Communication: Relation of centroid molecular dynamics and ring-polymer molecular dynamics to exact quantum dynamics

Timothy J H Hele; Michael J Willatt; Andrea Muolo; Stuart C Althorpe

doi:10.1063/1.4921234

Communication: Relation of centroid molecular dynamics and ring-polymer molecular dynamics to exact quantum dynamics

J Chem Phys. 2015 May 21;142(19):191101. doi: 10.1063/1.4921234.

Authors

Timothy J H Hele¹, Michael J Willatt¹, Andrea Muolo¹, Stuart C Althorpe¹

Affiliation

¹ Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

PMID: 26001438
DOI: 10.1063/1.4921234

Abstract

We recently obtained a quantum-Boltzmann-conserving classical dynamics by making a single change to the derivation of the "Classical Wigner" approximation. Here, we show that the further approximation of this "Matsubara dynamics" gives rise to two popular heuristic methods for treating quantum Boltzmann time-correlation functions: centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD). We show that CMD is a mean-field approximation to Matsubara dynamics, obtained by discarding (classical) fluctuations around the centroid, and that RPMD is the result of discarding a term in the Matsubara Liouvillian which shifts the frequencies of these fluctuations. These findings are consistent with previous numerical results and give explicit formulae for the terms that CMD and RPMD leave out.