Ab initio calculations of radiationless transitions between excited and ground singlet electronic states of ethylene

Abstract

General expressions for internal conversion (IC) rate constant calculations have been derived by taking into account displacements, distortions, and rotation (mixing) of normal modes. The electronic part of the rate constant has been computed through the ab initio calculations of vibronic coupling. The corresponding expressions for the simplest two-mode case as well as for the general $n$ -mode case have been derived. We demonstrate the effect of rotated (mixed) normal modes on the IC rate constants based on a model consisting of one promoting and two mixed modes. The dynamics of excited states of ${\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{4}}$ has been investigated based on the internal conversion mechanism. The calculated rate of internal conversion show that the lifetimes of the excited $\text{π–3p}$ and ${\mathrm{\pi –\pi }}^{*}$ states of ${\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{4}}$ are on the picosecond scale. We predict that if the molecule is excited to a Rydberg $\text{π–3p}$ state, it relaxes to the ground state via the cascade mechanism, ${\text{π–3p→π–3s(}}^1{B}_{\text{3u}}{\mathrm{)\to \pi –\pi }}^{*}{(}^1{B}_{\text{1u}}{\mathrm{)\to }}^1{A}_g.$