Density Functional Theory: Basic Results and Some Observations
We review first the basic results of density functional theory: the lemma of Hohenberg and Kohn establishing the density n(r) as a sufficient variable for a description of a non-degenerate or degenerate ground state; the energy variational principle, including recent reformulations by Levy and Lieb; the self-consistent Kohn-Sham equations and the most recent improved approximations for the exchange-correlation functional. This is followed by a number of observations: the issue of v-representability is discussed, including, depending on the context, its significance and non-significance in the light of recent work by Levy, Lieb, and Kohn; a discussion is presented of two different approaches to the basic functionals F[n(r)] and Exc[n(r)] -- by means of many-body tech-niques or by using the definition of F[n(r)] as a minimum over a constrained set of antisymmetric functions; other interesting recent developments of density functionals are briefly mentioned; some remarks are offered concerning a proposed concept of generalized local approximations; and finally a few other promising directions for future research are listed.
In these lectures, which come at the beginning of a workshop dedicated to density functional theory (DFT), I would like to attempt two objectives: to refresh your memory about the basic facts of DFT, and to present some remarks about the present situation and the outlook for the future.
KeywordsDensity Functional Theory Variational Principle Ground State Energy Local Density Approximation Schrodinger Equation
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- 1.L.H. Thomas, Proc. Camb. Phil. Soc. 23:542 (1927); E. Fermi, Rend. Acad. Naz. Linzei 6: 602 (1927).Google Scholar
- 4.M. Levy, Phys. Rev. A 26: 1200 (1982).Google Scholar
- 5.E.H. Lieb, in “Physics as Natural Philosophy: Essays in Honor of Laszlo Tisza on his 75th Birthday,” H. Feshbach and A. Shimoni, eds., MIT Press, Cambridge (1982).Google Scholar