Many-Electron Trial Wave Functions for Inhomogeneous Solids

Quantum Monte Carlo simulations of interacting electrons in solids often use Slater-Jastrow trial wave functions with Jastrow factors containing oneand two-body terms. In uniform systems the long-range behavior of the twobody term may be deduced from the random-phase approximation (RPA) of Bohm and Pines. Here we generalize the RPA to nonuniform systems. This gives the long-range behavior of the inhomogeneous two-body correlation term and provides an accurate analytic expression for the one-body term. It also explains why Slater-Jastrow trial wave functions incorporating determinants of Hartree-Fock or density-functional orbitals are close to optimal even in the presence of an RPA Jastrow factor. After adjusting the inhomogeneous RPA Jastrow factor to incorporate the known short-range behavior, we test it using variational Monte Carlo calculations. We find that the most important