Relaxation Paths from a Conical Intersection:  The Mechanism of Product Formation in the Cyclohexadiene/Hexatriene Photochemical Interconversion

Abstract

An algorithm for the computation of initial relaxation directions (IRD) from the tip of a conical intersection is discussed. The steepest descent paths that can be computed starting from these IRD provide a description of the ground state relaxation of the "cold" excited state species that occur in organic photochemistry where slow motion and/or thermal equilibration is possible (such as in cool jet, in matrices, and in solution). Under such conditions we show that the central conclusions drawn from a search for IRD and those obtained from semiclassical trajectory computations are the same. In this paper, IRD computations are used to investigate the mechanism of photoproduct formation and distribution in the photolysis of cyclohexadiene (CHD) and cZc-hexatriene (cZc-HT). A systematic search for the IRD in the region of the 2A 1 /1A 1 conical intersection (see Celani, P.; Ottani, S.; Olivucci, M.; Bernardi, F.; Robb, M. A. J. Am. Chem. Soc. 1994, 116, 10141-10151) located on the 2A 1 potential energy surface of these systems yields three relaxation paths. The first two paths, which start in the strict vicinity of the intersection, are nearly equivalent energetically and lead to production of CHD and cZc-HT, respectively. The third path, which begins at a much larger distance, lies higher in energy and ends at a methylenecyclopentene diradical (MCPD) minimum. Further, while the first two paths define directions that form a 60°angle with the excited state entry channel (i.e. the direction along where the conical intersection region is entered), the third path is orthogonal. It is shown that these findings are consistent with the experimental observations which show nearly equivalent quantum yields for CHD and cZc-HT and no production of MCPD. The results of the IRD computations have been validated by investigating the decay dynamics of trajectories starting from a "circle" of points around the conical intersection, with the initial kinetic energy distributed in randomly sampled vibrational modes. These computations have been carried out using a trajectory-surface-hopping (TSH) method and a hybrid molecular mechanics valence bond (MM-VB) force field to model the ab initio potentials.

How the Conical Intersection Seam Controls Chemical Selectivity in the Photocycloaddition of Ethylene and Benzene

“…The determination of possible reaction paths on the ground state from a CI point requires a different strategy 38,39 . There is no unique initial search vector (such as the transition vector at a transition state), so one must test several possibilities.…”

“…We have previously used the concept of an initial reaction direction (IRD) to provide an initial search direction for an MEP computation 38,39 , as discussed previously, this has not worked very well in this problem. Accordingly we have used SDP to define a qualitative reaction path.…”

“…We can also compute minimum energy paths from a saddle point (TS) on the seam (which we shall refer to as a seam-MEP) and thus map out a segment of the seam. In addition, one can perform a 'seam-scan", performing constrained optimizations along a distinguished co-ordinate (eg torsion in a biradical), to map out a particular part of the conical intersection seam.Reaction pathways from transition states were also characterized in forward and reverse direction by an intrinsic reaction coordinate (IRC) analysis 49,50 finding the minimum energy path (MEP).The determination of possible reaction paths on the ground state from a CI point requires a different strategy 38,39 . There is no unique initial search vector (such as the transition vector at a transition state), so one must test several possibilities.…”

“…Finally, reaction paths on the ground state, after decay at the conical intersection, can be traced using dynamics [35][36][37] or minimum energy paths (MEPs) 38,39 .…”

GPU-Accelerated State-Averaged Complete Active Space Self-Consistent Field Interfaced with Ab Initio Multiple Spawning Unravels the Photodynamics of Provitamin D3

“…Because vibrational relaxation occurs on the picosecond timescale, statistical methods, 8 such as transition state theory, are generally not valid. Even pathway-oriented reaction mechanisms, such as minimum energy 2 and intrinsic relaxation 9 pathways, cannot account for the nonequilibrium dynamical behavior of the system, which can be important for even a qualitative description of photochemical processes. As a result, one of the most effective theoretical methods for the study of photochemical reactions is explicit simulation of the nonadiabatic dynamics following light absorption.…”