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We present a new partially linearized mapping-based approach forapproximating real-time quantum correlation functions in condensed-phasenonadiabatic systems, called spin-PLDM. Within a classical trajectory picture,partially linearized methods treat the electronic dynamics along forward andbackward paths separately by explicitly evolving two sets of mapping variables.Unlike previously derived partially linearized methods based on theMeyer-Miller-Stock-Thoss mapping, spin-PLDM uses the Stratonovich-Weyltransform to describe the electronic dynamics for each path within thespin-mapping space; this automatically restricts the Cartesian mappingvariables to lie on a hypersphere and means that the classical equations ofmotion can no longer propagate the mapping variables out of the physicalsubspace. The presence of a rigorously derived zero-point energy parameter alsodistinguishes spin-PLDM from other partially linearized approaches. These newfeatures appear to give the method superior accuracy for computing dynamicalobservables of interest, when compared with other methods within the sameclass. The superior accuracy of spin-PLDM is demonstrated within this paperthrough application of the method to a wide range of spin-boson models, as wellas to the Fenna-Matthews-Olsen complex.

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