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 ofthe S system, the time-independent version is in terms of an energy functional of the ground state density p(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 varia-tional 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. As Q-DFT is a description of the S system in terms of 'classical' fields and quantal sources, it is possible then to provide a rigorous physical interpretation of the potential energy functional and its various components, and of their respective functional derivatives. Furthermore, as the fields are separately representative of the different electron correlations, the physical interpretation allows for an explicit understanding of the correlations these functionals and their derivatives are representative of. In this chapter we describe the rigorous physical interpretation [3, 4] of time-independent Kohn-Sham density functional theory. We begin with a description of the physics of the KS electron-interaction energy functional E!S [p], its Hartree EH [p] and 'exchange-correlation' E~s [p] energy components , and of their respective functional derivatives Vee (r), VH (r), and vxc(r). The physics underlying the KS 'exchange' E~S[p] and 'correlation' E~S[p] energy functionals and their derivatives vx(r) and vc(r) is arrived V. Sahni, Quantal Density Functional Theory