# Natural orbital population analysis in Gaussian

Within (restricted) density functional theory and Hartree-Fock, respectively the Kohn-Sham orbitals and spin orbitals are the natural orbitals, with occupation numbers either 2 or 0.

As I understood, this also applies to spin-unrestricted calculations, is this correct?

Now, when doing UDFT or UHF with Gaussian and specifying pop=NaturalOrbitals, the natural orbitals are different from the KS/canonical orbitals and some occupations numbers are also different from 2 and 0. Unfortunately Gaussian manual provides no reference to how the natural orbitals analysis is done exactly and the literature is fairly confusing (spin-projection vs non-spin projection etc.).

Could anybody give me an overview or reference regarding what Gaussian exactly does when this pop=NaturalOrbitals keyword is turned on?