ForceField Functor Theory: Classical ForceFields 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 BornOppenheimer 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 onedimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid parahydrogen, 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 BornOppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.
 Publication:

Frontiers in Chemistry
 Pub Date:
 October 2013
 DOI:
 10.3389/fchem.2013.00026
 arXiv:
 arXiv:1306.4332
 Bibcode:
 2013FrCh....1...26B
 Keywords:

 effective potentials;
 path integral molecular dynamics;
 nuclear quantum propagation;
 liquid hydrogen;
 Density Functional Theory;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Soft Condensed Matter;
 Physics  Chemical Physics;
 Quantum Physics
 EPrint:
 10 Pages, 5 figures