Monte Carlo energy and variance-minimization techniques for optimizing many-body wave functions

We investigate Monte Carlo energy and variance-minimization techniques for optimizing many-body wave functions. Several variants of the basic techniques are studied, including limiting the variations in the weighting factors that arise in correlated sampling estimations of the energy and its variance. We investigate the numerical stability of the techniques and identify two reasons why variance minimization exhibits superior numerical stability to energy minimization. The characteristics of each method are studied using a noninteracting 64-electron model of crystalline silicon. While our main interest is in solid-state systems, the issues investigated are relevant to Monte Carlo studies of atoms, molecules, and solids. We identify a robust and efficient variance-minimization scheme for optimizing wave functions for large systems.