Improving Variational Monte Carlo Optimization by Avoiding Statistically Difficult Parameters

Abstract: Modern quantum Monte Carlo (QMC) methods often capture electron correlation through both explicitly correlating Jastrow factors and small to mid-sized configuration interaction (CI) expansions. Here, we study the additional optimization difficulty created by including increasing numbers of CI parameters. We find evidence that the quality of Variational Mone Carlo (VMC) optimization can be limited by the ability to statistically resolve the CI parameters in the presence of a Jastrow factor. Although using larger statistical samples can mitigate this issue and bring an optimization closer to its true minimum, this approach is computationally intensive. We present evidence that similar gains to optimization quality can be had without increasing the sample size by avoiding CI parameters that are statistically the most difficult to resolve. Our findings suggest that, in addition to the value of using traditional selected configuration interaction (sCI) methods to prepare VMC wave functions, sCI-like methods can play an important role within VMC by improving the effectiveness of stochastic energy minimization.