A new perspective for nonadiabatic dynamics with phase space mapping models

Abstract

Based on the recently developed unified theoretical framework [J. Liu, J. Chem. Phys. 145(20), 204105 (2016)], we propose a new perspective for studying nonadiabatic dynamics with classical mapping models (CMMs) of the coupled multistate Hamiltonian onto the Cartesian phase space. CMMs treat the underlying electronic state degrees of freedom classically with a simple physical population constraint while employing the linearized semiclassical initial value representation to describe the nuclear degrees of freedom. We have tested various benchmark condensed phase models where numerically exact results are available, which range from finite temperature to more challenging zero temperature, from adiabatic to nonadiabatic domains, and from weak to strong system-bath coupling regions. CMMs demonstrate overall reasonably accurate dynamics behaviors in comparison to exact results even in the asymptotic long time limit for various spin-boson models and site-exciton models. Further investigation of the strategy used in CMMs may lead to practically useful approaches to study nonadiabatic processes in realistic molecular systems in the condensed phase.

Benchmarking Quasiclassical Mapping Hamiltonian Methods for Simulating Electronically Nonadiabatic Molecular Dynamics

“…In this paper we focus on QC/MH methods, 19,44,[51][52][53][54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69] which represent the electronic population and coherence operators, whose expectation values correspond to the diagonal and off-diagonal electronic density matrix elements, respectively, using mapping operators. The latter have the same commutation relations as the original electronic operators.…”

On-the-Fly Symmetrical Quasi-Classical Dynamics with Meyer–Miller Mapping Hamiltonian for the Treatment of Nonadiabatic Dynamics at Conical Intersections

“…In the Meyer-Miller (MM) mapping model, 36 a Hamiltonian with N discrete quantum states is mapped to an effective Hamiltonian (or a mapping Hamiltonian) with N coupled harmonic oscillators. 8,36,[39][40] It is possible to combine the MM mapping Hamiltonian with different dynamics approaches, such as various quasi-classical/semi-classical dynamics approaches, [41][42][43][44][45][46][47][48][49] quantum-classical Liouville equation (QCLE), [50][51][52][53] path integral and extension, [54][55][56][57][58][59] surface hopping, [60][61] centroid molecular dynamics (CMD), 62 and ring-polymer molecular dynamics (RPMD). [63][64][65][66][67][68][69] In the quasi-classical dynamics, the inclusion of the zero-point energy (ZPE) in the electronic mapping variables in principle provides better dynamical results than the Ehrenfest dynamics, 36 while the partial instead of full ZPE should be included in practice.…”

Analysis of the Bath Motion in the MM-SQC Dynamics Using Unsupervised Machine Learning Dimensionality Reduction Approaches: Principal Component Analysis

“…Hamiltonian model fall into some particular domains. Our choice is the symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (MM-SQC) [71][72][73][74][75][76][77][78][79][80][81][82][83][84][85] . Within this framework, the MM mapping Hamiltonian is constructed by the mapping from the discrete electronic states to coupled harmonic oscillators.…”