From explicit to implicit density functionals

The concept of orbital- and eigenvalue-dependent exchange-correlation (xc) energy functionals is reviewed. We show how such functionals can be derived in a systematic fashion via a perturbation expansion, utilizing the Kohn-S ham system as a noninteracting reference system. We demonstrate that the se cond-order contribution to this expansion of the re-energy functional inclu des the leading term of the van der Waals interaction. The optimized-potent ial method (OPM), which allows the calculation of the multiplicative re-pot ential corresponding to an orbital- and eigenvalue-dependent re-energy func tional via an integral equation, is discussed in detail. We examine an appr oximate analytical solution of the OPM integral equation, pointing out that , for eigenvalue-dependent functionals, the three paths used in the literat ure for the derivation of this approximation yield different results. Final ly, a number of illustrative results, both for the exchange-only Limit and for the combination of the exact exchange with various correlation function als, are given. (C) 1999 John Wiley & Sons, Inc.