Fixed-node quantum Monte Carlo for moleculesa) b)

The ground-state energies of H2, LiH, Li2, and H2O are calculated by a fixed-node quantum Monte Carlo method, which is presented in detail. For each molecule, relatively simple trial wave functions ΨT are chosen. Each ΨT consists of a single Slater determinant of molecular orbitals multiplied by a product of pair-correlation (Jastrow) functions. These wave functions are used as importance functions in a stochastic approach that solves the Schrödinger equation by treating it as a diffusion equation. In this approach, ΨT serves as a ‘‘guiding function’’ for a random walk of the electrons through configuration space. In the fixed-node approximation used here, the diffusion process is confined to connected regions of space, bounded by the nodes (zeros) of ΨT. This approximation simplifies the treatment of Fermi statistics, since within each region an electronic probability amplitude is obtained which does not change sign. Within these approximate boundaries, however, the Fermi problem is solved exactly. The energy obtained by this procedure is shown to be an upper bound to the true energy. For the molecular systems treated, at least as much of the correlation energy is accounted for with the relatively simple ΨT’s used here as by the best configuration interaction calculations presently available.