Optimization of quantum Monte Carlo wavefunctions using analytical derivatives

Abstract

We show how to optimize many-parameter wavefunctions for use in quantum Monte Carlo by deriving and utilizing formulas for analytical rather than numerical evaluation of the required derivatives. We present these in a form which is easily vectorizable for use on a supercomputer. We also discuss several technical issues of variational Monte Carlo to ensure both an unbiased and efficient optimization. Finally, we illustrate our optimization scheme's numerical performance by optimizing ground-state wavefunctions for LiH and H2O, each with more than 100 variational parameters. Keywords: quantum Monte Carlo, optimization, electron correlation, LiH, H2O.