Computing forces with quantum Monte Carlo

Abstract

We present a simple and stable quantum Monte Carlo approach for computing forces between atoms in a molecule. In this approach we propose to use as Monte Carlo estimator of the force the standard Hellmann–Feynman expression (local force expressed as the derivative of the total potential energy with respect to the internuclear coordinates). Invoking a recently introduced zero-variance principle it is shown how the infinite variance associated with the Hellmann–Feynman estimator can be made finite by introducing some suitably renormalized expression for the force. Practical calculations for the molecules H2, Li2, LiH, and C2 illustrate the efficiency of the method.