Many-electron problem in terms of the density: From Thomas-Fermi to modern density-functional theory

In this paper we focus on the use of electron density and current-density as basic variables in describing a many-electron system. We start with a discussion of the seminal Thomas-Fermi theory and its extension by Bloch for time-dependent hamiltonians. We then present modern density-functional theory (for both time-independent and time-dependent hamiltonians) and approximations involved in implementing it. Also discussed is perturbation theory in terms of electron density and its use for calculating various response properties and related quantities. In particular, van der Waals coefficient C-6 is calculated using density and current density in time-dependent perturbation theory. Throughout the paper, results for alkali-metal clusters are presented to demonstrate the strength of density-based theories.