Quantal Density Functional Theory

Abstract

Quantal density functional theory (Q-DFT) is a local effective potential energy theory [1]–[8] along the lines of Slater theory [9, 10] and traditional Hohenberg-Kohn-Sham density functional theory [11]–[14]. The basic idea, in common with Kohn-Sham density functional theory (KS-DFT) to be described more fully in the next chapter, is the construction of a model system of noninteracting Fermions whereby the density ρ(r t)/ρ(r) and energy E(t) / E equivalent to that of Schrödinger theory is obtained. Since these Fermions are noninteracting, their effective potential energy υ s (r t) / υ s (r) is the same. The corresponding quantum mechanical operator representative of this potential energy is therefore multiplicative, and it is said to be a local operator. We refer to this model as the S system, S being a mnemonic for ‘single Slater’ determinant. Within Q-DFT the potential energy of the noninteracting Fermions is defined explicitly in terms of the various electron correlations that must be accounted for by the S system. It is also possible to construct in the framework of Q-DFT, S systems such that the density and energy of both Hartree and Hartree-Fock theories is obtained. In a following chapter we will describe a Q-DFT whereby a system of noninteracting Bosons — the B system — is constructed such that the density and energy equivalent to that of Schrödinger theory is once again determined.KeywordsModel FermionSlater DeterminantElectron PositionEffective Potential EnergyFermi HoleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.