According to an answer to my question on whether the Kohn-Sham orbital energies theoretically exactly capture arbitrary ionisation potentials and/or excitation energies, the answer is no for both questions "due to the neglect of attractions between electrons and holes in K-S theory"- a reason I could not grasp.
I then looked the Kohn-Sham equations up on Wikipedia and found a concept called "Dyson orbitals" that are mathematically constructed purely from the N-electron wavefunction and the N+-1-electron wavefunction.
Since both of these are pure quantum chemical entities, a set of Dyson orbitals constructed from ground-state N-electron wavefunction(s) and ground-state N+-1-electron wavefunction(s), packed with their energies, should capture the exact energies of "everything"- from the arbitrary ionisation potentials and electron affinities (defined by the energy difference of the ground state and arbitarily ionised states) to excitation energies of arbitrary excited states.
Is this correct? (I'm asking this question because I found a couple of open-source papers on Dyson orbitals, only to realise that I could not grasp it at all)