An ergodic measure for Diffusion Monte Carlo ground state wavefunctions: Application to a hydrogen cluster with an isotopic impurity

Abstract

We propose methods to overcome the lack of reproducibility of wavefunctions in Diffusion Monte Carlo random walks, by (a) establishing a quantitative measure of the ergodicity of wavefunctions across independent samples, (b) developing a statistically convergent estimator of distributions of structural properties and (c) testing sampling enhancement strategies aimed at mitigating the entropy barriers that exist in large systems. We validate our methods with a hydrogen cluster containing a deuterium molecule (H2)19D2.