Surface hopping methodology in laser-driven molecular dynamics

TL;DR

This paper provides a theoretical foundation for the empirical surface hopping method in laser-driven molecular dynamics, demonstrating its validity and limitations through a solvable model and comparison with exact quantum dynamics.

Contribution

It offers a formal justification of surface hopping using the exact factorization approach and compares its effectiveness against other surface schemes in a quantum-classical framework.

Findings

Surface hopping on Floquet surfaces accurately reproduces quantum dynamics.

Born-Oppenheimer based hopping schemes fail in the tested scenarios.

The approach describes dissociation dynamics well across different cases.

Abstract

A theoretical justification of the empirical surface hopping method for the laser-driven molecular dynamics is given utilizing the formalism of the exact factorization of the molecular wavefunction [Abedi et al., PRL $\textbf{105}$, 123002 (2010)] in its quantum-classical limit. Employing an exactly solvable $\textrm H_2^{\;+}$-like model system, it is shown that the deterministic classical nuclear motion on a single time-dependent surface in this approach describes the same physics as stochastic (hopping-induced) motion on several surfaces, provided Floquet surfaces are applied. Both quantum-classical methods do describe reasonably well the exact nuclear wavepacket dynamics for extremely different dissociation scenarios. Hopping schemes using Born-Oppenheimer surfaces or instantaneous Born-Oppenheimer surfaces fail completely.