Physical Interpretation of Kohn–Sham Density Functional Theory via Quantal Density Functional Theory

Abstract

As time-independent ground state Quantal density functional theory (Q-DFT) is a description in terms of ‘classical’ fields and quantal sources of the mapping from the interacting system of electrons as described by Schrödinger theory to one of noninteracting fermions possessing the same nondegenrate ground state density, it provides a rigorous physical interpretation of the energy functionals and functional derivatives (potentials) of Kohn-Sham (KS) theory. The KS ‘exchange-correlation’ potential is the work done in a conservative effective field that is the sum of the Pauli-Coulomb and Correlation-Kinetic fields. The KS ‘exchange-correlation’ energy is the sum of the Pauli-Coulomb and the Correlation-Kinetic energies, these energies being defined in integral virial form in terms of the corresponding fields. Via adiabatic coupling constant perturbation theory applied to Q-DFT, it is shown that KS ‘exchange’ is representative of electron correlations due to the Pauli Exclusion Principle and lowest-order Correlation-Kinetic effects. KS ‘correlation’ in turn is representative of Coulomb correlations and second- and higher-order Correlation-Kinetic effects. The Optimized Potential Method (OPM) integro-differential equations are derived. As the OPM is equivalent to KS theory, Q-DFT thus also provides a physical interpretation of the OPM equations. It further provides the interpretation of the energy functionals and functional derivatives (potentials) of the KS Hartree and Hartree-Fock theories.