E Pluribus Unum

The fundamental tenet of density functional theory is that any property of a system of many interacting particles can be viewed as a functional of the ground state density n0(r); that is, one scalar function of position n0(r), in principle, determines all the information in the many-body wavefunctions for the ground state and all excited states. The existence proofs for such functionals, given in the original works of Hohenberg and Kohn and of Mermin, are disarmingly simple. However, they provide no guidance whatsoever for constructing the functionals, and no exact functionals are known for any system of more than one electron. Density functional theory (DFT)would remain a minor curiosity today if it were not for the ansatz made by Kohn and Sham, which has provided a way to make useful, approximate ground state functionals for real systems of many electrons. The subject of this chapter is density functional theory as a methodology for many-body systems; Ch. 7 describes the Kohn–Sham ansatz that replaces the interacting problem with an auxiliary independent-particle problem with all many-body effects included in an exchange–correlation functional; Ch. 8 deals with widely used approximations for the exchange–correlation functional; and Ch. 9 is devoted to solution of the Kohn–Sham independent-particle equations in a general form useful for all Kohn–Sham calculations. Following chapters in this volume are devoted to algorithms for actual calculations, and applications to problems in atomic, molecular, and condensed matter physics.