Is it possible to calculate electronic energy of a cation X+ without relaxation of its orbitals compared to those of netural X in DFT, HF, ...?! In other words, can one model a hypothetical atom with arbitrary orbital energies and then calculate its electronic enery?(keeping in mind the quantum mechanics doesn't allow the levels to have arbitrary energies!) I want to calculate vertical ionization potential (for atoms and molecules) using DFT or HF, and I need to reduce the effects of orbital relaxation, self interaction errors, derivative discontinuity and ... to obtain IP equal to negative value of HOMO (Koopman's theorem).  However, Koopman's theorem refers to cations that are neither electronically nor geometrically relaxed.

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