Fermi Holes and Coulomb Holes

Traditionally quantum chemical methods use the Hartree-Fock model as a starting point and explicitly or implicitly employ expansions of the wavefunction in determinants that are generated by orbital substitutions in the HF determinant. Increasingly sophisticated methods for the selection of determinants have been developed, such as threshold-based methods (MRDCI), direct-CI methods and coupled-cluster approaches. The development is driven by both advances in mathematical technique (algebraic as well as diagrammatical) and by computational convenience and feasibility. In contrast, density functional theory (DFT) concentrates on the form of the exchange-correlation part of the total energy expression and on the Kohn-Sham one-electron potential that enters the effective one-electron equations. The present interest in DFT from the (quantum)chemistry community stems from the notable improvement that is obtained over Hartree-Fock, in particular if also non-local corrections are included (cf. other papers in this volume). Evidently, it is desirable to understand precisely which effects of correlation are build into the exchange correlation potential and energy of present day DF appraoches. For two-electron systems such an analysis has been carried out for the exact Kohn-Sham potential by the present authors1. It has been shown that in this case V xc consists of three contributing terms, V cond , V kin and V N−1, that each have a clear physical meaning1. V cond , for instance, is the potential due to the conditional electron density that will be defined below (eq. 1.6): the density of the remaining electrons when one electron (the reference electron) is known to be at a given position r1· The conditional density thus incorporates exactly all effects of correlation (Fermi and Coulomb holes).