Coherent state mapping ring polymer molecular dynamics for non-adiabatic quantum propagations

207

We recently derived a spin-mapping approach for treating the nonadiabatic dynamics of a two-level system in a classical environment [J. Chem. Phys. 151, 044119 (2019)] based on the well-known quantum equivalence between a two-level system and a spin-1/2 particle. In the present paper, we generalize this method to describe the dynamics of N -level systems. This is done via a mapping to a classical phase space that preserves the SU (N )-symmetry of the original quantum problem. The theory reproduces the standard Meyer-Miller-Stock-Thoss Hamiltonian without invoking an extended phase space, and we thus avoid leakage from the physical subspace. In contrast with the standard derivation of this Hamiltonian, the generalized spin mapping leads to an N -dependent value of the zero-point energy parameter that is uniquely determined by the Casimir invariant of the N -level system. Based on this mapping, we derive a simple way to approximate correlation functions in complex nonadiabatic molecular systems via classical trajectories, and present benchmark calculations on the seven-state Fenna-Matthews-Olson complex. The results are significantly more accurate than conventional Ehrenfest dynamics, at a comparable computational cost, and can compete in accuracy with other state-ofthe-art mapping approaches.

“…Finally, we also believe that the spin mapping will be relevant in the search for a nonadiabatic extension to ring-polymer molecular dynamics. 58,[82][83][84][85]…”

Section: Discussionmentioning

confidence: 99%

Generalized spin mapping for quantum-classical dynamics

Runeson

Richardson

2020

207

“…A fundamental advantage compared to MMST is that the system cannot leave the physical subspace, so there is no need for additional projections. We believe that this fact will be particularly useful for the development of a nonadiabatic version of ring-polymer molecular dynamics (RPMD), [61][62][63][64] which would add nuclear quantum effects to the simulations, as well as to allow sampling from an exact thermal distribution.…”

Section: Conclusion and Future Prospectmentioning

confidence: 99%

Spin-mapping approach for nonadiabatic molecular dynamics

Runeson

Richardson

2019

163

We propose a trajectory-based method for simulating nonadiabatic dynamics in molecular systems with two coupled electronic states. Employing a quantum-mechanically exact mapping of the two-level problem to a spin-1 2 coherent state, we construct a classical phase space of a spin vector constrained to a spherical surface with a radius consistent with the quantum magnitude of the spin. In contrast with the singly-excited harmonic oscillator basis used in Meyer-Miller-Stock-Thoss (MMST) mapping, the theory requires no additional projection operators onto the space of physical states. When treated under a quasiclassical approximation, we show that the resulting dynamics is equivalent to that generated by the MMST Hamiltonian. What differs is the value of the zero-point energy parameter as well as the initial distribution and the measurement operators. For various spin-boson models the results of our method are seen to be a significant improvement compared to both standard Ehrenfest dynamics and linearized semiclassical MMST mapping, without adding any computational complexity.

“…Louiville equation (QCLE) [85][86][87][88][89][90] , path integral [91][92][93][94][95][96][97] , surface hopping [98][99][100][101] , centroid molecular dynamics (CMD) 102 and ring-polymer molecular dynamics (RPMD) [103][104][105][106][107] .…”

Section: Quantum Classicalmentioning

confidence: 99%

Performance evaluation of the symmetrical quasi-classical dynamics method based on Meyer-Miller mapping Hamiltonian in the treatment of site-exciton models

Xie

Zheng

Lan

2018

The symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian (MM-SQC) shows the great potential in the treatment of the nonadiabatic dynamics of complex systems. We performed the comprehensive benchmark calculations to evaluate the performance of the MM-SQC method in various site-exciton models with respect to the accurate results of quantum dynamics method multilayer multiconfigurational time-dependent Hartree (ML-MCTDH). The parameters of the site-exciton models are chosen to represent a few of prototypes used 2 in the description of photoinduced excitonic dynamics processes in photoharvesting systems and organic solar cells, which include the rather board situations with the fast or slow bath and different system-bath couplings. When the characteristic frequency of the bath is low, the MM-SQC method performs extremely well, and it gives almost the identical results to those of ML-MCTDH. When the fast bath is considered, the deviations exist between the MM-SQC and ML-MCTDH results if the high-frequency bath modes are improperly treated by the classical manner. When the so-called adiabatic renormalization was employed to construct the reduced Hamiltonian by freezing high-frequency modes, the MM-SQC dynamics can give the results comparable to the ML-MCTDH ones. Thus, the MM-SQC method itself provide reasonable results in all test site-exciton models, while the proper treatments of the bath modes must be employed. The possible dependence of the MM-SQC dynamics on the different initial sampling methods for the nuclear degrees of freedom is also discussed.3