Internal Conversion Rates from the Extended Thawed Gaussian Approximation: Theory and Validation

TL;DR

This paper introduces an advanced semiclassical method, the Extended Thawed Gaussian Approximation (ETGA), for accurately predicting nonradiative internal conversion rates in molecules, especially in anharmonic systems where traditional harmonic models fail.

Contribution

The paper develops and validates the ETGA method for calculating internal conversion rates, demonstrating its superiority over harmonic models in anharmonic potentials.

Findings

ETGA accurately predicts internal conversion rates in anharmonic systems.

Global harmonic models are insufficient for systems with significant anharmonicity.

ETGA outperforms traditional harmonic models in double well and Morse potentials.

Abstract

The theoretical prediction of the rates of nonradiative processes in molecules is fundamental to assess their emissive properties. In this context, global harmonic models have been widely used to simulate vibronic spectra as well as internal conversion rates and to predict photoluminescence quantum yields. However, these simplified models suffer from the limitations that are inherent to the harmonic approximation and can have a severe effect on the calculated internal conversion rates. Therefore, the development of more accurate semiclassical methods is highly desirable. Here, we introduce a procedure for the calculation of nonradiative rates in the framework of the time-dependent semi-classical Extended Thawed Gaussian Approximation (ETGA). We systematically investigate the performance of the ETGA method by comparing it to the the adiabatic and vertical harmonic method, which belong to the class of widely used global harmonic models. Its performance is tested in potentials that cannot be treated adequately by global harmonic models, beginning with Morse potentials of varying anharmonicity followed by a double well potential. The calculated radiative and nonradiative internal conversion rates are compared to reference values based on exact quantum dynamics. We find that the ETGA has the capability to predict internal conversion rates in anharmonic systems with an appreciable energy gap, whereas the global harmonic models prove to be insufficient.