Although we introduced density functional theory (DFT) in section 6.1 in the context of Lang and Kohn's work on metal surfaces, the concept itself is much broader. It consists of setting up a general single particle method to solve the Schrödinger equation for the ground state of a many electron system by: (1) showing that the equation can be solved variationally to give an upper bound to the energy of the system expressed in terms of the electron density n(r), sometimes written ρ(r); this theorem was introduced by Hohenberg & Kohn (1964); and (2) proposing practical schemes whereby this theorem can be implemented as an iterative computational method, starting from a set of approximate wave functions describing the ground state of the electron system. The main non-relativistic scheme in use is due to Kohn & Sham (1965). The pervasiveness of these methods was recognized in 1998 by the award of the Nobel prize for chemistry to Walter Kohn (Levi 1998).

Writing down too many equations specifically here will take too much space, and may encourage the reader to believe that the method is simpler than it actually is. Some of the key review articles have been cited in sections 6.1.2 and 7.1.3. So many words have already be spilt on the topic, the methods are so widespread, and yet no-one can give a measure of just how good an approximation DFT represents, or say categorically whether further developments such as GGA necessarily improve matters, that there is no sense in which I should try to confuse you further.