Koopmans Orbital Theorem with Hartree-Fock Picture

3 Koopman s Orbital Theorem with Hartree-Fock Picture 

Now one will make the essential difference between (Putz, 2013)  

All together, we can deal with the first lowest N spin-orbitals occupied in the overall wave-function while the rest 

The conceptual difference consist in the fact that when dealing with infinite number of orbitals one does not avoid the double counting since there will be always available virtual orbitals to be occupied since the infinite cardinal of this set of orbitals so we have with the actual subtle (mixed) notations  

FIGURE 4.3 The paradigmatic in silica spectra of the first three highest occupied and lowest unoccupied molecular orbitals HOMOs and LUMOs illustrating the respective, successive, ionization and affinities energies as provided by Koopmans theorem. Note KT implies ionization and affinity of one electron on successive levels and not of successive electrons on levels- see the marked occupied and virtual spin-orbitals (Putz, 2013). 

---