Computing forces with quantum Monte Carlo

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 H-2, Li-2, LiH, and C-2 illustrate the efficiency of the method. (C) 2000 American Institute of Physics. [S0021-9606(00)31330-7].