Theorem Koop man

The eigenvalues e are the well-known orbital energies, and represent (in absolute value) the amount of energy necessary to remove the electron from the respective orbital. According to Koop-mans theorem, e corresponds to the negative of the respective ionization potential (see Section IV). 

In the case of photoelectron spectroscopy the experimental data provide electronic term values for the excited states of the ion. By the use of Koop-mans theorem,5 estimates of these quantities can be obtained from orbital energies found in calculations on the closed-shell ground state of the molecule. This procedure can give a useful hint at the analysis of a spectrum but is on rather shaky ground theoretically,6 involving a number of assumptions of doubtful validity and giving spurious answers in several well-documented instances. 

In Table 7.1 we have summarized the results of this analysis. Single excitations of the type acontribute only to the second-order energy of the N - l)-particle system. Their effect is to stabilize the (N — l)-particle system relative to the "Trozen " orbital approximation implicit in the Koop-mans" theorem IP and thus they tend to decrease the IP. Excitations of the... 

Table 7.3 Orbital relaxation (ORX) and pair removal (PRM) contributions (in a.n.) to the correction to Koop-mans theorem IP for H2...

R. Ferreira Paradoxial Violations of Koop-man s Theorem with Special Reference to the 3 d Transition Elements and the Lanthanides. Cfionne/fe.-Band and Localized States in Metallic Thorium, Uranium, and Plutonium, and in some Compounds, Studied by X-Ray Spectroscopy V. Gutmann, H Mayer The Application of the Functional Approach to Bond Variations under Pressure... 

Table 16 First ionization potentials (eV) (Koop-man s theorem) for thiirane.

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