Hohenberg and Kohn realized that one does not even need the full many-electron wave function to find the ground state of a many-electron system and that instead the electron density n(r) alone is enough to determine the ground state. Within the Kohn-Sham framework of density-functional theory, the density is again determined from another set of effective single-particle wave functions, which can be obtained as solutions to the Kohn-Sham equations :