Which Algorithm Best Propagates the Meyer-Miller-Stock-Thoss Mapping Hamiltonian for Non-Adiabatic Dynamics?

Time-Reversible Implementation of MASH for Efficient Nonadiabatic Molecular Dynamics

In this work, we describe various improved implementations of the mapping approach to surface hopping (MASH) for simulating nonadiabatic dynamics. These include time-reversible and piecewise-continuous integrators, which are only formally possible because of the deterministic nature of the underlying MASH equations of motion. The new algorithms allow for the use of either wave-function overlaps or nonadiabatic coupling vectors to propagate the spin, which encodes the electronic state. For a given time-step, Δt, it is demonstrated that the global error for these methods is O ( Δ t 2 ) compared to the O ( Δ t ) error of standard implementations. This allows larger time-steps to be used for a desired error tolerance, or conversely, more accurate observables given a fixed value of Δt. The newly developed integrators thus provide further advantages for the MASH method, demonstrating that it can be implemented more efficiently than other surface-hopping approaches, which cannot construct time-reversible integrators due to their stochastic nature.

Benchmarking various nonadiabatic semiclassical mapping dynamics methods with tensor-train thermo-field dynamics

Accurate quantum dynamics simulations of nonadiabatic processes are important for studies of electron transfer, energy transfer, and photochemical reactions in complex systems. In this comparative study, we benchmark various approximate nonadiabatic dynamics methods with mapping variables against numerically exact calculations based on the tensor-train (TT) representation of high-dimensional arrays, including TT-KSL for zero-temperature dynamics and TT-thermofield dynamics for finite-temperature dynamics. The approximate nonadiabatic dynamics methods investigated include mixed quantum-classical Ehrenfest mean-field and fewest-switches surface hopping, linearized semiclassical mapping dynamics, symmetrized quasiclassical dynamics, the spin-mapping method, and extended classical mapping models. Different model systems were evaluated, including the spin-boson model for nonadiabatic dynamics in the condensed phase, the linear vibronic coupling model for electronic transition through conical intersections, the photoisomerization model of retinal, and Tully's one-dimensional scattering models. Our calculations show that the optimal choice of approximate dynamical method is system-specific, and the accuracy is sensitively dependent on the zero-point-energy parameter and the initial sampling strategy for the mapping variables.

Resonance Enhancement of Vibrational Polariton Chemistry Obtained from the Mixed Quantum-Classical Dynamics Simulations

We applied a variety of mixed quantum-classical (MQC) approaches to simulate the VSC-influenced reaction rate constant. All of these MQC simulations treat the key vibrational levels associated with the reaction coordinate in the quantum subsystem (as quantum states), whereas all other degrees of freedom (DOFs) are treated inside the classical subsystem. We find that, as long as we have the quantum state descriptions for the vibrational DOFs, one can correctly describe the VSC resonance condition when the cavity frequency matches the bond vibrational frequency. This correct resonance behavior can be obtained regardless of the detailed MQC methods that one uses. The results suggest that the MQC approaches can generate semiquantitative agreement with the exact results for rate constant changes when changing the cavity frequency, the light-matter coupling strength, or the cavity lifetime. The finding of this work suggests that one can use computationally economic MQC approaches to explore the collective coupling scenario when many molecules are collectively coupled to many cavity modes in the future.