In what areas of application are improvements needed? (4.3.1) Helgaker, Teale, and Laestadius : Current DFT (CDFT), in which the density functional depends on both the charge density ρ and the paramagnetic component of the current density j p , was introduced in 1987 by The initial works assumed a Hohenberg-Kohn-type theorem, but it was later recognized that no such theorem had been rigorously established. Moreover, the conclusion in ref. 36 was that the pair of densities ρ and j p cannot determine the scalar and vector potentials v and A since a wave function can be the ground state of infinitely many systems when the flexibility of a vector potential is added. This observation rules out a Hohenberg-Kohn theorem for the paramagnetic current density. Regarding the total (as opposed to paramagnetic) current, no Hohenberg-Kohn-type theorem has so far been established but it is not precluded either since no counterexamples have been found.