Physical Interpretation of Kohn-Sham Density Functional Theory

Abstract

Quantal density functional theory (Q-DFT) and traditional Kohn-Sham density functional theory (KS-DFT) are both descriptions of the S system of noninteracting Fermions whereby the density and energy equivalent to that of the Schrodinger theory of electrons is determined. The KS-DFT description of the model system, however, is distinctly different. Though founded in Schrodinger theory via the two theorems of Hohenberg and Kohn [1], the framework of KS-DFT [2] is mathematical in basis. With the assumption of existence of the S system, the time-independent version is in terms of an energy functional of the ground state density ρ(r). This functional is subdivided into a kinetic and a potential energy component. The local (multiplicative) potential energy of each model Fermion is then defined through the variational principle as the functional derivative of the corresponding potential energy component. The potential energy functional and its functional derivative are implicitly representative of the different many-body correlations that must be accounted for within the S system. In time-independent KS-DFT, these electron correlations, as noted previously, are those due to the Pauli exclusion principle, Coulomb repulsion, and Correlation-Kinetic effects. The explicit dependence of the potential energy functional and of its functional derivative on the various electron correlations, however, is not described by the theory.