  Density functional theory is currently the most widely applied method in
electronic structure theory. The Kohn-Sham method, based on a fictitious system
of non-interacting particles, is the work horse of the theory. The particular
form of the Kohn-Sham wavefunction admits only idem-potent one electron density
matrices whereas wavefunctions of correlated electrons in post-Hartree-Fock
methods invariably have fractional occupation numbers. Here we show that by
generalizing the orbital concept, and introducing a suitable dot-product as
well as a probability density a non-interacting system can be chosen that can
represent the one-electron density matrix of any system, even one with
fractional occupation numbers. This fictitious system ensures that the exact
electron density is accessible within density functional theory. It can also
serve as the basis for reduced density matrix functional theory. Moreover, to
aid the analysis of the results the orbitals may be assigned energies from a
mean-field Hamiltonian. This produces energy levels that are akin to
Hartree-Fock orbital energies such that conventional analyses based on Koopmans
theorem are available. Finally, this system is convenient in formalisms that
depend on creation and annihilation operators as they are trivially applied to
single determinant wavefunctions.
