Koopmans theorem breakdown

MO calculations of the SCF type for Nj place the state below the X g state. This discrepancy is an example of the breakdown of Koopmans theorem due to deficiencies in fhe calculations. 

A rather similar situation regarding the breakdown of Koopmans theorem exists for the metallocenes. The electronic structures of these interesting compounds have attracted the attention of both theoreticians and experimentalists for several years. Ferrocene is the metallocene that has been studied the most extensively. From the UPS standpoint this stems from the diamagnetism of the neutral molecule and the stability of the ferricenium cation. 

Koopmans theorem cannot be applied to this molecule- The SCF values are still in a rather poor agreement with experiment (partly owing to a small basis set used), but the order of ionization potentials is correct. The breakdown of the Koopmans theorem may be elucidated by a different extent of the electron reorganization involved in electron ionizations from the respective molecular orbitals. For ligand orbitals e or a2u little rearrangement upon ioniza-... 

The breakdown of the Koopmans theorem with the nitrogen molecule 468,469 notable because of its basis set dependence with the DZ basis set the order of orbital energies agrees with experiment whereas with the [4s3p] and larger basis sets the breakdown of Koopmans theorem occurs. Incorrect order of the 2, 3cT and lil ionization potentials is predicted even by the near Hartree-Fock ASCF calculations. This suggests that the correlation effects are extraordinar-... 

Such an orbital reorganization precludes a direct connection being established between the electronic configuration of lowest energy for N2 and the photoelectron spectrum which is shown in Fig. 6.9 that is, there is breakdown in Koopmans theorem. For example, the first band (ionization energy around 15eV) is attributed to the removal of one electron from 2crg,... 

An even more serious breakdown of Koopmans theorem is found for the third MO, 6a The corresponding Koopmans configuration, (6o) , interacts strongly with the configuration (7a) (27r) (Stt) which involves excitation of an electron... 

Correlation, or many-body effects, can be classified according to the many-body factor Xx- If Xx is close to 1, the MO picture, the aufbau principle, a Koopmans theorem and the quasi-particle picture hold. The analysis of the Auger spectrum can then be conducted solely in terms of MO theory. When more than one Xx enters in the wavefunction, we have hole-mixing effects and electronic interference in the transition cross sections, in analogy to the case of photoelectron spectra. When only one Xx is large, but this Xx is present in more than one state, one can then not associate a one-to-one correspondence between MOs (or MO factors in Eq. 3.39) and spectral bands (states). The states in question are thus associated with a breakdown of the MO picture. It could, finally, also be that no Xx is large, in which case we talk about a correlation-state satellite. 

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