Density Functional Theory: a brief introduction

Density Functional Theory (DFT) is one of the most widely used methods for ``ab initio'' calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. A brief undergraduate-level introduction to DFT is presented here -- an alternative to the customary introduction, which is often considered too lengthy to be included in various curricula. The central theme of DFT, i.e. the notion that it is possible and beneficial to replace the dependence on the external potential v(r) by a dependence on the density distribution n(r), is considered here to be a generalization of the idea of switching between different independent variables in thermodynamics. Specifically, it is a direct extension of the familiar Legendre transform from the chemical potential \mu to the number of particles N. This is used to obtain the Hohenberg-Kohn theorem and to derive the Kohn-Sham equations. The exchange-correlation energy and the local density approximation to it are then discussed, followed by a very brief survey of various applications and extensions