Robust wave function optimization procedures in quantum Monte Carlo methods

The energy variance optimization algorithm over a fixed ensemble of configurations in variational Monte Carlo often encounters problems of convergence. Being formally identical to a problem of fitting data, we re-examine it from a statistical maximum-likelihood point of view. We show that the assumption of an underlying Gaussian distribution of the local energy, implicit in the standard variance minimization scheme, is not theoretically nor practically justified, and frequently generates convergence problems. We propose alternative procedures for optimization of trial wave functions in quantum Monte Carlo and successfully test them by optimizing a trial wave function for the helium trimer.