Density functional theory

Summary

Density functional theory describes the ground state of a many-electron system through its electron density. The density is a function of only three variables, while the wave function of $N$ electrons depends on $3N$ variables. The Hohenberg–Kohn theorems show that the density determines the external potential. They also show that the ground state energy is the minimum of a functional of the density. The universal part of this functional is unknown, and practical DFT uses approximations of it, mostly through the Kohn–Sham scheme of non-interacting electrons. It is the most widely used method for computing the electronic structure of molecules and solids.