An analysis of nonadiabatic ring-polymer molecular dynamics and its application to vibronic spectra

Self Cite

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

Self Cite

207

“…37,55 This method allows for all the aspects discussed above and is a suitable method of choice, given an efficient simulation protocol is provided. 56 The cornerstone of (N)RPMD is the Kubo-transformed TCF, which is the most classicallike quantum TCF, since it is real-valued and symmetric with respect to time reversal. Nonetheless, when it comes to practical evaluation of vibronic spectra, the Kubo TCF either becomes non-tractable by MD methods or has to be decomposed into the contributions that do not have the beneficial properties of the original TCF, in particular they are no more real functions of time, see Sec.…”

Section: Introductionmentioning

confidence: 99%

Quasi-classical approaches to vibronic spectra revisited

Karsten

Ivanov

Bokarev

et al. 2018

The framework to approach quasi-classical dynamics in the electronic ground state is well established and is based on the Kubo-transformed time correlation function (TCF), being the most classical-like quantum TCF. Here we discuss whether the choice of the Kubo-transformed TCF as a starting point for simulating vibronic spectra is as unambiguous as it is for vibrational ones. A generalized quantum TCF is proposed that contains many of the well-established TCFs as particular cases. It provides a framework to develop numerical protocols for simulating vibronic spectra via quasi-classical trajectory-based methods that allow for dynamics on many potential energy surfaces and nuclear quantum effects. The performance of the methods based on the well-known TCFs is investigated on 1D anharmonic model systems at finite temperatures. The flexibility inherent to the formulation of the generalized TCF provides a route to construct new TCFs that may lead to better numerical protocols as is shown on the same models.

“…We note that this algorithm immediately extends to Hamiltonians containing a sum of Meyer-Miller-like terms such as the ring polymer Hamiltonians in Ref. 84.…”

Section: B Mmst Hamiltonian and The Mint Algorithmmentioning

confidence: 99%

Nonadiabatic semiclassical dynamics in the mixed quantum-classical initial value representation

Church

Ezra

Ananth

2017

126

We extend the Mixed Quantum-Classical Initial Value Representation (MQC-IVR), a semiclassical method for computing real-time correlation functions, to electronically nonadiabatic systems using the Meyer-MillerStock-Thoss (MMST) Hamiltonian to treat electronic and nuclear degrees of freedom (dofs) within a consistent dynamic framework. We introduce an efficient symplectic integration scheme, the MInt algorithm, for numerical time-evolution of the nuclear and electronic phase space variables as well as the Monodromy matrix, under the non-separable MMST Hamiltonian. We then calculate the probability of transmission through a curve-crossing in model two-level systems and show that in the quantum limit MQC-IVR is in good agreement with the exact quantum results, whereas in the classical limit the method yields results in keeping with mean-field approaches like the Linearized Semiclassical IVR. Finally, exploiting the ability of MQC-IVR to quantize different dofs to different extents, we present a detailed study of the extents to which quantizing the nuclear and electronic dofs improves numerical convergence properties without significant loss of accuracy.