Electron binding energy, Koopmans

The lowest order correction to the so-called Koopmans theorem, which equates the electron binding energies with spin orbital energies, can then be expressed as... 

The evaluation of elements such as the M n,fin s is a very difficult task, which is performed with different levels of accuracy. It is sufficient here to mention again the so called sudden approximation (to some extent similar to the Koopmans theorem assumption we have discussed for binding energies). The basic idea of this approximation is that the photoemission of one-electron is so sudden with respect to relaxation times of the passive electron probability distribution as to be considered instantaneous. It is worth noting that this approximation stresses the one-electron character of the photoemission event (as in Koopmans theorem assumption). 

In the one-electron picture the photoelectron spectrum thus consists of a number of sharp peaks (Fig. 4 d), one for each core level, with the binding energy given by the negative of the HF eigenvalue (Koopmans theorem261). 

Core binding energies also differ from the Koopmans estimate, the negative of the core orbital energy. When an inner electron leaves an atom of a molecule, the outer orbitals readjust because the nuclear charge is less effectively screened. The change due to outer shell readjustment is known as intra-atomic (or intramolecular) relaxation energy. 

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