A partially linearized spin-mapping approach for nonadiabatic dynamics. II. Analysis and comparison with related approaches

TL;DR

This paper compares a new partially linearized spin-mapping method, spin-PLDM, with fully linearized approaches, showing that spin-PLDM reduces errors and can be systematically improved for nonadiabatic quantum dynamics.

Contribution

It introduces and analyzes a partially linearized spin-mapping approach, spin-PLDM, demonstrating its advantages over fully linearized methods in accuracy and systematic improvability.

Findings

spin-PLDM contains an additional term reducing errors

Systematic improvement possible via re-sampling at intermediate times

Focused initial conditions reduce trajectory requirements

Abstract

In the previous paper [J. R. Mannouch and J. O. Richardson, J.~Chem.~Phys.~xxx, xxxxx (xxxx)] we derived a new partially linearized mapping-based classical-trajectory technique, called spin-PLDM. This method describes the dynamics associated with the forward and backward electronic path integrals, using a Stratonovich-Weyl approach within the spin-mapping space. While this is the first example of a partially linearized spin mapping method, fully linearized spin mapping is already known to be capable of reproducing dynamical observables for a range of nonadiabatic model systems reasonably accurately. Here we present a thorough comparison of the terms in the underlying expressions for the real-time quantum correlation functions for spin-PLDM and fully linearized spin mapping in order to ascertain the relative accuracy of the two methods. In particular, we show that spin-PLDM contains an additional term within the definition of its real-time correlation function, which diminishes many of the known errors that are ubiquitous for fully linearized approaches. One advantage of partially linearized methods over their fully linearized counterparts is that the results can be systematically improved by re-sampling the mapping variables at intermediate times. We derive such a scheme for spin-PLDM and show that for systems for which the approximation of classical nuclei is valid, numerically exact results can be obtained using only a few `jumps'. Additionally, we implement focused initial conditions for the spin-PLDM method, which reduces the number of classical trajectories that are needed in order to reach convergence of dynamical quantities, with seemingly little difference to the accuracy of the result.