Comment on “Functional derivative of the universal density functional in Fock space”

Zahariev and Wang [Phys. Rev. A, 70, 042503 (2004)] discuss the density functional theory of noninteger average particle numbers. Among their many results is one we dispute: that the exact exchange-correlation potential (more precisely, the exact functional derivative of the exchange-correlation energy with respect to the density) cannot have a discontinuity as the particle number crosses an integer, in contradiction to works by two of us (J.P.P. and M.L.) in collaboration with co-workers [Phys. Rev. Lett. 49, 1691 (1982); Phys. Rev. Lett.51, 1884 (1983)] and by Sham and Schl\"uter [Phys. Rev. Lett. 51, 1888 (1983)]. We point to a counterexample to Zahariev and Wang's claim, which two of us (E.S. and J.P.P.) have presented in a separate paper: A rigorous proof that, in the absence of external magnetic fields, the exchange-correlation potential jumps by the difference between the ionization potential $(I)$ and electron affinity $(A)$ when the particle number crosses 1, given that $I\ensuremath{\geqslant}A$. We point out that Zahariev and Wang's derivation neglects an order-of-limits problem. We also prove that $I>A$ for any one-electron system in the absence of magnetic fields.