Koopmans' Theorem.

Koopmans' theorem [59] can be understood as follows: for closed-shell systems, the negative of the HOMO energy is the ionization potential. That is, the energy required to form the cation provided that the ionization process is adequately represented by the removal of an electron from an orbital without change in the wave-functions of the other electrons.

The only alternative way to calculate the I.P. is to calculate the ΔHf  of the parent species, then, without allowing the geometry to relax, calculate the ΔHf  of the ionized system. The difference in ΔHf , in kcal.mol-1, divided by 23.06, is the predicted I.P., in eV.