title: Force-field functor theory: classical force-fields which reproduce equilibrium quantum distributions.
abstract: 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.
authors.affiliation: Department of Chemistry and Chemical Biology, Harvard University Cambridge, MA, USA.
authors.forename: Ryan
authors.initials: R
authors.lastname: Babbush
authors.affiliation: Department of Chemistry, The University of Notre Dame South Bend, IN, USA.
authors.forename: John
authors.initials: J
authors.lastname: Parkhill
authors.affiliation: Department of Chemistry and Chemical Biology, Harvard University Cambridge, MA, USA.
authors.forename: Alán
authors.initials: A
authors.lastname: Aspuru-Guzik
keywords: density functional theory; effective potentials; liquid hydrogen; nuclear quantum propagation; path integral molecular dynamics