Approximate one-electron density matrix functionals for the electron–electron repulsion energy from the hypervirial theorem

Abstract

Application of the hypervirial theorem to a certain class of two-electron operators yields the electron–electron repulsion energy as an approximate functional of the Hartree–Fock one-electron reduced density matrix. This functional is entirely parameterized by a single screening function that, upon the assumption of transferability, can be readily retrieved from the known correlation energy of the homogeneous electron gas. Invoking the properties of the actual electronic Hamiltonian, the new formalism explicitly incorporates dispersion effects that are not accounted for by the conventional density functional approaches. Even more importantly, it affords analogous functionals for other variational methods such as Monte Carlo self-consistent field (MC SCF). Since such functionals are bi- and trilinear in the occupied orbitals, their fully analytical computation should be feasible with a carefully chosen approximate representation of the screening function.