A perturbative formalism for electronic transitions through conical intersections in a fully quadratic vibronic model

TL;DR

This paper develops a perturbative approach for analyzing electronic transitions through conical intersections using a fully quadratic vibronic model, enabling analytical solutions and improved modeling of potential energy surfaces.

Contribution

It introduces a second order perturbative formalism for quadratic vibronic Hamiltonians, extending previous linear models and allowing more flexible potential energy surface representations.

Findings

Analytical expression for electronic population dynamics derived

Formalism shows good agreement with variational quantum dynamics

Applied to molecular systems with parameters from electronic structure calculations

Abstract

We consider a fully quadratic vibronic model Hamiltonian for studying photoinduced electronic transitions through conical intersections. Using a second order perturbative approximation for diabatic couplings we derive an analytical expression for the time evolution of electronic populations at a given temperature. This formalism extends upon a previously developed perturbative technique for a linear vibronic coupling Hamiltonian. The advantage of the quadratic model Hamiltonian is that it allows one to use separate quadratic representations for potential energy surfaces of different electronic states and a more flexible representation of interstate couplings. We explore features introduced by the quadratic Hamiltonian in a series of 2D models, and then apply our formalism to the 2,6-bis(methylene) adamantyl cation, and its dimethyl derivative. The Hamiltonian parameters for the molecular systems have been obtained from electronic structure calculations followed by a diabatization procedure. The evolution of electronic populations in the molecular systems using the perturbative formalism shows a good agreement with that from variational quantum dynamics.