A simple, clear and pedagogical way of introducing Density Functional Theory

Abstract

Density functional theory (DFT) plays a crucial role in computational chemistry, but its introduction in the chemistry curricula poses a challenge to lecturers when it comes to laying down its foundation without using a complex mathematical formalism and to establishing its scope and limitations. This article aims at presenting a simple and clear derivation of the theory that shows up its very general character. It is based on the constrained-search approach, that bears a close parallelism with the wave-function variational theorem, a familiar tool in any quantum chemistry introduction. Notwithstanding its simplicity, this approach shows appealing features, such as providing an explicit connection of the ground-state density with the electronic hamiltonian and an expression for the universal functional appearing in the definition of the energy functional. These lead to a more tangible insight into the theory than the original derivation by Hohenberg and Kohn, which only guarantees the existence of that connection and this functional. On the other hand, the approach highlights that the theory may, in principle, treat open and closed shell ground states on an equal footing, without the need to impose any restriction about the state spin. An interesting result is recalled that guarantees that a Kohn-Sham scheme may always be set up, no matter the open or closed shell character of the ground state nor its degree of electron correlation.