Abstract Density functional theory (DFT) is usually formulated in terms of the electron density as a function of position n ( r ). Here we discuss an alternative formulation of DFT in terms of the orbital occupation numbers { n α } associated with a local-orbital orthonormal basis set { ϕ α }. First, we discuss how the building blocks of DFT, namely the Hohenberg–Kohn theorems, the Levy–Lieb approach and the Kohn–Sham method, can be adapted for a description in terms of { n α }. In particular, the total energy is …