%A Babbush,Ryan
%A Parkhill,John
%A Aspuru-Guzik,Alan
%D 2013
%J Frontiers in Chemistry
%C
%F
%G English
%K effective potentials,path integral molecular dynamics,nuclear quantum propagation,liquid hydrogen,Density Functional Theory
%Q
%R 10.3389/fchem.2013.00026
%W
%L
%N 26
%M
%P
%7
%8 2013-October-25
%9 Original Research
%+ Prof Alan Aspuru-Guzik,Harvard University,Department of Chemistry and Chemical Biology,12 Oxford St Room M113,Department of Chemistry and Chemical Biology,Cambridge, MA,02138,MA,United States,alan@aspuru.com
%#
%! Force-Field Functor Theory
%*
%<
%T Force-field functor theory: classical force-fields which reproduce equilibrium quantum distributions
%U https://www.frontiersin.org/article/10.3389/fchem.2013.00026
%V 1
%0 JOURNAL ARTICLE
%@ 2296-2646
%X Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.