Hohenberg-Kohn theorem is valid

In a recent PRL, Gonze et al claim that the density functional theory in Hohenberg-Kohn formulation is not valid for crystalline solids in a homogenious electric field. They introduce another theory, density-and-polarization functional theory, which has to substitute the DFT in the calculations of the long-wave dielectric response. We show that the theorem proven by Gonzo et al holds in addition to, and not instead of, the Hohenberg-Kohn theorem.