What orbital energies mean

The SCF hands you a ladder of orbital energies ε. They are not slices of the total energy (summing them double-counts repulsion) — so what physical thing are they? Koopmans' theorem supplies the answer: yank an electron out of orbital i, freeze every other orbital in place, and the energy you pay is exactly −εᵢ. For the loosest electron:

The frozen-orbital assumption is obviously false — the cation relaxes — and Hartree-Fock is missing correlation on top. Yet Koopmans IPs land within a volt or so of experiment surprisingly often, and the reason is an error cancellation: relaxation (ignored) would lower the ion, so freezing overestimates the IP; correlation (ignored) stabilizes the electron-rich neutral more, so neglecting it underestimates the IP. Two wrongs, opposite signs.

This is also the cleanest example of a habit worth building: every quantity the calculation prints should be answerable to an experiment. Orbital energies answer to photoelectron spectroscopy — that is why the HOMO's ε matters and the absolute zero of the ladder doesn't.