Density Functional Calculations

Abstract

Density functional theory is based on the two Hohenberg-Kohn theorems, which state that the ground-state properties of an atom or molecule are determined by its electron density function, and that a trial electron density must give an energy greater than or equal to the true energy (the latter theorem is true only if the exact functional could be used). In the Kohn-Sham approach the energy of a system in formulated as a deviation from the energy of an idealized system with noninteracting electrons. From the energy equation, by minimizing the energy with respect to the Kohn-Sham orbitals the Kohn-Sham equations can be derived, analogously to the Hartree-Fock equations. Finding good functionals is the main problem in DFT. Various levels of DFT and kinds of functionals are discussed. The mutually related concepts of electronic chemical potential, electronegativity, hardness, softness, and the Fukui function are discussed.