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

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Hele, Timothy JH 
Willatt, Michael J 
Muolo, Andrea 
Althorpe, Stuart C 

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.

physics.chem-ph, physics.chem-ph, cond-mat.stat-mech
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J Chem Phys
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AIP Publishing
Engineering and Physical Sciences Research Council (EP/I002499/1)
TJHH, MJW and SCA acknowledge funding from the UK Science and Engineering Research Council. AM acknowledges the European Lifelong Learning Programme (LLP) for an Erasmus student placement scholarship. TJHH also acknowledges a Research Fellowship from Jesus College, Cambridge.