Assessing Orbital Optimization in Variational and Diffusion Monte Carlo

TL;DR

This study evaluates the impact of orbital optimization in variational Monte Carlo on diffusion Monte Carlo accuracy for magnetic systems, highlighting the role of optimization methods, Jastrow factors, and pseudopotentials.

Contribution

It demonstrates that stochastic reconfiguration is a robust optimizer and clarifies how orbital optimization affects various Monte Carlo energies and biases.

Findings

Stochastic reconfiguration is a reliable optimizer.

Short-range Jastrow factors improve diffusion Monte Carlo.

Orbital optimization can increase bias due to pseudopotential locality errors.

Abstract

In this work, we investigate the fidelity of orbital optimization in variational Monte Carlo to improve diffusion Monte Carlo results on correlated magnetic systems, using CrSBr as a model system. We compare the performance of different optimization methods, showing that stochastic reconfiguration is a robust and reliable optimizer. We show that short range Jastrow factors are important for improving diffusion Monte Carlo, regardless of the quality of orbitals. Large active spaces are required to converge the variational energy, but ulitmately orbital optimization produces worse diffusion Monte Carlo energies when compared to standard orbitals from density functional theory. We show that this increased bias is due to larger locality errors from the use of pseudopotentials, while the fixed-node error is actually improved by using orbital optimization. Additionally, for observables other than energy, orbital optimization produces a systematically smaller mixed-estimator bias. Ultimately, we believe orbital optimization provides a reliable method to improve variational and pure fixed-node energies as well as lower mixed-estimator bias.