# On-the-fly ab initio three thawed Gaussians approximation: A semiclassical approach to Herzberg-Teller spectra

## TL;DR

This paper introduces a novel on-the-fly ab initio semiclassical method using three thawed Gaussians to improve the accuracy of vibronic spectra calculations, especially for weakly-allowed transitions.

## Contribution

The paper develops and applies a three thawed Gaussians approximation to better capture anharmonic effects in vibronic spectra beyond traditional harmonic models.

## Key findings

- Improved spectral accuracy over harmonic and Condon models.
- Effective inclusion of Herzberg-Teller effects.
- Enhanced modeling of vibrationally resolved spectra.

## Abstract

Evaluation of symmetry-forbidden or weakly-allowed vibronic spectra requires treating the transition dipole moment beyond the Condon approximation. To include vibronic spectral features not captured in the global harmonic models, we have recently implemented an on-the-fly ab initio extended thawed Gaussian approximation, where the propagated wavepacket is a Gaussian multiplied by a linear polynomial. To include more anharmonic effects, here we represent the initial wavepacket by a superposition of three independent Gaussian wavepackets - one for the Condon term and two displaced Gaussians for the Herzberg-Teller part. Application of this ab initio "three thawed Gaussians approximation" to vibrationally resolved electronic spectra of the phenyl radical and benzene shows a clear improvement over the global harmonic and Condon approximations. The orientational averaging of spectra, the relation between the gradient of the transition dipole moment and nonadiabatic coupling vectors, and the details of the extended and three thawed Gaussians approximation are discussed.