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

TL;DR

This paper corrects a previous claim about the applicability of the Hellmann-Feynman theorem in fixed-node quantum Monte Carlo calculations, providing an explicit correction term and clarifying the conditions for its validity.

Contribution

It clarifies the conditions under which the Hellmann-Feynman theorem applies in fixed-node quantum Monte Carlo and introduces a correction term for cases where the nodal boundary varies.

Findings

The original claim about the theorem's applicability was incorrect.

An explicit correction term for the Hellmann-Feynman force is derived.

The correction term represents the linear response of energy to nodal variations.

Abstract

In our previous publication we have mistakenly claimed that the applicability of the Hellmann-Feynman theorem in fixed-node quantum Monte Carlo calculations is not subject to the manner how the nodal boundary depends on an external parameter. This statement is not correct in general, except where the Hellmann-Feynman force is calculated for a nodal boundary which coincides with that of the unconstrained exact eigenfunction. We point out the error in our arguments and present an explicit expression for the correction term which supplements the Hellmann-Feynman force. This term can be interpreted as the linear response of the energy with respect to variations of the the nodal region.