# A surface-hopping method for semiclassical calculations of cross sections for radiative association with electronic transitions

## TL;DR

This paper introduces a surface-hopping semiclassical method for modeling radiative association with electronic transitions, enabling trajectory tracking post-photon emission and quantum state resolution, validated against quantum mechanical results.

## Contribution

It extends existing semiclassical formulas to include trajectory fate after photon emission, allowing detailed state-resolved spectra in polyatomic systems.

## Key findings

- Method reproduces known cross sections for diatomic molecules.
- Allows trajectory follow-up after photon emission.
- Good agreement with quantum mechanical spectra.

## Abstract

A semicalssical method based on surface-hopping techniques is developed to model the dynamics of radiative association with electronic transitions in arbitrary polyatomic systems. It can be proven that our method is an extension of the established semiclassical formula used in the characterization of diatomic molecule- formation. Our model is tested for diatomic molecules. It gives the same cross sections as the former semiclassical formula, but contrary to the former method it allows us to follow the fate of the trajectories after the emission of a photon. This means that we can characterize the rovibrational states of the stabilized molecules: using semiclassial quantization we can obtain quantum state resolved cross sections or emission spectra for the radiative association process. The calculated semiclassical state resolved spectra show good agreement with the result of quantum mechanical perturbation theory. Furthermore our surface-hopping model is not only applicable for the description of radiative association but it can be use for semiclassical characterization of any molecular process where spontaneous emission occurs.