Axiomatic formulations of the Hohenberg-Kohn functional

Properties of the Hohenberg-Kohn functional are considered. In particular, the Hohenberg-Kohn functional should (a) give correct results in the variational principle and should be (b) continuous, (c) convex, and (d) size consistent. All of these properties are satisfied by the Legendre-transform functional (equivalently, the density matrix constrained search functional) and, moreover, this is the only functional that possesses all these …