Coming from a DFT background, I'm used to the concept that the DFT eigenvalues do not correspond to excitation energies (i.e., the band gap, ionization potentials, etc.). To correct for these it's common to go to many-body approaches like the GW approximation to the self-energy, which is said to explicitly deal with quasiparticle addition/removal energies.
I'm curious how excited states are calculated within Hartree Fock or CI. Can one do a ground state calculation in HF or CI and then get excitation energies from the difference in these ground-state eigenvalues? Or is this similarly not possible and one needs to explicitly consider excited states in order to get the excitation spectrum (band gap, band eigenvalues for removal/addition of electron,etc.).