Accurate forces in quantum Monte Carlo calculations with nonlocal pseudopotentials

Calculating accurate forces within variational and diffusion Monte Carlo (VMC and DMC) methods is a very challenging problem. We derive expressions for the contribution to the Hellmann-Feynman force from nonlocal pseudopotentials for use within the VMC and DMC methods. Equilibrium bond lengths and harmonic vibrational frequencies are calculated from the Hellmann-Feynman forces and compared with those obtained from the energies at the Hartree-Fock, VMC, and pure DMC levels. Results for five small molecules show that the equilibrium bond lengths obtained from the force and energy calculations differ by less than 0.007 Å at the DMC level.