  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.
