DERIVATION AND REINTERPRETATION OF APPROXIMATIONS IN SCHRODINGER AND KOHN-SHAM THEORY VIA A HIERARCHY WITHIN THE WORK FORMALISM

In this article, we derive and thereby reinterpret various approximations in Schrodinger theory and Kohn-Sham density-functional theory via a hierarchy within the work formalism of electronic structure due to Harbola and Sahni. In the work formalism, which is based on Coulomb's law, the local potential representing electron correlations as well as the electron correlation energy both arise from the same quantum mechanical source charge distribution that is the pair-correlation density. The potential is the work done to move an electron in the force field of the pair-correlation density, and the energy is the energy of interaction between the electronic and pair-correlation densities. The differential equation governing the system is a Sturm-Liouville equation so that the system wave function can, in principle, be obtained as an infinite linear combination of Slater determinants of the spin-orbitals corresponding to the occupied and virtual states. The hierarchy is achieved by improvement of the pair-correlation density either by systematic improvement of the wave function or, as is the case of Kohn-Sham theory, by an expansion of the pair-correlation density in gradients of the density about the uniform electron gas result. The derivations of the approximations of Kohn-Sham theory via the work formalism, in turn, exhibit the existence of additional correlations that are not evident through the Kohn-Sham prescription, whereby the potential is obtained by functional differentiation. The approximations considered within Schrodinger theory are the Hartree, Hartree-Fock, and configuration-interaction approximations. Those within Kohn-Sham theory are the density functional theory Hartree, local density, and gradient expansion approximations. (C) 1995 John Wiley & Sons, Inc.