Accurate, efficient and simple forces with Quantum Monte Carlo methods
  Computation of ionic forces using quantum Monte Carlo methods has long been a challenge. We introduce a simple procedure, based on known properties of physical electronic densities, to make the variance of the Hellmann-Feynman estimator finite. We obtain very accurate geometries for the molecules H$_2$, LiH, CH$_4$, NH$_3$, H$_2$O and HF, with a Slater-Jastrow trial wave function. Harmonic frequencies for diatomics are also in good agreement with experiment. An antithetical sampling method is also discussed for additional reduction of the variance. 
Simone Chiesa, David Ceperley, Shiwei Zhang