Generalized spin mapping for quantum-classical dynamics

TL;DR

This paper extends a spin-mapping approach to N-level quantum systems, enabling more accurate classical trajectory simulations of nonadiabatic dynamics while preserving symmetry and avoiding phase space leakage.

Contribution

The authors generalize a spin-mapping method to N-level systems, deriving an N-dependent zero-point energy parameter and improving the accuracy of classical trajectory-based nonadiabatic dynamics.

Findings

Benchmark on Fenna--Matthews--Olson complex shows improved accuracy.

Method outperforms conventional Ehrenfest dynamics.

Comparable in accuracy to other advanced mapping techniques.

Abstract

We recently derived a spin-mapping approach for treating the nonadiabatic dynamics of a two-level system in a classical environment [J. Chem. Phys. 151, 044119 (2019)] based on the well-known quantum equivalence between a two-level system and a spin-1/2 particle. In the present paper, we generalize this method to describe the dynamics of $N$-level systems. This is done via a mapping to a classical phase space that preserves the $SU(N)$-symmetry of the original quantum problem. The theory reproduces the standard Meyer--Miller--Stock--Thoss Hamiltonian without invoking an extended phase space, and we thus avoid leakage from the physical subspace. In contrast with the standard derivation of this Hamiltonian, the generalized spin mapping leads to an $N$-dependent value of the zero-point energy parameter that is uniquely determined by the Casimir invariant of the $N$-level system. Based on this mapping, we derive a simple way to approximate correlation functions in complex nonadiabatic molecular systems via classical trajectories, and present benchmark calculations on the seven-state Fenna--Matthews--Olson complex. The results are significantly more accurate than conventional Ehrenfest dynamics, at a comparable computational cost, and can compete in accuracy with other state-of-the-art mapping approaches.