State averaged ionization potential

A comparison of the experimental ionization potentials for N2, P2, and Asa. The dashed lines correlate the experimental state averaged ionization potentials from the atoms (from 2.9). 

Plot of the vertical ionization potentials for the eight electron AH4, AH3, AH2, AH, and A series. First row molecules are plotted in (a) and second row ones in (b). The dotted line indicates the state averaged ionization potentials for the A atoms. 

Plot of the s and of transition metal state-averaged Ionization potentials. The vertical ionization potentials for some common ligands are on the right side. 

The values for diagonal elements are taken as the negative of the average ionization potential for an electron in the appropriate valence orbital. Of course in many-election atoms, the valence-shell ionization potential (VSIP) for the ground-state atomic term may not necessarily be the best choice for the atom in a molecule, so this term is best regarded as an adjustable parameter, although one with a clear, physical basis. VSlPs have been tabulated for most of the atoms in the periodic table [211,212]. 

Other treatments " have led to scales that are based on different principles, for example, the average of the ionization potential and the electron affinity, " the average one-electron energy of valence shell electrons in ground-state free atoms, or the compactness of an atom s electron cloud.In some of these treatments electronegativities can be calculated for different valence states, for different hybridizations (e.g., sp carbon atoms are more electronegative than sp, which are still more electronegative than and even differently for primary, secondary,... 

Figure 3. Molecular-orbital diagrams as obtained by the ROHF method. Dashed lines indicate MOs dominated by the metal d-orbitals, the solid lines stand for doubly occupied or virtual ligand orbitals. Orbitals which are close in energy are presented as degenerate the average deviation from degeneracy is approximately 0.01 a.u. In the case of a septet state (S=3), the singly occupied open-shell orbitals come from a separate Fock operator and their orbital energies do not relate to ionization potentials as do the doubly occupied MOs (i.e. Koopmann s approximation). For these reasons, the open-shell orbitals appear well below the doubly occupied metal orbitals. Doubly occupying these gives rise to excited states, see text.

Here AEdiscr and A on are, respectively, the average energies of all the transitions into the discrete and continuous spectra E is the energy of the transition into the continuous spectrum and is the first ionization potential. The sudden-perturbation theory Eqs. (68) and (69) especially convenient for calculating A and A , since they involve only the ground-state wave function, allowing one to avoid the calculation of the spectrum of exited states. 

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