Thermal quantum time-correlation functions from classical-like dynamics

Abstract

Thermal quantum time-correlation functions are of fundamental importance in quantum dynamics, allowing experimentally-measurable properties such as reaction rates, diffusion constants and vibrational spectra to be computed from first principles. Since the exact quantum solution scales exponentially with system size, there has been considerable effort in formulating reliable linear-scaling methods involving exact quantum statistics and approximate quantum dynamics modelled with classical-like trajectories. Here we review recent progress in the field with the development of methods including Centroid Molecular Dynamics (CMD), Ring Polymer Molecular Dynamics (RPMD) and Thermostatted RPMD (TRPMD). We show how these methods have recently been obtained from `Matsubara dynamics', a form of semiclassical dynamics which conserves the quantum Boltzmann distribution. We also rederive t->0+ quantum transition-state theory (QTST) in the Matsubara dynamics formalism showing that Matsubara-TST, like RPMD-TST, is equivalent to QTST. We end by surveying areas for future progress.

25 pages, 8 figures. Submitted as a New View article to Molecular Physics on 11th January 2017

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• Routine Molecular Dynamics Simulations Including Nuclear Quantum Effects: from Force Fields to Machine Learning Potentials
• Testing the quasicentroid molecular dynamics method on gas-phase ammonia
• Mode-coupling theory of lattice dynamics for classical and quantum crystals
• Multi-time Formulation of Matsubara Dynamics
• Probing anharmonic phonons by quantum correlators: A path integral approach
• NQCDynamics.jl: A Julia Package for Nonadiabatic Quantum Classical Molecular Dynamics in the Condensed Phase
• Equilibrium-nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy