Selective correlation scheme within diffusion quantum Monte Carlo

Abstract

We present a selective correlation scheme allowing us to correlate only subsets of electrons, which can be assigned to arbitrary groups of orbitals, within diffusion quantum Monte Carlo calculations. The set of occupied orbitals, obtained from an all-electron mean-field calculation, is divided into two parts: frozen orbitals and explicitly considered orbitals. Electrons residing in frozen orbitals are excluded from the correlation treatment and handled within mean-field theory. The effects of such electrons on the remaining correlated electrons are represented by a model potential consisting of Coulomb and exchange parts, combined with a projectionlike operator to ensure orthogonality between the two sets of orbitals. Applying a localization procedure, similar to that used in connection with atomic semilocal pseudopotentials, to the exchange and projectionlike operators, local many-particle representations of these operators are obtained, which are suitable for use within quantum Monte Carlo calculations. While localizing the exchange part is rather straightforward, special care has to be taken to localize the projectionlike operator properly. As an illustrating example we consider the nitrogen dimer with the triple bond being correlated, while the nonbonding orbitals are kept frozen. By comparison with coupled cluster calculations, we demonstrate that with properly localized operators, the correlation energy of the triple bond can be quantitatively recovered.