Photoinduced dynamics of the valence states of ethene: A six-dimensional potential-energy surface of three electronic states with several conical intersections

Abstract

A six-dimensional analytic potential-energy surface of the three valence states (N, V, Z) of ethene has been constructed on the basis of complete-active-space ab initio calculations and ab initio calculations with perturbation theory of second order based on a complete active reference space. The nuclear coordinate space is spanned by the torsion, the C–C stretch coordinate, the left and right pyramidalization and the symmetric and antisymmetric scissor coordinates. The C–H stretch coordinates and the CH2 rocking angles are kept frozen at their ground-state equilibrium value. A diabatic representation of the valence states of ethene has been constructed within the framework of a Hückel-type model. The diabatic potential-energy elements are represented as analytic functions of the relevant coordinates. The parameters of the analytic functions have been determined by a least-squares fit of the eigenvalues of the diabatic potential-energy matrix to the ab initio data for one-dimensional and two-dimensional cuts of the six-dimensional surface. As a function of the torsion, the analytic potential-energy surface describes the intersections of the V and Z states for torsional angles near 90°, which are converted into conical intersections by the antisymmetric scissor mode. As a function of pyramidalization of perpendicular ethene, it describes the intersections of the diabatic N and Z states, which are converted into conical intersections by displacements in the torsional mode. The analytic potential-energy surfaces can provide the basis for a quantum wave packet description of the internal conversion of photoexcited ethene to the electronic ground state via conical intersections.