Variational Quantum Monte Carlo with Inclusion of Orbital Correlations

Abstract

Variational quantum Monte Carlo (VMC) method applied to interacting electron systems has played a pivotal role for the studies of electronic states of atoms, molecules and condensed matters. First, the many-body wave functions optimized by the VMC method provide good guiding functions in more accurate, diffusion quantum Monte Carlo (DMC) calculations for identical systems. Second, the VMC calculations themselves can give a good upper bound for the exact ground-state energy of many-electron systems when an appropriate form for the variational wave function is employed. In addition to a conventional form for the variational wave function that is expressed by the product of the Jastrow factor and the single Slater determinant, recent investigations have found that the expression in terms of many Slater determinants can provide a very accurate description of electronic states, especially for intrinsically multi-reference systems, which corresponds to the configuration interaction (CI) expansion method in conventional quantum chemistry. Although the CI method needs an extremely large number of expansion coefficients as variational parameters, the number of parameters can be reduced efficiently by using an idea of (molecular) orbital pair correlations. The purpose of the present paper is to examine the feasibility and usefulness of this idea within the framework of VMC method with the Jastrow–Slater wave function, where the ground state of a water molecule is investigated as a test case. In this study we rely on a variational wave function composed of a product of the Jastrow and Slater parts as 1⁄4 J S; ð1Þ