Orbital-Dependent Representation of the Correlation Energy Functional: Properties of Second-Order Kohn–Sham Perturbation Expansion

Exchange-correlation energy functionals depending on the Kohn–Sham (KS) orbitals and eigenvalues promise to resolve some of the most pressing 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, using the KS single-particle Hamiltonian as noninteracting reference Hamiltonian. In this way, one can establish an exact relation for the exchange-correlation functional, which provides several options for the derivation and treatment of approximate functionals. Straightforward expansion in powers of the electron–electron coupling constant gives, to first order, the exact exchange of density functional theory (DFT) and, to second order, the simplest first-principles correlation functional. The properties of this secondorder correlation functional are reviewed in detail. It is demonstrated that this functional reproduces both the shell structure in the exact correlation potential and dispersion effects. In response to the variational instability of the functional, observed for the Be atom, a simple and computationally efficient extension is suggested and is shown to be quite accurate for the atomic systems considered so far. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem 106: 3242–3259, 2006