Evaluation of the importance of spin-orbit couplings in the nonadiabatic quantum dynamics with quantum fidelity and with its efficient "on-the-fly" ab initio semiclassical approximation

TL;DR

This paper introduces a practical, semiclassical method using quantum fidelity and the multiple-surface dephasing representation to evaluate the significance of spin-orbit couplings in complex nonadiabatic molecular dynamics.

Contribution

It develops an efficient on-the-fly ab initio semiclassical approach to quantify the importance of spin-orbit couplings in nonadiabatic quantum dynamics.

Findings

MSDR accurately estimates quantum fidelity in model systems.

The method effectively assesses SOC importance in photoisomerization and collision processes.

The approach handles multiple electronic states with computational efficiency.

Abstract

We propose to measure the importance of spin-orbit couplings (SOCs) in the nonadiabatic molecular quantum dynamics rigorously with quantum fidelity. To make the criterion practical, quantum fidelity is estimated efficiently with the multiple-surface dephasing representation (MSDR). The MSDR is a semiclassical method that includes nuclear quantum effects through interference of mixed quantum-classical trajectories without the need for the Hessian of potential energy surfaces. Two variants of the MSDR are studied, in which the nuclei are propagated either with the fewest-switches surface hopping or with the locally mean field dynamics. The fidelity criterion and MSDR are first tested on one-dimensional model systems amenable to numerically exact quantum dynamics. Then, the MSDR is combined with "on-the-fly" computed electronic structure to measure the importance of SOCs and nonadiabatic couplings (NACs) in the photoisomerization dynamics of CH2NH2+ considering 20 electronic states and in the collision of F + H2 considering six electronic states.