Embedding of the saddle point of index two on the PES of the ring opening of cyclobutene

Abstract

The ring opening of cyclobutene is characterized by a competition of the two different pathways: a usual pathway over a saddle of index one (SP1) along the conrotatory behavior of the end groups, as well as a 'forbidden' pathway over a saddle point of index two (SP2) along the disrotatory behavior of the end CH2 groups. We use the system of ordinary differential equations for the method of the gentlest ascent dynamics (GAD) to determine saddle points of the potential energy surface (PES) of the ring opening of cyclobutene to cis-butadiene. We apply generalized GAD formulas for the search of a saddle point of index two. To understand the relation of the different regions of the PES (around minimums, around SPs of index one or two) we also calculate valley-ridge inflection (VRI) points on the PES using Newton trajectories (NT). VRIs and the corresponding singular NTs subdivide the regions of 'attraction' of the different SPs. We calculate the connections of the SP2 (in its different symmetry versions) with different SPs of index one of the PES by different 'reaction pathways.' We compare the possibilities of the tool of the GAD curves for the exploration of PESs with these of NT. The barrier of the disrotatory SP2 is somewhat higher than the barrier of the conrotatory SP1, however, pathways across the slope to the SP2 open additional reaction valleys.