Orbital-dependent Representation of Correlation Energy Functional

Abstract

Abstract Exchange-correlation energy functionals depending on the Kohn-Sham orbitals and eigenvalues resolve some of the well-known deficiencies of the local density and generalized gradient approximations. Such functionals can be derived in first-principles fashion by use of standard many-body techniques, if the Kohn-Sham Hamiltonian is utilized as non-interacting reference Hamiltonian. In this way one can establish an exact relation for the exchange-correlation functional, which opens several routes for the derivation of approximate functionals. Straightforward expansion in powers of the electron-electron coupling constant gives, to first order, the exact exchange of density functional theory and, to second order, a correlation functional which has the same structure as the second order Møller-Plesset term. This simplest first-principles correlation functional reproduces both the shell structure in the exact correlation potential and dispersion forces. On the other hand, it overestimates all correlation effects and is variationally instable for systems with a very small HOMO-LUMO gap. Both deficiences can be resolved by partial resummation of the Kohn-Sham perturbation expansion. In this contribution two such resummations are discussed, a minimum form designed to address the variational instability at no computational cost (based on the Epstein-Nesbet diagrams) and a more systematic variant (based on the ring diagrams).