Given an electronic system in its ground state, having N electrons moving in the field of nuclei generating a potential ${\mathrm{v}}_0$ and accurate electron density ${\mathrm{\rho }}_0$, it is demonstrated that the exact Kohn-Sham equations result from a minimization with respect to ρ, at some very high temperature θ, of a free energy functional ${\mathrm{A}}^{\mathrm{\theta }}$[ρ,${\mathrm{\rho }}_0$]=${\mathrm{T}}_{\mathrm{s}}$[ρ]+〈ρ|${\mathrm{v}}_0$〉+J[ρ](1-1/N)-θS[ρ,${\mathrm{\rho }}_0$], where S[ρ,${\mathrm{\rho }}_0$]=-〈ρ ln (ρ/${\mathrm{\rho }}_0$)〉. The infinite-θ minimum of ${\mathrm{A}}^{\mathrm{\theta }}$ is, within an error so far found to be less than the correlation energy, equal to the total electronic energy of the system.

DOI:https://doi.org/10.1103/PhysRevA.55.3226