PHYSICS OF TRANSFORMATION FROM SCHRODINGER-THEORY TO KOHN-SHAM DENSITY-FUNCTIONAL THEORY - APPLICATION TO AN EXACTLY SOLVABLE MODEL

According to Hohenberg-Kohn-Sham density-functional theory (DFT), and its constrained search formulation, the Schrodinger ground-state wave function Psi is a functional of the ground-state electronic density rh o(r). But the explicit functional dependence of Psi on rho is unknown. It is, however, possible to describe Kohn-Sham (KS) DFT and its elect ron-interaction energy functional and functional derivative rigorously in terms of the wave function Psi. This description involves a conser vative field which is a sum of two fields, the first representative of electron correlations due to the Pauli exclusion principle and Coulom b repulsion, and the second of correlation-kinetic effects. The source s of these fields are expectations of Hermitian operators with respect to Psi. The energy functional is expressed in integral virial form in terms of these fields, whereas the functional derivative is the work done to move an electron in the conservative held of their sum. In thi s paper we illustrate the physics of transformation from Schrodinger t o KS theory by application of this description to a ground state of th e exactly solvable Hooke's atom. As such we determine properties such as the pair-correlation density, the Fermi and Coulomb holes, the Schr odinger and KS kinetic-energy-density tensors and kinetic fields, and the electron-interaction and correlation-kinetic fields, potentials, a nd energies, the majority of these constituent properties of the trans formation being obtained analytically. In this manner we demonstrate t he separate contributions and significance of each type of electron co rrelation to the KS electron-interaction energy and its functional der ivative. Based on this study and previous work, it is proposed that in the construction of approximate energy functionals and their derivati ves for application to more complex systems, it is the fields that be directly approximated.