Variational and diffusion Monte Carlo techniques for quantum clusters

The ${\mathrm{H}}_2$ ${\mathrm{-}}^4$He dimer and small ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ clusters are studied using Monte Carlo sampling techniques. We consider alternative wave-function forms in order to obtain high accuracy efficiently. For the smaller systems, both guided and unguided Metropolis walks are used and the effciencies are studied. Of particular concern is accurate sampling at small particle separations and the behavior of the local energy in this regime. As a final step, we compute exact energies by a diffusion Monte Carlo method. We obtain converged energies significantly below the Green’s-function Monte Carlo values, which employed an earlier He-He potential with a slightly shallower well. For ${\mathrm{He}}_3$ and ${\mathrm{He}}_{20}$, the Green’s-function Monte Carlo energies are reproduced when employing the same potential. However, for the 112-atom cluster, our converged energy lies below the Green’s-function Monte Carlo value. Second-order estimates of the exact density profiles and particle separation distributions, p, are also determined. For the 14- and 20-atom clusters, second-order estimates of p show enhanced structure in comparison to variational Monte Carlo results. Statistically meaningful oscillations in the second-order estimates of the exact density profiles are not observed.