# Analytical derivative coupling for multistate CASPT2 theory

## TL;DR

This paper develops an analytical method for derivative couplings in multistate CASPT2 theory, enabling efficient and accurate simulations of photochemical processes involving non-radiative transitions.

## Contribution

It introduces an algorithm for analytical evaluation of derivative couplings in MS-CASPT2 and XMS-CASPT2, matching the computational cost of energy gradient calculations.

## Key findings

- Geometries and energies at MECIs agree with multireference CI results.
- The method successfully optimized MECIs for stilbene and GFP chromophore.
- Computational efficiency is comparable to nuclear energy gradient calculations.

## Abstract

The probability of non-radiative transitions in photochemical dynamics is determined by the derivative couplings, the couplings between different electronic states through the nuclear degrees of freedom. Efficient and accurate evaluation of the derivative couplings is, therefore, of central importance to realize reliable computer simulations of photochemical reactions. In this work, the derivative couplings for multistate multireference second-order perturbation theory (MS-CASPT2) and its 'extended' variant (XMS-CASPT2) are studied, in which we present an algorithm for their analytical evaluation. The computational costs for evaluating the derivative couplings are essentially the same as those for calculating the nuclear energy gradients. The geometries and energies calculated with XMS-CASPT2 for small molecules at minimum energy conical intersections (MECIs) are in good agreement with those computed by multireference configuration interaction. As numerical examples, MECIs are optimized using XMS-CASPT2 for stilbene and a GFP model chromophore (the 4-para-hydroxybenzylidene-1,2-dimethyl-imidazolin-5-one anion).