Wave function optimization with a fixed sample in quantum Monte Carlo

Abstract

The optimization of trial functions consisting of a product of a single determinant and simple correlation functions is studied. The method involves minimizing the variance of the local energy over a finite number of points (sample). The role of optimization parameters, e.g., sample characteristics, initial trial function parameters, and reference energy, is examined for H2, Li2, and H2O. The extent to which cusp conditions are satisfied is also discussed. The resulting variational Monte Carlo energies 〈ΨT‖H‖ΨT〉 recover 46%–95% of the correlation energy for the simple trial function forms studied. When used as importance functions for quantum Monte Carlo calculations, these optimized trial functions recover 90%–100% of the correlation energy. Time-step bias of the computed quantum Monte Carlo energies is found to be small.