Comment on "Quantum Monte Carlo study of the dipole moment of CO" [J. Chem. Phys. 110, 11700 (1999)]

TL;DR

This paper critiques a recent claim about the Hellmann-Feynman theorem's applicability in fixed-node diffusion quantum Monte Carlo, highlighting that the theorem does not generally hold when the nodal surface varies with parameters.

Contribution

It clarifies the conditions under which the Hellmann-Feynman theorem applies in DMC, emphasizing the dependence of the nodal surface on parameters.

Findings

The Hellmann-Feynman theorem does not always equal the energy derivative in DMC.

Dependence of the nodal surface on parameters affects the theorem's validity.

The paper challenges previous conclusions about the theorem's applicability in DMC.

Abstract

Recently Schautz and Flad concluded that the Hellmann-Feynman theorem holds within the fixed-node diffusion quantum Monte Carlo (DMC) method. We show that the Hellmann-Feynman expression is not in general equal to the derivative of the DMC energy with respect to some parameter $\lambda$ if the nodal surface depends on $\lambda$.