A partially linearized spin-mapping approach for nonadiabatic dynamics. I. Derivation of the theory

TL;DR

This paper introduces spin-PLDM, a novel partially linearized spin-mapping approach for nonadiabatic quantum dynamics that improves accuracy by restricting electronic variables to a physical subspace using the Stratonovich-Weyl transform.

Contribution

The paper develops spin-PLDM, a new partially linearized method employing spin-mapping and the Stratonovich-Weyl transform, enhancing accuracy in simulating nonadiabatic dynamics.

Findings

Spin-PLDM shows superior accuracy over previous methods.

The method effectively models spin-boson systems.

Application to FMO complex demonstrates practical utility.

Abstract

We present a new partially linearized mapping-based approach for approximating real-time quantum correlation functions in condensed-phase nonadiabatic systems, called spin-PLDM. Within a classical trajectory picture, partially linearized methods treat the electronic dynamics along forward and backward paths separately by explicitly evolving two sets of mapping variables. Unlike previously derived partially linearized methods based on the Meyer-Miller-Stock-Thoss mapping, spin-PLDM uses the Stratonovich-Weyl transform to describe the electronic dynamics for each path within the spin-mapping space; this automatically restricts the Cartesian mapping variables to lie on a hypersphere and means that the classical equations of motion can no longer propagate the mapping variables out of the physical subspace. The presence of a rigorously derived zero-point energy parameter also distinguishes spin-PLDM from other partially linearized approaches. These new features appear to give the method superior accuracy for computing dynamical observables of interest, when compared with other methods within the same class. The superior accuracy of spin-PLDM is demonstrated within this paper through application of the method to a wide range of spin-boson models, as well as to the Fenna-Matthews-Olsen complex.