Density Functional Theory

Abstract

A short overview is given of fundamentals of the modern Density Functional Theory (DFT), an alternative approach to the quantum many-body problem. Basic theorems of Hohenberg and Kohn (HK) are summarized and their extensions for general densities and mixed quantum states are outlined, with the ensemble formulation covering the open molecular systems at finite temperatures. General forms of density functionals for the kinetic and potential energy contributions in both the local density and gradient approximations are then qualitatively examined using the virial theorem and the uniform scaling of the system electron density. The orbital scheme of Kohn and Sham (KS) for DFT computations is described and its ensemble extension is briefly outlined. The exchange correlation (xc) energy is introduced and partitioned into the Fermi (exchange) and Coulomb (correlation) contributions. By using the Adiabatic Connection (AC) between the real molecular system of fully interacting electrons and the hypothetical KS system of noninteracting (separable) electrons, both exhibiting the same ground state density, these energy terms are expressed in terms of the effective correlation holes averaged over the coupling constant which scales the electron interaction. The Euler equation for the optimum density and the associated KS equations for the optimum orbitals are formulated and the system electronic energy is expressed in terms of the KS eigenvalues.