Energy binding, Koopmans’ theorem

If the primary peak is the only peak with a binding energy less than the Koopmans theorem energy (this is usually the case), then an increase in the primary relaxation energy must be accompanied by an increase in the quantity 2 ( )- KTX/ for the shake-up and shake-off bands, where the intensities If are... 

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). 

Adams and Clark78 used a large basis set of better than DZ quality and calculated core binding energies and shifts for several fluoro- and chloro-methanes, including CF4. These were obtained using Koopmans theorem, hole state calculations, and equivalent cores calculations,79 the latter giving the best results for minimal basis sets, but there was little difference between the three methods for the more extended basis sets. NF4+ was also studied in this paper. 

By Koopmans theorem only half the interelectronic repulsion is computed in the calculation of the ionization energy, which will be therefore too large by Dewar, Hashmall and Venier 47) have also shown that if one treats the closed-shell and the open-shell systems separately, but if the open-shell system is also described by s single Slater determinant, an error of j remains in the calculation of binding energies. 

Since the excess energy can be measured and E is known, the binding energy can be determined. Koopmans theorem... 

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... 

Koopmans theorem provides the theoretical justification for interpreting Hartree-Fock orbital energies as ionization potentials and electron affinities. For the series of molecules we are using, the lowest virtual orbital always has a positive orbital energy, and thus Hartree-Fock theory predicts that none of these molecules will bind an electron to form a negative ion. Hartree-Fock almost always provides a very poor description of the electron affinity, and we will not consider the energies of virtual orbitals further. 

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