A closed local-orbital unified description of DFT and many-body effects

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(alpha)} associated with a local-orbital orthonormal basis set {phi(alpha)}. 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(alpha)}. In particular, the total energy is now a function of {n(alpha)}, E[{n(alpha)}], and a Kohn-Sham-like Hamiltonian is derived introducing the effects of the electron-electron interactions via effective potentials, {V-alpha(eff) = partial derivative E-ee[{n(beta)}]/partial derivative n(alpha)}. In a second step we consider the IIartree and exchange energies and discuss how to describe them, in the spirit of a DFT approach, in terms of the orbital occupation numbers. In this contribution special attention is paid to the description of the (intra-atomic) correlation energy and corresponding correlation potentials {V-corr,(alpha)}. For this purpose, a model system is analyzed in detail, whereby an atomic Hamiltonian interacts with the environment via a simplified model; the use of this model allows us to obtain the correlation energy and potentials (in terms of {n(alpha)}) for different cases corresponding to low, intermediate and high electron correlations.