There are several programs that can calculate the "energies" of the natural atomic orbitals(NAO) that come from NBO analysis. However, I have several evidence that, unlike the energies of the "normal" MO's, the energies of NAO's are not trivially determined:
- Practically, they're not always equal to the ground-state energies of the same orbital in the neutral atom, even when the oxidation states are the same; for example, the five 3d orbital energies are not the same in a lone palladium atom([Kr]3d¹⁰) and in tetrakis(phosphine)palladium(0).
- Theoretically, NAO's are not true eigenfunctions of the relevant Hamiltonial operator, so their "energies", strictly speaking, should not be able to be well-defined at all.
My question now follows- exactly what methods are used to calculate the NAO "energies", assuming that a wavefunction (from HF, DFT, or any other method) is already given?