Cumulant expansion for fast estimate of non-Condon effects in vibronic transition profiles

TL;DR

This paper extends a cumulant expansion method to efficiently estimate non-Condon vibronic transition profiles, enabling better approximation of weak or forbidden spectral features in molecular spectroscopy.

Contribution

It introduces an analytical and numerical approach to evaluate cumulants for non-Condon vibronic profiles considering the Duschinsky effect within the harmonic approximation.

Findings

Successfully applied to benzene UV absorption spectrum

Accurately captures non-Condon effects at different temperatures

Provides a computationally efficient alternative to full spectral calculations

Abstract

When existing, cumulants can provide valuable information about a given distribution and can in principle be used to either fully reconstruct or approximate the parent distribution function. A previously reported cumulant expansion approach for Franck-Condon profiles [Faraday Discuss., 150, 363 (2011)] is extended to describe also the profiles of vibronic transitions that are weakly allowed or forbidden in the Franck-Condon approximation (non-Condon profiles). In the harmonic approximation the cumulants of the vibronic spectral profile can be evaluated analytically and numerically with a coherent state-based generating function that accounts for the Duschinsky effect. As illustration, the one-photon $1 ^{1}\mathrm{A_{g}}\rightarrow1 ^{1}\mathrm{B_{2u}}$ UV absorption spectrum of benzene in the electric dipole and (linear) Herzberg-Teller approximation is presented herein for zero Kelvin and finite temperatures.