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 CH 2 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.

Photoinduced dynamics of ethene in the N, V, and Z valence states: A six-dimensional nonadiabatic quantum dynamics investigation

“…It takes Ӎ10 fs for the wave packet to reach the twist angle ϭ82°, where the first conical intersection is localized. 19 In 20 fs, the wave packet has completely spread and reaches ͉͉ϭ. At longer times, the probability occupies the full range of and becomes more structured, which indicates that a large amount of energy is available for the torsional motion.…”

“…From these results as well as from the inspection of the time-dependent projected probabilities ͑espe-cially along the pyramidalization coordinate͒, it is obvious that the wave packet does not find the conical intersection between S 1 and S 0 on the time scale of 50 fs. A closer look at the potential-energy surface 19 reveals that the potential along the pyramidalization coordinate does not favor pyramidalization of twisted ethylene.…”

“…The parameters of these expansions have be determined by a least-squares fit to accurate CASPT2 ab initio data. 19 In this model, the V and Z ͑and the V and N) diabatic states are coupled linearly by the antisymmetric scissoring mode and quadratically by the pyramidalizations. As a function of pyramidalization of perpendicular ethylene, the model describes the intersections of the diabatic N and Z states, which are converted into conical intersections by displacements in the torsional mode.…”

“…Recently, the present research group has developed a sixdimensional ab initio PE surface of the three valence states of ethene 19 ͑henceforth referred as paper I͒. The torsion, the CC stretch coordinate, the left and right pyramidalizations, and the left and right scissors angles have been considered, while CH stretch coordinates and left and right rocking angles have been kept frozen ͑at their ground-state equilibrium values͒.…”

“…The parameters of the analytic diabatic PE functions have been determined by a least-squares fit of the eigenvalues of the diabatic 3ϫ3 PE matrix to the ab initio data for onedimensional and two-dimensional cuts of the adiabatic PE surfaces. 19 In the present work, the valence-state spectroscopy and photochemistry of ethene has been explored via timedependent quantum wave-packet calculations on the nonadiabatically coupled 6D PE surfaces of paper I. The multiconfigurational time-dependent Hartree ͑MCTDH͒ methodology [23][24][25] is used.…”