# A general method to describe intersystem crossing dynamics in trajectory surface hopping

## TL;DR

This paper reviews methods for modeling intersystem crossing, focusing on a new trajectory surface hopping approach called SHARC that includes spin-orbit and non-adiabatic couplings for large molecular systems.

## Contribution

The paper introduces and details the SHARC method, a general trajectory surface hopping technique capable of incorporating arbitrary couplings, including spin-orbit interactions, for excited-state dynamics simulations.

## Key findings

- SHARC can include any arbitrary coupling in surface hopping.
- The method is applicable to large systems with many degrees of freedom.
- Different electronic bases for spin-orbit coupling are analyzed.

## Abstract

Intersystem crossing is a radiationless process that can take place in a molecule irradiated by UV-Vis light, thereby playing an important role in many environmental, biological and technological processes. This paper reviews different methods to describe intersystem crossing dynamics, paying attention to semiclassical trajectory theories, which are especially interesting because they can be applied to large systems with many degrees of freedom. In particular, a general trajectory surface hopping methodology recently developed by the authors, which is able to include non-adiabatic and spin-orbit couplings in excited-state dynamics simulations, is explained in detail. This method, termed SHARC, can in principle include any arbitrary coupling, what makes it generally applicable to photophysical and photochemical problems, also those including explicit laser fields. A step-by-step derivation of the main equations of motion employed in surface hopping based on the fewest-switches method of Tully, adapted for the inclusion of spin-orbit interactions, is provided. Special emphasis is put on describing the different possible choices of the electronic bases in which spin-orbit can be included in surface hopping, highlighting the advantages and inconsistencies of the different approaches.