Differentiability in density-functional theory

The differentiability of different functionals used in density-functional theory (DFT) is investigated, and it is shown that the so-called Levy-Lieb functional FLL[ρ] and the Lieb functional FL[ρ] are Gâteaux differentiable at pure-state v-representable and ensemble v-representable densities, respectively. The conditions for the Fréchet differentiability of these functionals are also discussed. The Gâteaux differentiability of the Lieb functional has been demonstrated by Englisch and Englisch (Phys. Stat. Solidi 123, 711 and 124, 373 (1984)), but the differentiability of the Levy-Lieb functional has not been shown before. © 2003 Elsevier B.V. All rights reserved.