Roaming is a novel and counter-intuitive mechanism of dissociation involving far-wandering fragments that return and abstract another component from the parent before dissociating. The mechanism is often an alternative route to closed-shell products in systems where both molecular and radical products are accessible and seems to be widespread. In the case of the photodissociation of formaldehyde (H2CO), where roaming was first observed, a small, but non-trivial fraction of the molecular products are formed by roaming, bypassing the clear transition state that would otherwise be traversed. Barring a few reduced-degree-of-freedom examples where the dynamics can be treated analytically, most attempts at theories of roaming have entirely sidestepped the question of ``why?'' Transition state and associated theories take the inherently local perspective that the dynamics of a chemical reaction can be understood in terms of the various minima of a potential surface and transitions between them. But, such a perspective lacks explanatory power over the roaming mechanism. At issue is the manifest irrelevance of transition states. We suggest a global perspective instead: that roaming may be understood in terms of the geodesic (most efficient) pathways across the energy surface. To make such an analysis, we develop the techniques necessary to calculate and analyze geodesics on a small-molecule system, and then compute them on an established surface for formaldehyde. Even though roaming manifests on the flat, asymptotic region of the potential, the properties of geodesics in the region of the excited reactant well are quite informative. The distribution of lengths of geodesics leading to roaming is much broader than those leading directly to molecular or radical products. Indeed, the entropy of the roaming distributions is significantly higher. Measuring these entropies as a function of energy correctly predicts the decline in roaming as energy increases. It appears that the wider space of dynamical options available to the roaming mechanism gives it an entropic advantage over the other two channels. In light of these observations, we suggest that the presence of roaming is less about the existence of a localized "roaming transition state" and more about an entire region of the potential where the system's frustrated ability to navigate gives rise to multiple equivalent pathways.
Cofer-Shabica, Dylan Vale,
"Potential landscape perspectives on roaming: Insights on formaldehyde from geodesic paths"
Chemistry Theses and Dissertations.
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