Construction of Two-Dimensional Potential Energy Surfaces of Reactions with Post-Transition-State Bifurcations

Reactions with post-transition-state bifurcations (PTSBs) involve initial ambimodal transition-state structures followed by an unstable region leading to two possible products. PTSBs are seen in many organic, organometallic, and biosynthetic reactions, but analyzing the origins of selectivity for these reactions is challenging, in large part due to the complex nature of the potential energy surfaces involved, which precludes analyses based on single intrinsic reaction coordinate (IRC; steepest-descent path in mass-weighted coordinate). While selectivity can be predicted using molecular dynamics simulation, connecting results from such calculations to the topography of potential energy surfaces is difficult. In the present work, a method for generating two-dimensional potential energy surfaces for PTSBs is described. The first dimension starts with the IRC for the first transition-state structure, followed by a modified reaction coordinate that reaches the second transition-state structure, which interconverts the two products of a bifurcating reaction path. The IRC for the second transition-state structure constitutes the second dimension. In addition, a method for mapping trajectories from Born-Oppenheimer molecular dynamics simulations onto these surfaces is described. Both approaches are illustrated with representative examples from the field of organic chemistry. The 2D-PESs for five asymmetric cases tested have clear tilted topography after the first transition-state structure, and the tilted direction correlates well with the selectivity observed from previous dynamic simulation. Instead of selecting reaction coordinates by chemical intuition, our method provides a general means to construct two-dimensional potential energy surfaces for reactions with post-transition-state bifurcations.