What is special about how roaming chemical reactions traverse their potential surfaces? Differences in geodesic paths between roaming and non-roaming events.

With the notable exception of some illustrative two-degree-of-freedom models whose surprising classical dynamics has been worked out in detail, theories of roaming have largely bypassed the issue of when and why the counterintuitive phenomenon of roaming occurs. We propose that a useful way to begin to address these issues is to look for the geodesic (most efficient) pathways through the potential surfaces of candidate systems. Although roaming manifests itself in an unusual behavior at asymptotic geometries, we found in the case of formaldehyde dissociation that it was the pathways traversing the parts of the potential surface corresponding to highly vibrationally excited reactants that were the most revealing. An examination of the geodesics for roaming pathways in this region finds that they are much less tightly defined than the geodesics in that same region that lead directly to dissociation (whether into closed-shell products or into radical products). Thus, the broader set of options available to the roaming channel gives it an entropic advantage over more conventional reaction channels. These observations suggest that what leads to roaming in other systems may be less the presence of a localized "roaming transition state," than the existence of an entire region of the potential surface conducive to multiple equivalent pathways.