# On-the-fly ab initio semiclassical evaluation of absorption spectra of polyatomic molecules beyond the Condon approximation

## TL;DR

This paper extends the on-the-fly ab initio thawed Gaussian approximation to include Herzberg-Teller effects, enabling more accurate vibronic spectra calculations beyond the Condon approximation for polyatomic molecules.

## Contribution

It introduces a method that incorporates Herzberg-Teller contributions into the thawed Gaussian approximation, improving spectral accuracy beyond standard harmonic models.

## Key findings

- Calculated spectra match experimental data more closely.
- Anharmonicity is more significant than Herzberg-Teller in phenyl radical.
- Herzberg-Teller effects are crucial for benzene's forbidden transition.

## Abstract

To evaluate vibronic spectra beyond the Condon approximation, we extend the on-the-fly ab initio thawed Gaussian approximation by considering the Herzberg-Teller contribution due to the dependence of the electronic transition dipole moment on nuclear coordinates. The extended thawed Gaussian approximation is tested on electronic absorption spectra of phenyl radical and benzene: Calculated spectra reproduce experimental data and are much more accurate than standard global harmonic approaches, confirming the significance of anharmonicity. Moreover, the extended method provides a tool to quantify the Herzberg-Teller contribution: we show that in phenyl radical, anharmonicity outweighs the Herzberg-Teller contribution, whereas in benzene, the Herzberg-Teller contribution is essential, since the transition is electronically forbidden and Condon approximation yields a zero spectrum. Surprisingly, both adiabatic harmonic spectra outperform those of the vertical harmonic model, which describes the Franck-Condon region better. Finally, we provide a simple recipe for orientationally averaging spectra, valid beyond Condon approximation, and a relation among the transition dipole, its gradient, and nonadiabatic coupling vectors.