Density Functional Theory and Local Potential Approximations from Momentum Space Considerations

Abstract

In this article we shall be concerned with three topics. The first of these is the relationship between position and momentum space and among various quantities defined in the respective spaces. We shall consider next the basic theorems of density functional theory from the point of view of quantum mechanics in momentum space. We turn then to consideration of the Schrodinger equation in momentum space and in particular the Hartree-Fock equations. By following the approach of Huo and Lassettre, we shall show that a family of local exchange potentials may be derived starting from either the exchange potential in the Hartree-Fock equations or from the exchange-correlation term in the density functional expression for the energy. These correspond respectively to the Slater and Kohn-Sham-Gaspar approaches to the derivation of the ρ 175 exchange potential, i.e. α=1 and α=2/3 respectively in the xα exchange potential.