Total forces in the diffusion Monte Carlo method with nonlocal pseudopotentials

TL;DR

This paper derives exact expressions for atomic forces in diffusion Monte Carlo with nonlocal pseudopotentials, introduces approximate schemes for practical calculations, and validates them through molecular vibrational studies.

Contribution

It provides the first calculation of the pseudopotential Pulay and Pulay nodal terms in pure DMC, enhancing force estimation accuracy.

Findings

Bond lengths differ by less than 0.002 Å between force and energy methods.

Force-based vibrational frequencies agree closely with energy-based results.

New schemes enable more accurate atomic force calculations in DMC simulations.

Abstract

We report exact expressions for atomic forces in the diffusion Monte Carlo (DMC) method when using nonlocal pseudopotentials. We present approximate schemes for estimating these expressions in both mixed and pure DMC calculations, including the pseudopotential Pulay term which has not previously been calculated and the Pulay nodal term which has not been calculated for real systems in pure DMC simulations. Harmonic vibrational frequencies and equilibrium bond lengths are derived from the DMC forces and compared with those obtained from DMC potential energy curves. Results for four small molecules show that the equilibrium bond lengths obtained from our best force and energy calculations differ by less than 0.002 Angstrom.