Why do mixed quantum-classical methods describe short-time dynamics through conical intersections so well? Analysis of geometric phase effects

TL;DR

This paper investigates why mixed quantum-classical methods like surface hopping and Ehrenfest accurately simulate short-time dynamics through conical intersections despite not explicitly including geometric phase effects, revealing their effective mimicry of key GP influences.

Contribution

The study uncovers how MQC methods implicitly replicate essential geometric phase effects, explaining their success in modeling non-adiabatic dynamics at conical intersections.

Findings

MQC methods compensate for non-adiabatic couplings.

They enhance transfer for symmetric nuclear components.

Methods reproduce exact quantum dynamics surprisingly well.

Abstract

Adequate simulation of non-adiabatic dynamics through conical intersection requires account for a non-trivial geometric phase (GP) emerging in electronic and nuclear wave-functions in the adiabatic representation. Popular mixed quantum-classical (MQC) methods, surface hopping and Ehrenfest, do not carry a nuclear wave-function to be able to incorporate the GP into nuclear dynamics. Surprisingly, the MQC methods reproduce ultra-fast interstate crossing dynamics generated with the exact quantum propagation so well as if they contained information about the GP. Using two-dimensional linear vibronic coupling models we unravel how the MQC methods can effectively mimic the most significant dynamical GP effects: 1) compensation for repulsive diagonal second order non-adiabatic couplings and 2) transfer enhancement for a fully cylindrically symmetric component of a nuclear distribution.