Spin-density functionals for the electron correlation energy with automatic freedom from orbital self-interaction

Abstract

Using two different interpretations of the concept of the Fermi hole curvature, the author derives a class of correlation energy expressions for the inhomogeneous interacting electron gas. Their properties include freedom from spurious orbital self-interaction, invariance under unitary transformations among occupied orbitals, correct values in the homogeneous limit, correctly normalized correlation hole, inclusion of kinetic energy (KE) as well as potential energy of correlation, and non-vanishing values for fully spin-polarized systems (in contrast with some similar schemes developed for chemical applications). Minimization of the energy with respect to the orbitals leads to a Euler-Lagrange equation resembling the Hartree-Fock one-electron effective Schrodinger equation, with the addition of a term resembling the KE operator for an inhomogeneous effective mass. For current-carrying states there is a further term involving an effective dynamically induced vector potential. Despite these complications the effective one-electron Hamiltonian is Hermitian, so that the canonical orbitals are orthogonal, in contrast with those of the commonest self-interaction correction scheme.