF3− (C3v), (c) UF4− (D2d). 330 Table 8.5 Observed VDEs and the first ADE for UFx− (x = 2 − 4) and the U-F stretching frequencies of the neutral ground state. − − − Observed features UF2 UF3 UF4 VDEs (eV) X 1.18(3)a 1.16(3) 1.97(3) A 1.31(3) ~1.8 1.98(3) B 1.76(3) ~2.2 2.50(3) C 1.84(3) ~4.5 ~5.1 D 1.90(3) E ~4.3 a ~2.2 b ~2.7 c ~3.2 b ADE (eV) 1.16(3) 1.09(3) 1.58(3) −1 Frequency (cm ) 580(30) 530(50) 620(20) a Numbers in parentheses represent the uncertainty in the last digits. b This also represents the EA of the neutral UFx species. Table 8.6 Molecular symmetries, electron configurations, geometries and energies of UFx and UFx− (x = 1 – 6).a Symmetry Configuration U-F bond length (Å)b FUF ()b ADESO (eV) UF6− Oh (5f)1(7s)0 2.095 90.0 4.07 − 2 0 UF5 C4v (5f) (7s) 2.128(a), 2.125(e) 102.6, 87.3 2.63 − 2 1 UF4 D2d (5f) (7s) 2.147 106.5, 110.0 1.66 − 3 1 UF3 C3v (5f) (7s) 2.136 110.0 0.89 − 3 2 UF2 C2v (5f) (7s) 2.092 105.2 0.88 − 3 2 1 UF Cv (5f) (7s) (6d) 2.075 - 0.25 UF6 Oh (5f)0(7s)0 2.021 90.0 1 0 UF5 C4v (5f) (7s) 2.032(a), 2.036(e) 95.89(ae), 89.4(ee) UF4 D2d (5f)2(7s)0 2.067 109.2, 109.8 3 0 UF3 C3v (5f) (7s) 2.066 102.0 3 1 UF2 C2v (5f) (7s) 2.054 101.7 3 2 UF Cv (5f) (7s) 2.022 - a All the electron configurations, bond lengths, and bond angles are calculated using PBE functional with SO-ZORA Hamiltonian. b a and e denote axial and equatorial ligands, respectively. 331 Table 8.7 The calculated Mulliken charges and bond orders of UFx− (x = 1−6) based on different bonding index schemes. charge Bond Order Q(U) Q(F) Mayer G-J N-M(1) N-M(2) N-M(3) − UF6 2.32 -0.55 0.64 1.02 1.36 1.64 1.41 − UF5 1.90 -0.57 0.56, 0.62 0.88, 0.93 1.34, 1.39 1.67,1.69 1.35,1.39 − UF4 1.19 -0.55 0.53 0.90 1.50 1.72 1.50 − UF3 0.51 -0.50 0.43 0.93 1.63 1.74 1.58 UF2− -0.25 -0.38 0.30 1.09 1.90 1.81 1.79 − UF -0.62 -0.38 0.36 1.20 2.78 2.28 2.23 Trend of chemical bonding in UFx− ( x = 1 – 6): The calculated Mulliken charges and bond orders of UFx− ( x = 1 – 6) from different bond index schemes are summarized in Table 8.7. The electron density on the U atom decreases steadily from UF − to UF6−, with the net charge increment of 0.37 | e|, 0.76 | e|, 0.68 |e|, 0.71 | e|, and 0.42 | e| with each additional F coordination from UF− to UF6−. These results suggest that the U–F bonds are highly ionic in UF5− and UF6− with U at higher oxidation states. We observed similarly strong ionic bonding in UCl5− in a recent study.172 Except for the Mayer bond orders, the G-J and all N-M bond orders suggest that the U–F bond becomes weaker from UF− to UF6−. This trend is consistent with the bond dissociation energies calculated for UFx ( x = 1 – 6).456,460 The U–F bond length increases from UF− to UF4− and decreases from UF4− to UF6−. The UF5− and UF6− molecules have larger electrostatic interactions between the U and F atoms due to the large positive charge on U (Table 8.6). The calculated ADEs based on the SO-ZORA approach with the PBE functional are systematically underestimated in comparison to the experimental values, consistent with our previous finding that DFT with approximate GGA exchange-correlation functionals fail to predict accurate electron 332 detachment energies.40,461-463 However, the trend of the calculated ADEs is consistent with the experimental observations: when the oxidation state of the U increases from 0 in UF− to V in UF6−, the ADE increases significantly. The higher EA with increasing F coordination is derived from the increased positive charge on the U center in neutral UFx. 8.2.5 Conclusion The low oxidation-state UFx− (x = 2 − 4) species are observed and investigated using photoelectron spectroscopy and theoretical calculations. Vibrationally resolved photoelectron spectra are reported for all three species and the electron affinities of the three neutral UFx ( x = 2−4) species are accurately measured. The observed spectral features are qualitatively understood on the basis of the calculated electron configurations and the large differences of detachment cross sections from 5f or 7s-based orbitals. The electron binding energies of F2p- based orbitals are quite high and increases steadily from x = 2 − 4. Strong multi-electron transitions are observed for UF2−, due to its 5f37s2 configuration. As the F coordination increases in UFx−, the U−F bond lengths increase and the bond strengths decrease, consistent with the calculated bond orders. The low oxidation-state UFx− species possess rich electronic structures and are ideal test cases to verify computational methods for accurate treatment of actinide compounds. 333 Chapter 9 Concluding Remarks and Perspective In this thesis, I have demonstrated that the structures of anionic boron clusters can be established through joint photoelectron spectroscopy and quantum chemistry studies. I have also discussed some of the exciting insights we have gained about their structures and stability via chemical bonding analyses. I have shown that the anionic pure boron clusters continue to be planar or quasi- planar at least up to 24 atoms and at 30, 35, 36 and 40 atoms, as summarized in Figure 9.1. This planarity is the result of two-dimensional electron delocalization, rendering multiple aromaticity/antiaromaticity. The structure evolution of the planar boron displays a tendency for larger defect sizes from tetragonal  pentagonal  hexagonal holes as the cluster size increases. Two clusters, B30− and B36−/0, were found to possess quasiplanar structures, each with an isolated hexagonal hole in the all triangular lattice. The hexagonal defect is reminiscent of the hexagonal vacancies in the predicted boron α-sheet. Adjacent hexagonal holes were found in the clusters of B35−/0 and B40−, which can be used to construct borophenes related to the -sheet. The observation of isolated and adjacent hexagonal vacancies in the boron clusters suggest the viability of extended atom-thin boron sheet, for which a name “borophene” is coined. It is also expected that the hexagonal hole should be a defining feature for large planar boron clusters. The first all-boron fullerene occurs at the size of 40 atoms, giving rise to an extremely small EA comparing to the flat boron clusters. The B40 fullerene-like case is called “borospherene”. The observation of borospherene enriches the chemistry of boron and may lead to new boron-based nanomaterials. This result also 334 suggests that a new world of borospherenes, like the fullerenes, clusters may arise around n = 40. Figure 9.1 The structures of the main contributors to the photoelectron spectra of boron clusters (Bn−, n = 3 − 24, 30, 35, 36, 40). Doped boron clusters exhibit various interesting structural and electronic properties depending on the dopant element as well as the number of dopants and boron atoms. A new series of doubly aromatic molecular wheels (Dnh-M©Bnk–) was discovered with n = 8, 9, and 10 (Figure 9.2), each having a transition metal center and monocyclic boron ring. As the 335 number of boron atom increases, “boat”-like (VB10−) and half-sandwiches (C3v-M©B12−) were found as stable structures, which could be viewed as a metal atom coordinate to their corresponding bare boron clusters. The observation of the D6h-Ta2B6−/0 bipyramid, which bears high similarity to the structure motifs in [(Cp*Re)2B6H4Cl2]322 and Ti7Rh4Ir2B8,317 provides an intrinsic link between clusters and solid-phase materials. The exposed metal atom in these doped boron clusters provide ideal sites for appropriate ligands, allowing syntheses of this new class of novel borometallic complexes in the solid phase. On the other side, the H and BO doped boron possess ladder-like molecular wires (H2Bn−, Bn(BO)2−), which could potentially be synthesized or deposited on surfaces to give a new family of molecular wires. Doped boron clusters may exhibit unpredictable properties. Continued investigations of the doped boron clusters may lead to the discovery of new structural motifs for the design of novel boride materials. It seems that after more than a decade of investigation of size-selected boron clusters, interesting structures and novel chemical bonding are continued to be discovered. It is expected that boron have more surprises in store, the field of boron cluster has a bright future. 336 Figure 9.2 The structures of the main contributors to the photoelectron spectra of M©Bn− (n = 8, 9, 10). 337 In the last part of this thesis, I have also demonstrated that PES is the most powerful experimental technique to probe electron correlation effects in many-electron systems via the observation of shakeup transitions.409 Numerous well resolved shakeup peaks were observed for the linear UO2− due to the strong electron correlation in the two U7s-type electrons. A systematic investigation of UFx− (x = 2 – 4) have further confirmed that the electron correlation is strong between the U7s-type electrons. The current PES data for UO2− and UFx− provide both a challenge and an opportunity for various WFT and DFT methods aimed at treating molecular systems with strong electron correlation. These experimental observations provide new features for the calibration of theoretical methods for actinide systems. As the most powerful technique to probe the electronic and geometric structures of clusters, PES combined with laser vaporization technique and quantum chemistry calculation will continue to play an important role in discovering new clusters and elucidating their chemical and physical properties, which could potentially be used to rationally design new materials to solve the energy crisis and other environmental problems. 338 References (1) Haruta, M. Cattech 2002, 6, 102. (2) Taketoshi, A.; Haruta, M. Chem. Lett. 2014, 43, 380. (3) Cho, A. Science 2003, 299, 1684. (4) Cotton, F. A.; Wilkinson, G.; Murrillo, C. A.; Bochmann, M. Advanced Inorganic Chemistry; 6th ed.; Wiley: New York, 1999. (5) Kroto, H. W.; Heath, J. R.; Obrien, S. C.; Curl, R. F.; Smalley, R. E. Nature 1985, 318, 162. (6) Kratschmer, W.; Lamb, L. D.; Fostiropoulos, K.; Huffman, D. R. Nature 1990, 347, 354. (7) Fehlner, T. P.; Halet, J. F.; Saillard, J. Y. Molecular Clusters: A Bridge to Solid-State Chemitry.; Cambridge University Press, U.K., 2007. (8) Zheng, L. S.; Karner, C. M.; Brucat, P. J.; Yang, S. H.; Pettiette, C. L.; Craycraft, M. J.; Smalley, R. E. J. Chem. Phys. 1986, 85, 1681. (9) Yang, S. H.; Pettiette, C. L.; Conceicao, J.; Cheshnovsky, O.; Smalley, R. E. Chem. Phys. Lett. 1987, 139, 233. (10) Nagai, T.; Uehara, A.; Fujii, T.; Shirai, O.; Sato, N.; Yamana, H. Electrochemistry 2009, 77, 614. (11) Katakuse, I.; Ichihara, T.; Fujita, Y.; Matsuo, T.; Sakurai, T.; Matsuda, H. Int. J. Mass Spectrom. 1985, 67, 229. (12) Lieberman, M. A.; Lichtenberg, A. J. Principles of Plasma Discharges and Materials Processing; 2nd ed.; Wiley & Sons, Incorporated, 2005. (13) Haberland, H. Cluster o f Atoms and Molecules I Theory, Experiment, and Clusters of Atoms; Springer Series in Chemical Physics: Springer, Berlin, 1995. (14) Siegbahn, K.; Edvarson, K. Nucl. Phys. 1956, 1, 137. (15) Eland, J. H. D. Photoelectron Spectroscopy Butterworths, London, 1984. (16) Aljoboury, M. I.; Turner, D. W. J. Chem. Soc. 1963, 5141. (17) Brehm, B.; Gusinow, M. A.; Hall, J. L. Phys. Rev. Lett. 1967, 19, 737. (18) Leopold, D. G.; Ho, J.; Lineberger, W. C. J. Chem. Phys. 1987, 86, 1715. (19) Pettiette, C. L.; Yang, S. H.; Craycraft, M. J.; Conceicao, J.; Laaksonen, R. T.; Cheshnovsky, O.; Smalley, R. E. J. Chem. Phys. 1988, 88, 5377. (20) Gantefor, G.; Gausa, M.; Meiwesbroer, K. H.; Lutz, H. O. J. Chem. Soc. Faraday T. 1990, 86, 2483. 339 (21) Fancher, C. A.; de Clercq, H. L.; Thomas, O. C.; Robinson, D. W.; Bowen, K. H. J. Chem. Phys. 1998, 109, 8426. (22) Arnold, C. C.; Neumark, D. M. In Advances in Metal and Semiconductor clusters; Duncan, M. A., Ed.; JAI Press: Greenwich, CT, 1995; Vol. III, p 113. (23) Bragg, A. E.; Verlet, J. R. R.; Kammrath, A.; Cheshnovsky, O.; Neumark, D. M. Science 2004, 306, 669. (24) Paik, D. H.; Lee, I. R.; Yang, D. S.; Baskin, J. S.; Zewail, A. H. Science 2004, 306, 672. (25) Pramann, A.; Koyasu, K.; Nakajima, A.; Kaya, K. J. Chem. Phys. 2002, 116, 6521. (26) Wang, L. S.; Wu, H. In Advances in Metal and Semiconductor Clusters; Duncan, M. A., Ed.; JAI: Greenwich, CT, 1998; Vol. 4, p 299. (27) Wu, H. B.; Desai, S. R.; Wang, L. S. Phys. Rev. Lett. 1996, 77, 2436. (28) Li, X.; Wu, H. B.; Wang, X. B.; Wang, L. S. Phys. Rev. Lett. 1998, 81, 1909. (29) Hoffmann, M. A.; Wrigge, G.; von Issendorff, B.; Muller, J.; Gantefor, G.; Haberland, H. Eur. Phys. J. D 2001, 16, 9. (30) Hoffmann, M. A.; Wrigge, G.; von Issendorff, B. Phys. Rev. B 2002, 66, 041404R. (31) Prinzbach, H.; Weller, A.; Landenberger, P.; Wahl, F.; Worth, J.; Scott, L. T.; Gelmont, M.; Olevano, D.; von Issendorff, B. Nature 2000, 407, 60. (32) Gantefor, G.; Eberhardt, W. Phys. Rev. Lett. 1996, 76, 4975. (33) Muller, J.; Liu, B.; Shvartsburg, A. A.; Ogut, S.; Chelikowsky, J. R.; Siu, K. W. M.; Ho, K. M.; Gantefor, G. Phys. Rev. Lett. 2000, 85, 1666. (34) Moravec, V. D.; Jarrold, C. C. J. Chem. Phys. 1998, 108, 1804. (35) Xu, H. G.; Zhang, Z. G.; Feng, Y.; Yuan, J. Y.; Zhao, Y. C.; Zheng, W. J. Chem. Phys. Lett. 2010, 487, 204. (36) Liu, X. J.; Zhang, X.; Han, K. L.; Xing, X. P.; Sun, S. T.; Tang, Z. C. J. Phys. Chem. A 2007, 111, 3248. (37) Wang, L. S.; Cheng, H. S.; Fan, J. W. J. Chem. Phys. 1995, 102, 9480. (38) Li, W. L.; Su, J.; Jian, T.; Lopez, G. V.; Hu, H. S.; Cao, G. J.; Li, J.; Wang, L. S. J. Chem. Phys. 2014, 140, 094306. (39) Li, W. L.; Hu, H. S.; Jian, T.; Lopez, A. G.; Su, J.; Li, J.; Wang, L. S. J. Chem. Phys. 2013, 139, 244303. (40) Dau, P. D.; Su, J.; Liu, H. T.; Huang, D. L.; Wei, F.; Li, J.; Wang, L. S. J. Chem. Phys. 2012, 136, 194304. (41) Mullerdethlefs, K.; Sander, M.; Schlag, E. W. Chem. Phys. Lett. 1984, 112, 291. (42) Mullerdethlefs, K.; Schlag, E. W. Annu. Rev. Phys. Chem. 1991, 42, 109. 340 (43) Neumark, D. M. In Ion and Cluster Ion Spectroscopy and Structure; Maier, J. P., Ed.; Elsevier: Amsterdam, 1989, p 155. (44) Li, S. G.; Fuller, J. F.; Wang, X.; Sohnlein, B. R.; Bhowmik, P.; Yang, D. S. J. Chem. Phys. 2004, 121, 7692. (45) Goncharov, V.; Heaven, M. C. J. Chem. Phys. 2006, 124, 064312. (46) Wigner, E. P. Phys. Rev. 1948, 73, 1002. (47) Chandler, D. W.; Houston, P. L. J. Chem. Phys. 1987, 87, 1445. (48) Helm, H.; Bjerre, N.; Dyer, M. J.; Huestis, D. L.; Saeed, M. Phys. Rev. Lett. 1993, 70, 3221. (49) Pinaré, J. C.; Baguenard, B.; Bordas, C.; Broyer, M. Phys. Rev. Lett. 1998, 81, 2225. (50) Leon, I.; Yang, Z.; Wang, L. S. J. Chem. Phys. 2013, 138, 184304. (51) Wu, X.; Qin, Z.; Xie, H.; Cong, R.; Wu, X.; Tang, Z.; Fan, H. J. Chem. Phys. 2010, 133, 044303. (52) McCunn, L. R.; Gardenier, G. H.; Guasco, T. L.; Elliott, B. M.; Bopp, J. C.; Relph, R. A.; Johnson, M. A. J. Chem. Phys. 2008, 128, 234311. (53) Sobhy, M. A.; Castleman, A. W. J. Chem. Phys. 2007, 126, 154314. (54) Davis, A. V.; Wester, R.; Bragg, A. E.; Neumark, D. M. J. Chem. Phys. 2003, 118, 999. (55) Surber, E.; Sanov, A. J. Chem. Phys. 2002, 116, 5921. (56) Eppink, A. T. J. B.; Parker, D. H. Rev. Sci. Instrum. 1997, 68, 3477. (57) Osterwalder, A.; Nee, M. J.; Zhou, J.; Neumark, D. M. J. Chem. Phys. 2004, 121, 6317. (58) Cavanagh, S. J.; Gibson, S. T.; Gale, M. N.; Dedman, C. J.; Roberts, E. H.; Lewis, B. R. Phys. Rev. A 2007, 76, 052708. (59) Neumark, D. M. J. Phys. Chem. A 2008, 112, 13287. (60) Baguenard, B.; Pinare, J. C.; Bordas, C.; Broyer, M. Phys. Rev. A 2001, 63, 3204. (61) Baguenard, B.; Pinare, J. C.; Lepine, F.; Bordas, C.; Broyer, M. Chem. Phys. Lett. 2002, 352, 147. (62) Surber, E.; Sanov, A. Phys. Rev. Lett. 2003, 90, 093001. (63) Wu, X.; Qin, Z. B.; Xie, H.; Wu, X. H.; Cong, R.; Tang, Z. C. Chin. J. Chem. Phys. 2010, 23, 373. (64) Hockett, P.; Staniforth, M.; Reid, K. L.; Townsend, D. Phys. Rev. Lett. 2009, 102, 253002. (65) Advances in Metal and Semiconductor Clusters, edited by Duncan, M. A., JAI Press, Inc.; 1993-1998, Vol. 1-4. (66) Knickelbein, M. B. Phil. Os. Mag. B 1999, 79, 1379. (67) Zewail, A. H. J. Phys. Chem. A 2000, 104, 5660. (68) Neumark, D. M. Annu. Rev. Phys. Chem. 2001, 52, 255. 341 (69) Greenblatt, B. J.; Zanni, M. T.; Neumark, D. M. Science 1997, 276, 1675. (70) Pontius, N.; Bechthold, P. S.; Neeb, M.; Eberhardt, W. Phys. Rev. Lett. 2000, 84, 1132. (71) McDaniel, E. W.; Mason, E. A. The Mobility and Diffusion of Ions in Gases; John Wiley & Sons: New York, USA, 1973. (72) Karasek, F. W. Anal. Chem. 1974, 46, 710A. (73) Mason, E. A.; McDaniel, E. W. Transport Properties of Ions in Gases; Wiley, 1988. (74) Kemper, P. R.; Bowers, M. T. J. Phys. Chem. 1991, 95, 5134. (75) Jarrold, M. F.; Bower, J. E. J. Chem. Phys. 1992, 96, 9180. (76) Hunter, J.; Fye, J.; Jarrold, M. F. Science 1993, 260, 784. (77) Dugourd, P.; Hudgins, R. R.; Clemmer, D. E.; Jarrold, M. F. Rev. Sci. Instrum. 1997, 68, 1122. (78) Weis, P.; Gilb, S.; Gerhardt, P.; Kappes, M. M. Int. J. Mass Spectrom. 2002, 216, 59. (79) Mark, H.; Wierl, R. Naturwissenschaften 1930, 18, 205. (80) Davisson, C.; Germer, L. H. Phys. Rev. 1927, 30, 705. (81) Thomson, G. P.; Reid, A. Nature 1927, 119, 890. (82) Pauling, L.; Brockway, L. O. J. Am. Chem. Soc. 1935, 57, 2684. (83) Fink, M.; Bonham, R. A. Rev. Sci. Instrum. 1970, 41, 389. (84) Rood, A. P.; Milledge, J. J. Chem. Soc. Farad. T. 2 1984, 80, 1145. (85) Bartell, L. S.; Dibble, T. S. J. Am. Chem. Soc. 1990, 112, 890. (86) Ewbank, J. D.; Faust, W. L.; Luo, J. Y.; English, J. T.; Monts, D. L.; Paul, D. W.; Dou, Q.; Schafer, L. Rev. Sci. Instrum. 1992, 63, 3352. (87) Mourou, G.; Williamson, S. Appl. Phys. Lett. 1982, 41, 44. (88) Aeschlimann, M.; Hull, E.; Cao, J.; Schmuttenmaer, C. A.; Jahn, L. G.; Gao, Y.; Elsayedali, H. E.; Mantell, D. A.; Scheinfein, M. R. Rev. Sci. Instrum. 1995, 66, 1000. (89) Bartell, L. S. Chem. Rev. 1986, 86, 491. (90) Parks, J. H.; Pollack, S.; Hill, W. J. Chem. Phys. 1994, 101, 6666. (91) Parks, J. H.; Szoke, A. J. Chem. Phys. 1995, 103, 1422. (92) Maier-Borst, M.; Cameron, D. B.; Rokni, M.; Parks, J. H. Phys. Rev. A 1999, 59, R3162. (93) Kruckeberg, S.; Schooss, D.; Maier-Borst, M.; Parks, J. H. Phys. Rev. Lett. 2000, 85, 4494. (94) Billas, I. M. L.; Chatelain, A.; deHeer, W. A. J. Magn. Magn. Mater. 1997, 168, 64. (95) Cox, D. M.; Trevor, D. J.; Whetten, R. L.; Rohlfing, E. A.; Kaldor, A. Phys. Rev. B 1985, 32, 7290. (96) Billas, I. M. L.; Chatelain, A.; Deheer, W. A. Science 1994, 265, 1682. (97) Bucher, J. P.; Douglass, D. C.; Bloomfield, L. A. Phys. Rev. Lett. 1991, 66, 3052. 342 (98) Apsel, S. E.; Emmert, J. W.; Deng, J.; Bloomfield, L. A. Phys. Rev. Lett. 1996, 76, 1441. (99) Cox, A. J.; Louderback, J. G.; Bloomfield, L. A. Phys. Rev. Lett. 1993, 71, 923. (100) Moro, R.; Xu, X. S.; Yin, S. Y.; de Heer, W. A. Science 2003, 300, 1265. (101) Armentrout, P. B.; Beauchamp, J. L. Chem. Phys. 1980, 50, 21. (102) Alexandrova, A. N.; Boldyrev, A. I. J. Chem. Theory Comput. 2005, 1, 566. (103) Sergeeva, A. P.; Averkiev, B. B.; Zhai, H. J.; Boldyrev, A. I.; Wang, L. S. J. Chem. Phys. 2011, 134, 224304. (104) Huang, W.; Sergeeva, A. P.; Zhai, H. J.; Averkiev, B. B.; Wang, L. S.; Boldyrev, A. I. Nature Chem. 2010, 2, 202. (105) Wales, D. J.; Doye, J. P. K. J. Phys. Chem. A 1997, 101, 5111. (106) Piazza, Z. A.; Li, W. L.; Romanescu, C.; Sergeeva, A. P.; Wang, L. S.; Boldyrev, A. I. J. Chem. Phys. 2012, 136, 104310. (107) Zubarev, D. Y.; Boldyrev, A. I. Phys. Chem. Chem. Phys. 2008, 10, 5207. (108) Sergeeva, A. P.; Piazza, Z. A.; Romanescu, C.; Li, W. L.; Boldyrev, A. I.; Wang, L. S. J. Am. Chem. Soc. 2012, 134, 18065. (109) Popov, I. A.; Piazza, Z. A.; Li, W. L.; Wang, L. S.; Boldyrev, A. I. J. Chem. Phys. 2013, 139, 144307. (110) Piazza, Z. A.; Hu, H. S.; Li, W. L.; Zhao, Y. F.; Li, J.; Wang, L. S. Nat. Commun. 2014, 5:3113 doi: 10.1038/ncomms4113. (111) Li, W. L.; Zhao, Y. F.; Hu, H. S.; Li, J.; Wang, L. S. Angew. Chem. Int. Ed. 2014, 53, 5540. (112) Li, W. L.; Chen, Q.; Tian, W. J.; Bai, H.; Zhao, Y. F.; Hu, H. S.; Li, J.; Zhai, H. J.; Li, S. D.; Wang, L. S. 2014, submitted. (113) Romanescu, C.; Galeev, T. R.; Sergeeva, A. P.; Li, W. L.; Wang, L. S.; Boldyrev, A. I. J. Organomet. Chem. 2012, 721, 148. (114) Romanescu, C.; Galeev, T. R.; Li, W. L.; Boldyrev, A. I.; Wang, L. S. Angew. Chem. Int. Ed. 2011, 50, 9334. (115) Romanescu, C.; Galeev, T. R.; Li, W. L.; Boldyrev, A. I.; Wang, L. S. J. Chem. Phys. 2013, 138, 134315. (116) Li, W. L.; Romanescu, C.; Piazza, Z. A.; Wang, L. S. Phys. Chem. Chem. Phys. 2012, 14, 13663. (117) Galeev, T. R.; Romanescu, C.; Li, W. L.; Wang, L. S.; Boldyrev, A. I. Angew. Chem. Int. Ed. 2012, 51, 2101. (118) Li, W. L.; Ivanov, A. S.; Federic, J.; Romanescu, C.; Cernusak, I.; Boldyrev, A. I.; Wang, L. S. J. Chem. Phys. 2013, 139, 104312. 343 (119) Xie, L.; Li, W. L.; Romanescu, C.; Huang, X.; Wang, L. S. J. Chem. Phys. 2013, 138, 034308. (120) Romanescu, C.; Galeev, T. R.; Li, W. L.; Boldyrev, A. I.; Wang, L. S. Acc. Chem. Res. 2013, 46, 350. (121) Li, W. L.; Romanescu, C.; Galeev, T. R.; Piazza, Z. A.; Boldyrev, A. I.; Wang, L. S. J. Am. Chem. Soc. 2012, 134, 165. (122) Albert, B.; Hillebrecht, H. Angew. Chem. Int. Ed. 2009, 48, 8640. (123) Hoard, J. L.; Sullenger, D. B.; Kennard, C. H. L.; Hughes, R. E. J. Solid State Chem. 1970, 1, 268. (124) Oganov, A. R.; Chen, J. H.; Gatti, C.; Ma, Y. Z.; Ma, Y. M.; Glass, C. W.; Liu, Z. X.; Yu, T.; Kurakevych, O. O.; Solozhenko, V. L. Nature 2009, 457, 863. (125) Fujimori, M.; Nakata, T.; Nakayama, T.; Nishibori, E.; Kimura, K.; Takata, M.; Sakata, M. Phys. Rev. Lett. 1999, 82, 4452. (126) Vast, N.; Baroni, S.; Zerah, G.; Besson, J. M.; Polian, A.; Grimsditch, M.; Chervin, J. C. Phys. Rev. Lett. 1997, 78, 693. (127) Decker, B. F.; Kasper, J. S. Acta Crystallographica 1959, 12, 503. (128) Zhai, H. J.; Wang, L. S.; Alexandrova, A. N.; Boldyrev, A. I. J. Chem. Phys. 2002, 117, 7917. (129) Zhai, H. J.; Wang, L. S.; Alexandrova, A. N.; Boldyrev, A. I. J. Phys. Chem. A 2003, 107, 9319. (130) Alexandrova, A. N.; Boldyrev, A. I.; Zhai, H. J.; Wang, L. S.; Steiner, E.; Fowler, P. W. J. Phys. Chem. A 2003, 107, 1359. (131) Alexandrova, A. N.; Boldyrev, A. I.; Zhai, H. J.; Wang, L. S. J. Phys. Chem. A 2004, 108, 3509. (132) Zhai, H. J.; Alexandrova, A. N.; Birch, K. A.; Boldyrev, A. I.; Wang, L. S. Angew. Chem. Int. Ed. 2003, 42, 6004. (133) Zhai, H. J.; Kiran, B.; Li, J.; Wang, L. S. Nat. Mater. 2003, 2, 827. (134) Alexandrova, A. N.; Zhai, H. J.; Wang, L. S.; Boldyrev, A. I. Inorg. Chem. 2004, 43, 3552. (135) Kiran, B.; Bulusu, S.; Zhai, H. J.; Yoo, S.; Zeng, X. C.; Wang, L. S. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 961. (136) Alexandrova, A. N.; Boldyrev, A. I.; Zhai, H. J.; Wang, L. S. J. Chem. Phys. 2005, 122, 054313. (137) Pan, L. L.; Li, J.; Wang, L. S. J. Chem. Phys. 2008, 129, 024302. (138) Sergeeva, A. P.; Zubarev, D. Y.; Zhai, H. J.; Boldyrev, A. I.; Wang, L. S. J. Am. Chem. Soc. 2008, 130, 7244. 344 (139) Oger, E.; Crawford, N. R. M.; Kelting, R.; Weis, P.; Kappes, M. M.; Ahlrichs, R. Angew. Chem. Int. Ed. 2007, 46, 8503. (140) Iijima, S. Nature 1991, 354, 56. (141) Cheng, L. J. J. Chem. Phys. 2012, 136, 104301. (142) Szwacki, N. G.; Sadrzadeh, A.; Yakobson, B. I. Phys. Rev. Lett. 2007, 98, 166804. (143) Wang, X.-Q. Phys. Rev. B 2010, 82, 153409. (144) Sadrzadeh, A.; Pupysheva, O. V.; Singh, A. K.; Yakobson, B. I. J. Phys. Chem. A 2008, 112, 13679. (145) Sadrzadeh, A.; Yakobson, B. I. In Handbook of Nanophysics; Sattler, K. D., Ed.; CRC Press: Boca Raton, 2010; Vol. 2, p 1. (146) Yakobson, B. I.; Ding, F. ACS Nano 2011, 5, 1569. (147) Tang, H.; Ismail-Beigi, S. Phys. Rev. Lett. 2007, 99, 115501. (148) Yang, X. B.; Ding, Y.; Ni, J. Phys. Rev. B 2008, 77, 041402R. (149) Tang, H.; Ismail-Beigi, S. Phys. Rev. B 2009, 80, 134113. (150) Tang, H.; Ismail-Beigi, S. Phys. Rev. B 2010, 82, 115412 (151) Galeev, T. R.; Chen, Q.; Guo, J. C.; Bai, H.; Miao, C. Q.; Lu, H. G.; Sergeeva, A. P.; Li, S. D.; Boldyrev, A. I. Phys. Chem. Chem. Phys. 2011, 13, 11575. (152) Penev, E. S.; Bhowmick, S.; Sadrzadeh, A.; Yakobson, B. I. Nano Lett. 2012, 12, 2441. (153) Liu, Y. Y.; Penev, E. S.; Yakobson, B. I. Angew. Chem. Int. Ed. 2013, 52, 3156. (154) Özdoğan, C.; Mukhopadhyay, S.; Hayami, W.; Güvenç, Z. B.; Pandey, R.; Boustani, I. J. Phys. Chem. C 2010, 114, 4362. (155) Singh, A. K.; Sadrzadeh, A.; Yakobson, B. I. Nano Lett. 2008, 8, 1314. (156) Boustani, I.; Quandt, A. Europhys. Lett. 1997, 39, 527. (157) Gindulyte, A.; Lipscomb, W. N.; Massa, L. Inorg. Chem. 1998, 37, 6544. (158) Saxena, S.; Tyson, T. A. Phys. Rev. Lett. 2010, 104, 245502. (159) Li, H.; Shao, N.; Shang, B.; Yuan, L. F.; Yang, J.; Zeng, X. C. Chem. Commun. 2010, 46, 3878. (160) Zhao, J.; Wang, L.; Li, F.; Chen, Z. J. Phys. Chem. A 2010, 114, 9969. (161) Wang, L.; Zhao, J.; Li, F.; Chen, Z. Chem. Phys. Lett. 2010, 501, 16. (162) Li, F.; Jin, P.; Jiang, D.-e.; Wang, L.; Zhang, S. B.; Zhao, J.; Chen, Z. J. Chem. Phys. 2012, 136. (163) Wu, X. J.; Dai, J.; Zhao, Y.; Zhuo, Z. W.; Yang, J. L.; Zeng, X. C. ACS Nano 2012, 6, 7443. (164) Laplaca, S. J.; Roland, P. A.; Wynne, J. J. Chem. Phys. Lett. 1992, 190, 163. (165) Wiley, W. C.; McLaren, I. H. Rev. Sci. Instrum. 1955, 26, 1150. 345 (166) de Heer, W. A.; Milani, P. Rev. Sci. Instrum. 1991, 62, 670. (167) Markovich, G.; Pollack, S.; Giniger, R.; Cheshnovsky, O. J. Chem. Phys. 1994, 101, 9344. (168) Kruit, P.; Read, F. H. J. Phys. E-Sci. Instrum. 1983, 16, 313. (169) Cheshnovsky, O.; Yang, S. H.; Pettiette, C. L.; Craycraft, M. J.; Smalley, R. E. Rev. Sci. Instrum. 1987, 58, 2131. (170) Akola, J.; Manninen, M.; Hakkinen, H.; Landman, U.; Li, X.; Wang, L. S. Phys. Rev. B 1999, 60, 11297. (171) Wang, L. S.; Li, X. In Proceedings of the International Symposium on Clusters and Nanostructure Interfaces; Jena, P., Khanna, S. N., Rao, B. K., Eds.; World Scientific, NJ, 2000: Richmond, VA, 1999, p 293. (172) Huang, W.; Wang, L. S. Phys. Rev. Lett. 2009, 102, 153401. (173) Huang, W.; Bulusu, S.; Pal, R.; Zeng, X. C.; Wang, L. S. ACS Nano 2009, 3, 1225. (174) Huang, W.; Wang, L. S. Phys. Chem. Chem. Phys. 2009, 11, 2663. (175) Kirkpatrick, S.; Gelatt, C. D.; Vecchi, M. P. Science 1983, 220, 671. (176) Wales, D. J.; Scheraga, H. A. Science 1999, 285, 1368. (177) Zhao, Y. F. & Li, J. TGMin: a global minimum search code based on basin hopping and divide-and-concur strategy. Nano Res. (in press). (178) Čížek, J. In Adv. Chem. Phys.; John Wiley & Sons, Inc.: 2007, p 35. (179) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Headgordon, M. Chem. Phys. Lett. 1989, 157, 479. (180) Knowles, P. J.; Hampel, C.; Werner, H. J. J. Chem. Phys. 1993, 99, 5219. (181) Purvis, G. D.; Bartlett, R. J. J. Chem. Phys. 1982, 76, 1910. (182) Bauernschmitt, R.; Ahlrichs, R. Chem. Phys. Lett. 1996, 256, 454. (183) Casida, M. E.; Jamorski, C.; Casida, K. C.; Salahub, D. R. J. Chem. Phys. 1998, 108, 4439. (184) Zakrzewski, V. G.; Ortiz, J. V.; Nichols, J. A.; Heryadi, D.; Yeager, D. L.; Golab, J. T. Int. J. Quantum Chem. 1996, 60, 29. (185) Cederbaum, L. S. J. Phys. B-At. Mol. Opt. 1975, 8, 290. (186) Ortiz, J. V. Int. J. Quantum Chem. 1989, 321. (187) Lin, J. S.; Ortiz, J. V. Chem. Phys. Lett. 1990, 171, 197. (188) Popov, I. A.; Boldyrev, A. I. J. Phys. Chem. C 2012, 116, 3147. (189) Popov, I. A.; Bozhenko, K. V.; Boldyrev, A. I. Nano Res. 2012, 5, 117. (190) Popov, I. A.; Li, Y.; Chen, Z.; Boldyrev, A. I. Phys. Chem. Chem. Phys. 2013, 15, 6842. (191) Foster, J. P.; Weinhold, F. J. Am. Chem. Soc. 1980, 102, 7211. (192) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. Rev. 1988, 88, 899. 346 (193) Greenwood, N. N. Chemistry of the Elements; 2nd ed.; Butterworth-Heinemann: Oxford, 1997. (194) Dilthey, W. Angew. Chem. 1921, 34, 596. (195) Price, W. C. J. Chem. Phys. 1947, 15, 614. (196) Price, W. C. J. Chem. Phys. 1948, 16, 894. (197) Longuethiggins, H. C.; Roberts, M. D. P. Roy. Soc. Lond. A Mat. 1954, 224, 336. (198) Longuethiggins, H. C.; Roberts, M. D. P. Roy. Soc. Lond. A Mat. 1955, 230, 110. (199) Hedberg, K.; Schomaker, V. J. Am. Chem. Soc. 1951, 73, 1482. (200) Lipscomb, W. N. Boron Hydrides New York, 1963. (201) Brown, H. C.; Zweifel, G. J. Am. Chem. Soc. 1959, 81, 247. (202) Kawai, R.; Weare, J. H. J. Chem. Phys. 1991, 95, 1151. (203) Kawai, R.; Weare, J. H. Chem. Phys. Lett. 1992, 191, 311. (204) Hanley, L.; Whitten, J. L.; Anderson, S. L. J. Phys. Chem. 1988, 92, 5803. (205) Hernandez, R.; Simons, J. J. Chem. Phys. 1991, 94, 2961. (206) Martin, J. M. L.; Francois, J. P.; Gijbels, R. Chem. Phys. Lett. 1992, 189, 529. (207) Kato, H.; Yamashita, K.; Morokuma, K. Chem. Phys. Lett. 1992, 190, 361. (208) Boustani, I. Int. J. Quantum Chem. 1994, 52, 1081. (209) Boustani, I. Phys. Rev. B 1997, 55, 16426. (210) Boustani, I. Surf. Sci. 1997, 370, 355. (211) Ricca, A.; Bauschlicher, C. W. Chem. Phys. 1996, 208, 233. (212) Niu, J.; Rao, B. K.; Jena, P. J. Chem. Phys. 1997, 107, 132. (213) Gu, F. L.; Yang, X. M.; Tang, A. C.; Jiao, H. J.; Schleyer, P. V. J. Comput. Chem. 1998, 19, 203. (214) Zubarev, D. Y.; Boldyrev, A. I. J. Comput. Chem. 2007, 28, 251. (215) Alexandrova, A. N.; Boldyrev, A. I.; Zhai, H. J.; Wang, L. S. Coord. Chem. Rev. 2006, 250, 2811. (216) Fowler, J. E.; Ugalde, J. M. J. Phys. Chem. A 2000, 104, 397. (217) Aihara, J. J. Phys. Chem. A 2001, 105, 5486. (218) Jimenez-Halla, J. O. C.; Islas, R.; Heine, T.; Merino, G. Angew. Chem. Int. Ed. 2010, 49, 5668. (219) Martinez-Guajardo, G.; Sergeeva, A. P.; Boldyrev, A. I.; Heine, T.; Ugalde, J. M.; Merino, G. Chem. Commun. 2011, 47, 6242. (220) Zhang, J.; Sergeeva, A. P.; Sparta, M.; Alexandrova, A. N. Angew. Chem. Int. Ed. 2012, 51, 8512. 347 (221) Tai, T. B.; Ceulemans, A.; Nguyen, M. T. Chem. Eur. J. 2012, 18, 4510. (222) Romanescu, C.; Harding, D. J.; Fielicke, A.; Wang, L. S. J. Chem. Phys. 2012, 137, 014317. (223) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J. Am. Chem. Soc. 1980, 102, 939. (224) Adamo, C.; Barone, V. J. Chem. Phys. 1999, 110, 6158. (225) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (226) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1997, 78, 1396. (227) Headgordon, M.; Pople, J. A.; Frisch, M. J. Chem. Phys. Lett. 1988, 153, 503. (228) Saebo, S.; Almlof, J. Chem. Phys. Lett. 1989, 154, 83. (229) Gordon, M. S.; Binkley, J. S.; Pople, J. A.; Pietro, W. J.; Hehre, W. J. J. Am. Chem. Soc. 1982, 104, 2797. (230) Pietro, W. J.; Francl, M. M.; Hehre, W. J.; Defrees, D. J.; Pople, J. A.; Binkley, J. S. J. Am. Chem. Soc. 1982, 104, 5039. (231) Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. V. J. Comput. Chem. 1983, 4, 294. (232) Hung Tan, P.; Long Van, D.; Buu Quoc, P.; Minh Tho, N. Chem. Phys. Lett. 2013, 577, 32. (233) Ruatta, S. A.; Hintz, P. A.; Anderson, S. L. J. Chem. Phys. 1991, 94, 2833. (234) Jayatilaka, D.; Lee, T. J. J. Chem. Phys. 1993, 98, 9734. (235) Lee, T. J.; Rice, J. E.; Scuseria, G. E.; Schaefer, H. F. Theor. Chim. Acta 1989, 75, 81. (236) Lee, T. J.; Taylor, P. R. Int. J. Quantum Chem. 1989, 199. (237) Rienstra-Kiracofe, J. C.; Allen, W. D.; Schaefer, H. F. J. Phys. Chem. A 2000, 104, 9823. (238) Tao, J.; Perdew, J. P.; Staroverov, V. N.; Scuseria, G. E. Phys. Rev. Lett. 2003, 91, 146401. (239) Zubarev, D. Y.; Boldyrev, A. I. J. Org. Chem. 2008, 73, 9251. (240) Boustani, I.; Quandt, A.; Hernandez, E.; Rubio, A. J. Chem. Phys. 1999, 110, 3176. (241) Evans, M. H.; Joannopoulos, J. D.; Pantelides, S. T. Phys. Rev. B 2005, 72, 045434. (242) Kunstmann, J.; Quandt, A. Phys. Rev. B 2006, 74, 035413. (243) Lau, K. C.; Pandey, R. J. Phys. Chem. C 2007, 111, 2906. (244) An, W.; Bulusu, S.; Gao, Y.; Zeng, X. C. J. Chem. Phys. 2006, 124, 154310. (245) Li, S. D.; Zhai, H. J.; Wang, L. S. J. Am. Chem. Soc. 2008, 130, 2573. (246) Tai, T. B.; Tam, N. M.; Nguyen, M. T. Chem. Phys. Lett. 2012, 530, 71. (247) Prasad, D. L. V. K.; Jemmis, E. D. Phys. Rev. Lett. 2008, 100, 165504. (248) De, S.; Willand, A.; Amsler, M.; Pochet, P.; Genovese, L.; Goedecker, S. Phys. Rev. Lett. 2011, 106, 225502. (249) Er, S.; de Wijs, G. A.; Brocks, G. J. Phys. Chem. C 2009, 113, 18962. (250) Ettl, R.; Chao, I.; Diederich, F.; Whetten, R. L. Nature 1991, 353, 149. 348 (251) Lechtken, A.; Schooss, D.; Stairs, J. R.; Blom, M. N.; Furche, F.; Morgner, N.; Kostko, O.; von Issendorff, B.; Kappes, M. M. Angew. Chem. Int. Ed. 2007, 46, 2944. (252) Santizo, I. E.; Hidalgo, F.; Perez, L. A.; Noguez, C.; Garzon, I. L. J. Phys. Chem. C 2008, 112, 17533. (253) Chernozatonskii, L. A.; Sorokin, P. B.; Yakobson, B. I. Jetp Lett. 2008, 87, 489. (254) Ding, Y.; Yang, X.; Ni, J. Appl. Phys. Lett. 2008, 93, 043107. (255) Tai, T. B.; Duong, L. V.; Pham, H. T.; Mai, D. T. T.; Nguyen, M. T. Chem. Comm. 2014, 50, 1558. (256) Henkelman, G.; Jonsson, H. J. Chem. Phys. 1999, 111, 7010. (257) Olson, J. K.; Boldyrev, A. I. Chem. Phys. Lett. 2011, 517, 62. (258) Lu, H. G.; Mu, Y. W.; Bai, H.; Chen, Q.; Li, S. D. J. Chem. Phys. 2013, 138, 024701. (259) Yu, X.; Li, L.; Xu, X.-W.; Tang, C.-C. J. Phys. Chem. C 2012, 116, 20075. (260) Lau, K. C.; Pandey, R. J. Phys. Chem. B 2008, 112, 10217. (261) Liu, H.; Gao, J.; Zhao, J. Scientific Reports. 2013. (262) Li, W. L.; Romanescu, C.; Jian, T.; Wang, L. S. J. Am. Chem. Soc. 2012, 134, 13228. (263) Li, D. Z.; Chen, Q.; Wu, Y. B.; Lu, H. G.; Li, S. D. Phys. Chem. Chem. Phys. 2012, 14, 14769. (264) Zhai, H. J.; Chen, Q.; Bai, H.; Lu, H. G.; Li, W. L.; Li, S. D.; Wang, L. S. J. Chem. Phys. 2013, 139, 174301. (265) Bai, H.; Chen, Q.; Miao, C. Q.; Mu, Y. W.; Wu, Y. B.; Lu, H. G.; Zhai, H. J.; Li, S. D. Phys. Chem. Chem. Phys. 2013, 15, 18872. (266) Research highlight: new balls, p. N., 4 (2007). (267) Sergeeva, A. P.; Popov, I. A.; Piazza, Z. A.; Li, W.-L.; Romanescu, C.; Wang, L. S.; Boldyrev, A. I. Acc. Chem. Res. 2014, 47, 1349. (268) Quandt, A.; Boustani, I. ChemPhysChem 2005, 6, 2001. (269) Yan, Q. B.; Sheng, X. L.; Zheng, Q. R.; Zhang, L. Z.; Su, G. Phys. Rev. B 2008, 78, 201401. (270) Zope, R. R.; Baruah, T.; Lau, K. C.; Liu, A. Y.; Pederson, M. R.; Dunlap, B. I. Phys. Rev. B 2009, 79, 161403. (271) Sheng, X.-L.; Yan, Q.-B.; Zheng, Q.-R.; Su, G. Phys. Chem. Chem. Phys. 2009, 11, 9696. (272) Muya, J. T.; Gopakumar, G.; Nguyen, M. T.; Ceulemans, A. Phys. Chem. Chem. Phys. 2011, 13, 7524. (273) Zope, R. R.; Baruah, T. Chem. Phys. Lett. 2011, 501, 193. (274) Polad, S.; Ozay, M. Phys. Chem. Chem. Phys. 2013, 15, 19819. (275) Boulanger, P.; Morinière, M.; Genovese, L.; Pochet, P. J. Chem. Phys. 2013, 138, 184302. 349 (276) Shang, C.; Liu, Z. P. J. Chem. Theory Comput. 2013, 9, 1838. (277) Tang, A. C.; Li, Q. S.; Liu, C. W.; Li, J. Chem. Phys. Lett. 1993, 201, 465. (278) Zhai, H. J.; Zhao, Y. F.; Li, W. L.; Chen, Q.; Bai, H.; Hu, H. S.; Piazza, Z. A.; Tian, W. J.; Lu, H. G.; Wu, Y. B.; Mu, Y. W.; Wei, G. F.; Liu, Z.-P.; Li, J.; Li, S.-D.; Wang, L. S. Nat. Chem. 2014, doi:10.1038/nchem.1999. (279) Schleyer, P. V.; Maerker, C.; Dransfeld, A.; Jiao, H. J.; Hommes, N. J. R. V. J. Am. Chem. Soc. 1996, 118, 6317. (280) Wang, L. S.; Alford, J. M.; Chai, Y.; Diener, M.; Zhang, J.; Mcclure, S. M.; Guo, T.; Scuseria, G. E.; Smalley, R. E. Chem. Phys. Lett. 1993, 207, 354. (281) Li, M.; Li, Y. F.; Zhou, Z.; Shen, P. W.; Chen, Z. F. Nano Lett. 2009, 9, 1944. (282) Cui, L. F.; Huang, X.; Wang, L. M.; Zubarev, D. Y.; Boldyrev, A. I.; Li, J.; Wang, L. S. J. Am. Chem. Soc. 2006, 128, 8390. (283) Cui, L. F.; Huang, X.; Wang, L. M.; Li, J.; Wang, L. S. J. Phys. Chem. A 2006, 110, 10169. (284) Bulusu, S.; Li, X.; Wang, L. S.; Zeng, X. C. Proc. Natl. Acad. Sci. U. S. A. 2006, 103, 8326. (285) Exner, K.; Schleyer, P. V. Science 2000, 290, 1937. (286) Wang, Z. X.; Schleyer, P. V. Science 2001, 292, 2465. (287) Islas, R.; Heine, T.; Ito, K.; Schleyer, P. V. R.; Merino, G. J. Am. Chem. Soc. 2007, 129, 14767. (288) Erhardt, S.; Frenking, G.; Chen, Z. F.; Schleyer, P. V. Angew. Chem. Int. Ed. 2005, 44, 1078. (289) Wang, L. M.; Huang, W.; Averkiev, B. B.; Boldyrev, A. I.; Wang, L. S. Angew. Chem. Int. Ed. 2007, 46, 4550. (290) Galeev, T. R.; Ivanov, A. S.; Romanescu, C.; Li, W. L.; Bozhenko, K. V.; Wang, L. S.; Boldyrev, A. I. Phys. Chem. Chem. Phys. 2011, 13, 8805. (291) Averkiev, B. B.; Zubarev, D. Y.; Wang, L. M.; Huang, W.; Wang, L. S.; Boldyrev, A. I. J. Am. Chem. Soc. 2008, 130, 9248. (292) Galeev, T. R.; Romanescu, C.; Li, W. L.; Wang, L. S.; Boldyrev, A. I. J. Chem. Phys. 2011, 135, 104301. (293) Li, W. L.; Romanescu, C.; Galeev, T. R.; Wang, L. S.; Boldyrev, A. I. J. Phys. Chem. A 2011, 115, 10391. (294) Romanescu, C.; Sergeeva, A. P.; Li, W. L.; Boldyrev, A. I.; Wang, L. S. J. Am. Chem. Soc. 2011, 133, 8646. (295) Zhai, H. J.; Miao, C. Q.; Li, S. D.; Wang, L. S. J. Phys. Chem. A 2010, 114, 12155. (296) Lein, M.; Frunzke, J.; Frenking, G. Angew. Chem. Int. Ed. 2003, 42, 1303. (297) Averkiev, B. B.; Boldyrev, A. I. Russ. J. Gen. Chem. 2008, 78, 769. 350 (298) Luo, Q. Sci. China Ser. B-Chem 2008, 51, 607. (299) Ito, K.; Pu, Z.; Li, Q. S.; Schleyer, P. V. R. Inorg. Chem. 2008, 47, 10906. (300) Pu, Z. F.; Ito, K.; Schleyer, P. V.; Li, Q. S. Inorg. Chem. 2009, 48, 10679. (301) Miao, C. Q.; Guo, J. C.; Li, S. D. Sci. China Ser. B-Chem 2009, 52, 900. (302) Averkiev, B. B.; Wang, L. M.; Huang, W.; Wang, L. S.; Boldyrev, A. I. Phys. Chem. Chem. Phys. 2009, 11, 9840. (303) Li, J.; Li, X.; Zhai, H. J.; Wang, L. S. Science 2003, 299, 864. (304) Wang, X. B.; Ding, C. F.; Wang, L. S. J. Chem. Phys. 1999, 110, 8217. (305) Rowe, D. J. Rev. Mod. Phy. 1968, 40, 153. (306) Simons, J.; Smith, W. D. J. Chem. Phys. 1973, 58, 4899. (307) Sekino, H.; Bartlett, R. J. Int. J. Quantum Chem. 1984, 255. (308) Stanton, J. F.; Bartlett, R. J. J. Chem. Phys. 1993, 98, 7029. (309) Levchenko, S. V.; Krylov, A. I. J. Chem. Phys. 2004, 120, 175. (310) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650. (311) Bersuker, I. B. Chem. Rev. 2001, 101, 1067. (312) Bersuker, I. B. Chem. Rev. 2013, 113, 1351. (313) Boustani, I.; Pandey, R. Solid State Sci. 2012, 14, 1591. (314) Wu, Q.; Tang, Y.; Zhang, X. Sci. China Ser. B-Chem 2009, 52, 288. (315) Heine, T.; Merino, G. Angew. Chem. Int. Ed. 2012, 51, 4275. (316) Cordero, B.; Gomez, V.; Platero-Prats, A. E.; Reves, M.; Echeverria, J.; Cremades, E.; Barragan, F.; Alvarez, S. Dalton Trans. 2008, 2832. (317) Fokwa, B. P. T.; Hermus, M. Angew. Chem. Int. Ed. 2012, 51, 1702. (318) Kuznetsov, A.; Boldyrev, A. Struct. Chem. 2002, 13, 141. (319) Li, Q. S.; Jin, Q. J. Phys. Chem. A 2003, 107, 7869. (320) Li, Q. S.; Jin, Q. J. Phys. Chem. A 2004, 108, 855. (321) Ghosh, S.; Beatty, A. M.; Fehlner, T. P. J. Am. Chem. Soc. 2001, 123, 9188. (322) Le Guennic, B.; Jiao, H.; Kahlal, S.; Saillard, J. Y.; Halet, J. F.; Ghosh, S.; Shang, M.; Beatty, A. M.; Rheingold, A. L.; Fehlner, T. P. J. Am. Chem. Soc. 2004, 126, 3203. (323) Alexandrova, A. N.; Boldyrev, A. I. Inorg. Chem. 2004, 43, 3588. (324) Alexandrova, A. N.; Birch, K. A.; Boldyrev, A. I. J. Am. Chem. Soc. 2003, 125, 10786. (325) Lupan, A.; Bruce King, R. Polyhedron 2013, 60, 151. (326) Fehlner, T. P. J. Organomet. Chem. 2009, 694, 1671. (327) Bose, S. K.; Ghosh, S.; Noll, B. C.; Halet, J. F.; Saillard, J. Y.; Vega, A. Organometallics 2007, 26, 5377. 351 (328) Bose, S. K.; Geetharani, K.; Varghese, B.; Mobin, S. M.; Ghosh, S. Chem. Eur. J. 2008, 14, 9058. (329) Dhayal, R. S.; Chakrahari, K. K. V.; Ramkumar, V.; Ghosh, S. J. Cluster Sci. 2009, 20, 565. (330) Geetharani, K.; Bose, S. K.; Pramanik, G.; Saha, T. K.; Ramkumar, V.; Ghosh, S. Eur. J. Inorg. Chem. 2009, 1483. (331) Sahoo, S.; Reddy, K. H. K.; Dhayal, R. S.; Mobin, S. M.; Ramkumar, V.; Jemmis, E. D.; Ghosh, S. Inorg. Chem. 2009, 48, 6509. (332) Dhayal, R. S.; Chakrahari, K. K. V.; Varghese, B.; Mobin, S. M.; Ghosh, S. Inorg. Chem. 2010, 49, 7741. (333) Bose, S. K.; Geetharani, K.; Ghosh, S. Chem. Comm. 2011, 47, 11996. (334) Geetharani, K.; Krishnamoorthy, B. S.; Kahlal, S.; Mobin, S. M.; Halet, J. F.; Ghosh, S. Inorg. Chem. 2012, 51, 10176. (335) Krishnamoorthy, B. S.; Kahlal, S.; Le Guennic, B.; Saillard, J.-Y.; Ghosh, S.; Halet, J. F. Solid State Sci. 2012, 14, 1617. (336) Lupan, A.; King, R. B. Inorg. Chem. 2012, 51, 7609. (337) Ohishi, Y.; Kimura, K.; Yamaguchi, M.; Uchida, N.; Kanayama, T. J. Chem. Phys. 2008, 128, 124304. (338) Bai, H.; Li, S. D. J. Cluster Sci. 2011, 22, 525. (339) Ricca, A.; Bauschlicher, C. W. J. Chem. Phys. 1997, 106, 2317. (340) Alexandrova, A. N.; Koyle, E.; Boldyrev, A. I. J. Mol. Model. 2006, 12, 569. (341) Zhai, H. J.; Wang, L. S.; Zubarev, D. Y.; Boldyrev, A. I. J. Phys. Chem. A 2006, 110, 1689. (342) Chen, Q.; Li, S. D. J. Cluster Sci. 2011, 22, 513. (343) Chen, Q.; Bai, H.; Guo, J. C.; Miao, C. Q.; Li, S. D. Phys. Chem. Chem. Phys. 2011, 13, 20620. (344) Olson, J. K.; Boldyrev, A. I. Chem. Phys. 2011, 379, 1. (345) Szwacki, N. G.; Weber, V.; Tymczak, C. J. Nanoscale Res. Lett. 2009, 4, 1085. (346) Ohishi, Y.; Kimura, K.; Yamaguchi, M.; Uchida, N.; Kanayama, T. J. Chem. Phys. 2010, 133, 074305. (347) Olson, J. K.; Boldyrev, A. I. Inorg. Chem. 2009, 48, 10060. (348) Nguyen, V. S.; Matus, M. H.; Nguyen, M. T.; Dixon, D. A. J. Phys. Chem. C 2007, 111, 9603. (349) Wang, L. S. Phys. Chem. Chem. Phys. 2010, 12, 8694. (350) Kiran, B.; Li, X.; Zhai, H. J.; Cui, L. F.; Wang, L. S. Angew. Chem. Int. Ed. 2004, 43, 2125. 352 (351) Bock, H.; Cederbaum, L. S.; Vonniessen, W.; Paetzold, P.; Rosmus, P.; Solouki, B. Angew. Chem. Int. Ed. 1989, 28, 88. (352) Braunschweig, H.; Radacki, K.; Schneider, A. Science 2010, 328, 345. (353) Zhai, H. J.; Wang, L. M.; Li, S. D.; Wang, L. S. J. Phys. Chem. A 2007, 111, 1030. (354) Zhai, H. J.; Li, S. D.; Wang, L. S. J. Am. Chem. Soc. 2007, 129, 9254. (355) Zhai, H. J.; Guo, J. C.; Li, S. D.; Wang, L. S. ChemPhysChem 2011, 12, 2549. (356) Lykke, K. R.; Murray, K. K.; Lineberger, W. C. Phys. Rev. A 1991, 43, 6104. (357) Chen, Q.; Zhai, H. J.; Li, S. D.; Wang, L. S. J. Chem. Phys. 2012, 137, 044307. (358) Tai, T. B.; Nguyen, M. T.; Dixon, D. A. J. Phys. Chem. A 2010, 114, 2893. (359) Li, Y.; Liu, Y. J.; Wu, D.; Li, Z. R. Phys. Chem. Chem. Phys. 2009, 11, 5703. (360) Nguyen, K. A.; Lammertsma, K. J. Phys. Chem. A 1998, 102, 1608. (361) Yao, W. Z.; Yao, J. B.; Li, X. B.; Li, S. D. Acta Phys.-Chim. Sin. 2013, 29, 1219. (362) Wang, L. S.; Conceicao, J.; Jin, C. M.; Smalley, R. E. Chem. Phys. Lett. 1991, 182, 5. (363) Ceulemans, A.; Gopakumar, G.; Nguyen, M. T. Chem. Phys. Lett. 2008, 450, 175. (364) Zhai, H. J.; Li, S.; Dixon, D. A.; Wang, L. S. J. Am. Chem. Soc. 2008, 130, 5167. (365) Li, W. L.; Xie, L.; Jian, T.; Romanescu, C.; Huang, X.; Wang, L. S. Angew. Chem. Int. Ed. 2014, 53, 1288. (366) Nayak, S. K.; Rao, B. K.; Jena, P.; Li, X.; Wang, L. S. Chem. Phys. Lett. 1999, 301, 379. (367) Li, S. D.; Miao, C. Q.; Guo, J. C.; Ren, G. M. J. Comput. Chem. 2006, 27, 1858. (368) Jia, J.; Ma, L.; Wang, J. F.; Wu, H. S. J. Mol. Model. 2013, 19, 3255. (369) Levason, W.; McAuliffe, C. A. Coord. Chem. Rev. 1974, 12, 151. (370) Morss, L. R.; Edelstein, N. M.; Fuger, J. The Chemistry of the Actinide and Transactinide Elements; Springer: Dordrecht, Netherlands, 2006; Vol. 1. (371) Gabelnic, S. d.; Reedy, G. T.; Chasanov, M. G. J. Chem. Phys. 1973, 58, 4468. (372) Hunt, R. D.; Andrews, L. J. Chem. Phys. 1993, 98, 3690. (373) Zhou, M. F.; Andrews, L.; Ismail, N.; Marsden, C. J. Phys. Chem. A 2000, 104, 5495. (374) Gagliardi, L.; Roos, B. O.; Malmqvist, P. A.; Dyke, J. M. J. Phys. Chem. A 2001, 105, 10602. (375) Chang, Q., Master of Science thesis, The Ohio State University, 2002. (376) Han, J. D.; Kaledin, L. A.; Goncharov, V.; Komissarov, A. V.; Heaven, M. C. J. Am. Chem. Soc. 2003, 125, 7176. (377) Han, J. D.; Goncharov, V.; Kaledin, L. A.; Komissarov, A. V.; Heaven, M. C. J. Chem. Phys. 2004, 120, 5155. (378) Lue, C. J.; Jin, J.; Ortiz, M. J.; Rienstra-Kiracofe, J. C.; Heaven, M. C. J. Am. Chem. Soc. 2004, 126, 1812. 353 (379) Li, J.; Bursten, B. E.; Andrews, L.; Marsden, C. J. J. Am. Chem. Soc. 2004, 126, 3424. (380) Clavaguera Sarrio, C.; V, V.; Maynau, D.; Marsden, C. J. J. Chem. Phys. 2004, 121, 5312. (381) Gagliardi, L.; Heaven, M. C.; Krogh, J. W.; Roos, B. O. J. Am. Chem. Soc. 2005, 127, 86. (382) Fleig, T.; Jensen, H. J. A.; Olsen, J.; Visscher, L. J. Chem. Phys. 2006, 124, 104106. (383) Infante, I.; Eliav, E.; Vilkas, M. J.; Ishikawa, Y.; Kaldor, U.; Visscher, L. J. Chem. Phys. 2007, 127, 124308. (384) Merritt, J. M.; Han, J.; Heaven, M. C. J. Chem. Phys. 2008, 128, 084304. (385) Infante, I.; Andrews, L.; Wang, X. F.; Gagliardi, L. Chem. Eur. J. 2010, 16, 12804. (386) Pepper, M.; Bursten, B. E. Chem. Rev. 1991, 91, 719. (387) Marcalo, J.; Santos, M.; de Matos, A. P.; Gibson, J. K. Inorg. Chem. 2009, 48, 5055. (388) Michelini, M. D.; Marcalo, J.; Russo, N.; Gibson, J. K. Inorg. Chem. 2010, 49, 3836. (389) ADF2010.02, SCM, Vrije Universiteit, Amsterdam, see http://www.scm.com. (390) Guerra, C. F.; Snijders, J. G.; te Velde, G.; Baerends, E. J. Theor. Chem. Acc. 1998, 99, 391. (391) te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Guerra, C. F.; Van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. J. Comput. Chem. 2001, 22, 931. (392) Van Lenthe, E.; Baerends, E. J. J. Comput. Chem. 2003, 24, 1142. (393) Van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1993, 99, 4597. (394) H. J. Werner; P. J. Knowles; G. Knizia; F. R. Manby; M. Schütz; 2012.1 ed. 2010, p MOLPRO. (395) Andersson, K.; Malmqvist, P. A.; Roos, B. O. J. Chem. Phys. 1992, 96, 1218. (396) Ghigo, G.; Roos, B. O.; Malmqvist, P. A. Chem. Phys. Lett. 2004, 396, 142. (397) Malmqvist, P. A.; Roos, B. O.; Schimmelpfennig, B. Chem. Phys. Lett. 2002, 357, 230. (398) Roos, B. O.; Malmqvist, P. A. Phys. Chem. Chem. Phys. 2004, 6, 2919. (399) Cao, X. Y.; Dolg, M.; Stoll, H. J. Chem. Phys. 2003, 118, 487. (400) Cao, X. Y.; Dolg, M. J. Mol. Struct.. Theochem 2004, 673, 203. (401) See http://www.theochem.uni-stuttgart.de/pseudopotentials for the pseudopotentials and basis sets. (402) Kendall, R. A.; Dunning, T. H.; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796. (403) Dolg, M.; Cao, X. J. Phys. Chem. A 2009, 113, 12573. (404) Denning, R. G. Struct. Bonding 1992, 79, 215. (405) Denning, R. G. J. Phys. Chem. A 2007, 111, 4125. (406) Ryzhkov, M. V.; Gubanov, V. A. J. Radioan. Nucl. Ch. Ar. 1990, 143, 85. (407) Mcglynn, S. P.; Smith, J. K. J. Mol. Spectrosc. 1961, 6, 164. (408) Su, J.; Zhang, K.; Schwarz, W. H. E.; Li, J. Inorg. Chem. 2011, 50, 2082. 354 (409) Suzer, S.; Lee, S. T.; Shirley, D. A. Phys. Rev. A 1976, 13, 1842. (410) Su, J.; Wang, Y. L.; Wei, F.; Schwarz, W. H. E.; Li, J. J. Chem. Theory Comput. 2011, 7, 3293. (411) Li, Y.; Su, J.; Mitchell, E.; Zhang, G.; Li, J. Sci. China Chem. 2013, 56, 1671. (412) Kimura, M.; Schomake.V; Smith, D. W. J. Chem. Phys. 1968, 48, 4001. (413) Levy, J. H.; Taylor, J. C.; Wilson, P. W. J. Chem. Soc. Dalton 1976, 219. (414) Mcdowell, R. S.; Asprey, L. B.; Paine, R. T. J. Chem. Phys. 1974, 61, 3571. (415) Paine, R. T.; Mcdowell, R. S.; Asprey, L. B.; Jones, L. H. J. Chem. Phys. 1976, 64, 3081. (416) Jones, L. H.; Swanson, B. I.; Ekberg, S. A. J. Phys. Chem. 1984, 88, 1285. (417) Kunze, K. R.; Hauge, R. H.; Hamill, D.; Margrave, J. L. J. Chem. Phys. 1976, 65, 2026. (418) Kunze, K. R.; Hauge, R. H.; Hamill, D.; Margrave, J. L. J. Phys. Chem. 1977, 81, 1664. (419) Lewis, W. B.; Asprey, L. B.; Jones, L. H.; Mcdowell, R. S.; Rabideau, S. W.; Zeltmann, A. H.; Paine, R. T. J. Chem. Phys. 1976, 65, 2707. (420) Mcdiarmid, R. J. Chem. Phys. 1976, 65, 168. (421) Bernstein, E. R.; Meredith, G. R. Chem. Phys. 1977, 24, 289. (422) Bosworth, Y. M.; Clark, R. J. H.; Rippon, D. M. J. Mol. Spectrosc. 1973, 46, 240. (423) Miller, J. C.; Allison, S. W.; Andrews, L. J. Chem. Phys. 1979, 70, 3524. (424) Rianda, R.; Frueholz, R. P.; Kuppermann, A. J. Chem. Phys. 1979, 70, 1056. (425) Cartwright, D. C.; Trajmar, S.; Chutjian, A.; Srivastava, S. J. Chem. Phys. 1983, 79, 5483. (426) Martensson, N.; Malmquist, P. A.; Svensson, S.; Johansson, B. J. Chem. Phys. 1984, 80, 5458. (427) Hay, P. J.; Martin, R. L. J. Chem. Phys. 1998, 109, 3875. (428) Onoe, J.; Sekine, R.; Takeuchi, K.; Nakamatsu, H.; Mukoyama, T.; Adachi, H. Chem. Phys. Lett. 1994, 217, 61. (429) Onoe, J.; Takeuchi, K.; Nakamatsu, H.; Mukoyama, T.; Sekine, R.; Kim, B. I.; Adachi, H. J. Chem. Phys. 1993, 99, 6810. (430) Case, D. A.; Yang, C. Y. J. Chem. Phys. 1980, 72, 3443. (431) Larsson, S.; Tse, J. S.; Esquivel, J. L.; Kai, A. T. Chem. Phys. 1984, 89, 43. (432) Gagliardi, L.; Willetts, A.; Skylaris, C.-K.; Handy, N. C.; Spencer, S.; Ioannou, A. G.; Simper, A. M. J. Am. Chem. Soc. 1998, 120, 11727. (433) Schreckenbach, G.; Hay, P. J.; Martin, R. L. J. Comput. Chem. 1999, 20, 70. (434) Han, Y. K.; Hirao, K. J. Chem. Phys. 2000, 113, 7345. (435) Batista, E. R.; Martin, R. L.; Hay, P. J.; Peralta, J. E.; Scuseria, G. E. J. Chem. Phys. 2004, 121, 2144. 355 (436) Shamov, G. A.; Schreckenbach, G.; Vo, T. N. Chem. Eur. J. 2007, 13, 4932. (437) Perez-Villa, A.; David, J.; Fuentealba, P.; Restrepo, A. Chem. Phys. Lett. 2011, 507, 57. (438) Wei, F.; Wu, G. S.; Schwarz, W. H. E.; Li, J. J. Chem. Theory Comput. 2011, 7, 3223. (439) Hay, P. J.; Wadt, W. R.; Kahn, L. R.; Raffenetti, R. C.; Phillips, D. H. J. Chem. Phys. 1979, 71, 1767. (440) Larsson, S.; Pyykko, P. Chem. Phys. 1986, 101, 355. (441) Jackson, G. P.; Gibson, J. K.; Duckworth, D. C. J. Phys. Chem. A 2004, 108, 1042. (442) Hunt, R. D.; Thompson, C.; Hassanzadeh, P.; Andrews, L. Inorg. Chem. 1994, 33, 388. (443) Kunze, K. R.; Hauge, R. H.; Margrave, J. L. Inorg. Nucl. Chem. Lett. 1979, 15, 65. (444) Dau, P. D.; Liu, H. T.; Huang, D. L.; Wang, L. S. J. Chem. Phys. 2012, 137, 116101. (445) Girichev, G. V.; Petrov, V. M.; Giricheva, N. I.; Zasorin, E. Z.; Krasnov, K. S.; Kiselev, Y. M. J. Struct. Chem 1983, Medium: X; Size: P61. (446) Konings, R. J. M.; Booij, A. S.; Kovacs, A.; Girichev, G. V.; Giricheva, N. I.; Krasnova, O. G. J. Mol. Struct. 1996, 378, 121. (447) Hildenbrand, D. L. J. Chem. Phys. 1977, 66, 4788. (448) Hildenbrand, D. L. Pure Appl. Chem. 1988, 60, 303. (449) Hildenbrand, D. L.; Lau, K. H.; Brittain, R. D. J. Chem. Phys. 1991, 94, 8270. (450) Bukhmarina, V. N.; Predtechensky, Y. B.; Shcherba, L. D. J. Mol. Struct. 1990, 218, 33. (451) Konings, R. J. M.; Hildenbrand, D. L. J. Alloys Compd. 1998, 271-273, 583. (452) Antonov, I. O.; Heaven, M. C. J. Phys. Chem. A 2013, 117, 9684. (453) Joubert, L.; Maldivi, P. J. Phys. Chem. A 2001, 105, 9068. (454) Zaitsevskii, A. V. Radiochemistry 2013, 55, 353. (455) Batista, E. R.; Martin, R. L.; Hay, P. J. J. Chem. Phys. 2004, 121, 11104. (456) Peralta, J. E.; Batista, E. R.; Scuseria, G. E.; Martin, R. L. J. Chem. Theory Comput. 2005, 1, 612. (457) Pantazis, D. A.; Neese, F. J. Chem. Theory Comput. 2011, 7, 677. (458) Yang, Z.; Leon, I.; Wang, L. S. J. Chem. Phys. 2013, 139, 021106. (459) Su, J.; Dau, P. D.; Xu, C. F.; Huang, D. L.; Liu, H.-T.; Wei, F.; Wang, L. S.; Li, J. Chem. Asian J. 2013, 8, 2489. (460) Hildenbrand, D. L.; Lau, K. H. J. Chem. Phys. 1991, 94, 1420. (461) Dau, P. D.; Su, J.; Liu, H. T.; Liu, J. B.; Huang, D. L.; Li, J.; Wang, L. S. Chem. Sci. 2012, 3, 1137. (462) Dau, P. D.; Su, J.; Liu, H. T.; Huang, D. L.; Li, J.; Wang, L. S. J. Chem. Phys. 2012, 137, 064315. 356 (463) Su, J.; Dau, P. D.; Qiu, Y. H.; Liu, H. T.; Xu, C. F.; Huang, D. L.; Wang, L. S.; Li, J. Inorg. Chem. 2013, 52, 6617. 357