Which Algorithm Best Propagates the Meyer-Miller-Stock-Thoss Mapping Hamiltonian for Non-Adiabatic Dynamics?
arXiv:2306.16164 · doi:10.1021/acs.jctc.3c00709
Abstract
A common strategy to simulate mixed quantum-classical dynamics is by propagating classical trajectories with mapping variables, often using the Meyer-Miller-Stock-Thoss (MMST) Hamiltonian or the related spin-mapping approach. When mapping the quantum subsystem, the coupled dynamics reduce to a set of equations of motion to integrate. Several numerical algorithms have been proposed, but a thorough performance comparison appears to be lacking. Here, we compare three time-propagation algorithms for the MMST Hamiltonian: the Momentum Integral (MInt) (arXiv:1709.07474), the Split-Liouvillian (SL) (arXiv:1609.00644), and the algorithm in arXiv:1201.1042 that we refer to as the Degenerate Eigenvalue (DE) algorithm due to the approximation required during derivation. We analyse the accuracy of individual trajectories, correlation functions, energy conservation, symplecticity, Liouville's theorem and the computational cost. We find that the MInt algorithm is the only rigorously symplectic algorithm. However, comparable accuracy at a lower computational cost can be obtained with the SL algorithm. The approximation implicitly made within the DE algorithm conserves energy poorly, even for small timesteps, and thus leads to slightly different results. These results should guide future mapping-variable simulations.
arXiv comment15 pages, 4 figures. To be submitted to JCTC
References in corpus (27)
- How to remove the spurious resonances from ring polymer molecular dynamics
- Mapping Variable Ring Polymer Molecular Dynamics: A Path-Integral Based Method for Nonadiabatic Processes
- Boltzmann-conserving classical dynamics in quantum time-correlation functions: Matsubara dynamics
- Mapping quantum-classical Liouville equation: projectors and trajectories
- Generalized spin mapping for quantum-classical dynamics
- Derivation of a true (t->0+) quantum transition-state theory. Part I: Uniqueness and equivalence to ring-polymer molecular dynamics transition-state-theory
- Spin-mapping approach for nonadiabatic molecular dynamics
- Relation of centroid molecular dynamics and ring-polymer molecular dynamics to exact quantum dynamics
- A mapping approach to surface hopping
- Surface hopping from the perspective of quantum-classical Liouville dynamics
- Coherent State Mapping Ring-Polymer Molecular Dynamics for Non-Adiabatic quantum propagations
- Cayley modification for strongly stable path-integral and ring-polymer molecular dynamics
- An analysis of nonadiabatic ring-polymer molecular dynamics and its application to vibronic spectra
- Derivation of a true (t->0+) quantum transition-state theory. II. Recovery of the exact quantum rate in the absence of recrossing
- A partially linearized spin-mapping approach for nonadiabatic dynamics. I. Derivation of the theory
- Nonadiabatic semiclassical dynamics in the mixed quantum-classical initial value representation
- Deriving the exact nonadiabatic quantum propagator in the mapping variable representation
- A partially linearized spin-mapping approach for nonadiabatic dynamics. II. Analysis and comparison with related approaches
- A partially linearized spin-mapping approach for simulating nonlinear optical spectra
- Validating and Implementing Modified Filinov Phase Filtration in Semiclassical Dynamics
- On the uniqueness of t->0+ quantum transition-state theory
- Efficient geometric integrators for nonadiabatic quantum dynamics. II. The diabatic representation
- How to obtain thermostatted ring polymer molecular dynamics from exact quantum dynamics and when to use it
- Should Thermostatted Ring Polymer Molecular Dynamics be used to calculate thermal reaction rates?
- A Semiclassical Framework for Mixed Quantum Classical Dynamics
- Quantum entanglement from classical trajectories
- On detailed balance in nonadiabatic dynamics: From spin spheres to equilibrium ellipsoids