Combining the mapping Hamiltonian linearized semiclassical approach with the generalized quantum master equation to simulate electronically nonadiabatic molecular dynamics

Abstract

The generalized quantum master equation (GQME) provides a powerful framework for simulating electronically nonadiabatic molecular dynamics. Within this framework, the effect of the nuclear degrees of freedom on the time evolution of the electronic reduced density matrix is fully captured by a memory kernel superoperator. In this paper, we consider two different procedures for calculating the memory kernel of the GQME from projection-free inputs obtained via the combination of the mapping Hamiltonian (MH) approach and the linearized semiclassical (LSC) approximation. The accuracy and feasibility of the two procedures are demonstrated on the spin-boson model. We find that although simulating the electronic dynamics by direct application of the two LSC-based procedures leads to qualitatively different results that become increasingly less accurate with increasing time, restricting their use to calculating the memory kernel leads to an accurate description of the electronic dynamics. Comparison with a previously proposed procedure for calculating the memory kernel via the Ehrenfest method reveals that MH/LSC methods produce memory kernels that are better behaved at long times and lead to more accurate electronic dynamics.

Generalized spin mapping for quantum-classical dynamics

“…In the future we expect that the accuracy can be extended to longer times by combining the dynamics with a general-ized quantum master equation, as has been successfully done for other mapping approaches. [78][79][80][81] Another natural extension would be to develop an FBTS or PLDM method based on spin mapping. Finally, we also believe that the spin mapping will be relevant in the search for a nonadiabatic extension to ring-polymer molecular dynamics.…”

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

“…For instance, memory kernels within the generalized quantum master equation formalism normally decay relatively rapidly, and hence it is expected that such quantities can be accurately computed using spin-PLDM, as has been done with other methods. 83,[95][96][97][98] Dipole-dipole correlation functions and other optical response functions from which linear and non-linear spectra can be obtained also often have short coherence times and, hence, perhaps can also be accurately computed using spin-PLDM.…”

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

“…Other classicaltrajectory based techniques have already been successively used to calculate memory kernels, in order to accurately obtain the long-time dynamics of real-time correlation functions. 51,[83][84][85] Dipole-dipole correlation functions and other optical response functions, from which linear and non-linear spectra can be obtained, also often have short coherence times and hence perhaps can also be accurately computed accurately using spin-PLDM. Several questions still remain unanswered.…”