Ionisation Potentials, Electron Affinities and Koopmans Theorem

1 Ionisation Potentials, Electron Affinities and Koopmans Theorem 

Theoretical IPs for TM compounds can generally be computed to within about 1 eV (8066 cm - ) of experiment given a sufficiently high level of theory. Simpler models often get the qualitative details correct and are therefore often employed to aid the assignments of the observed bands. However, one needs to be aware of how the IPs are calculated. 

A commonly used method for interpreting IP energies from Photo-Electron Spectroscopy (PES) is to employ Koopmans Theorem [25] which states that the IP (or EA) is equal to the negative of the MO energy from which the electron is ejected (or the energy of the acceptor MO for EAs). Loosely speaking, one can extend the analogy to excitations from one MO to another in as much as the combination of ionisation and electron capture is equivalent to an excitation. However, there are several caveats to bear in mind. 

Koopmans Theorem applies rigorously only to Hartree-Fock theory2. Focussing on IPs, the difference between the HF total energy, EHF, of the neutral molecule, A, and the generated cation, A+, is equal, in the HF approximation, to the energy of the MO from which the electron is removed, e . 

This will be a resonable approximation to the actual IP only if i) the HF method is appropriate in the first place and ii) there is little or no electronic relaxation accompanying the ionisation. In general, for TM systems neither of 

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