Hellman-Feynman operator sampling in Diffusion Monte Carlo calculations

TL;DR

This paper introduces a new Hellman-Feynman-based method for accurately sampling all diagonal operators in Diffusion Monte Carlo calculations, improving upon the traditional second-order accuracy limitations.

Contribution

The paper presents a simple, implementable Hellman-Feynman operator sampling technique that enhances the accuracy of DMC for non-commuting operators.

Findings

Method correctly samples all diagonal operators in DMC.

Easy to implement in existing DMC codes.

Improves accuracy for potential energy and density calculations.

Abstract

Diffusion Monte Carlo (DMC) calculations typically yield highly accurate results in solid-state and quantum-chemical calculations. However, operators that do not commute with the Hamiltonian are at best sampled correctly up to second order in the error of the underlying trial wavefunction, once simple corrections have been applied. This error is of the same order as that for the energy in variational calculations. Operators that suffer from these problems include potential energies and the density. This paper presents a new method, based on the Hellman-Feynman theorem, for the correct DMC sampling of all operators diagonal in real space. Our method is easy to implement in any standard DMC code.