On the non-interacting $v$-representability conjecture within density functional theory

Jérémie Messud

Published 2021-02-06Version 1

Density functional theory together with the Kohn-Sham (KS) scheme represent an efficient framework to recover the ground state density and energy of a many-body quantum system from an auxiliary "non-interacting" system (one-body with a local potential that is a density functional). However, to fully achieve establishing the KS scheme, a general proof of the validity of the so-called "non-interacting $v$-representability" conjecture is still required. In this article, we propose such a proof. We reduce the demonstration to proving (1) that the KS potential is differentiable for all non-interacting $v$-representable densities and (2) that its derivative is bounded. Then, we demonstrate points (1) and (2) applying static linear response to the non-interacting system.