(2.2.24) Savin : The Hohenberg-Kohn theorem is valid for many Hamiltonians, including those with no interaction between particles. The latter case shows already the difficulty of constructing closed-form approximations to an energy density functional. Kohn and Sham decided to alleviate the treatment of electronic systems by treating accurately a (model) noninteracting system and by using density-functional corrections only for the difference between the energy of this system and the system of interest, with interacting electrons. Note that this idea is easily extended to other model Hamiltonians, making it possible to go beyond the use of a single Slater-determinant reference within DFT -see, for example, ref. 106.