Gelius model

The model is valid when the contribution of the overlap electron density to the cross section is neghgible and the effects of the anisotropy of the molecular ion potential on the outgoing electron wavefunction are small. Both of these conditions are most likely to hold when the photoelectron KE is high. At low photon energies, molecular effects on ionization cross sections are well documented, but even in these regions atomic effects are evident and the Gelius model provides a good basis for molecular cross section interpretation. 

Empirical observations such as these are best rationalized using what has become known as the Gelius Model 25). In this the one electron ionization cross section Uj for the jth M.O. is given by... 

A rigorous theory of p.e. cross-section is beyond the scope of this chapter and, so, we shall be solely concerned with a simple, experimental approach to the problem that is the Gelius model [20]. 

Photoelectron spectroscopy proved crucial in this area [2] the technique has certainly had the merit of providing the first evidence of a synergic involvement of 6d and 5f subshells in the bonding [2e]. It is, however, difficult to ascertain which of them is dominant and the limits of p.e.s. in discriminating between 5f and 6d contributions depend both upon the little theoretical and experimental information available on "frequency dependence" of 6d cross-sections (vide supra) and upon the "first order" approximation of the Gelius model. Therefore p.e.s. studies, when limited to a purely experimental approach without the support of suitable theoretical investigations, may suffer because of these ambiguities. 

Upon switching to the He-II radiation notable changes in relative band intensities are observed. The most striking effect is the remarkable increase in the Intensity of band b. This is in reality an expected result since the, corresponding MO s have the largest metal 5f contribution and, hence, adopting the Gelius model for p.e. cross-... 

A common method of calculating the approximate photo-ionisation cross-sections is to use the Gelius intensity model [79]. Here the cross-section for a particular orbital, , is expressed in terms of atomic contributions based on population analysis. 

A practical and quite successful approach is the intensity model proposed by Gelius (1 ) which involves Mulliken population analysis and considers relative atomic photoionization cross-... 

K. Helenelund, U. Gelius, P. Froelich, O. Goscinski Photon Induced Post-CoUisional Auger Decay A Modified Shake-Down Model J. Phys. B19, 379 (1986). 

The intensity of valence XPS was estimated from the relative photoionization cross section for A1 Ka radiation using the Gelius intensity model [7]. For the relative atomic photoionization cross-section, we used the theoretical values from Yeh [8]. In the intensity calculations, we used the LCAO coefficients of eigenvectors for the ground state of the model molecules derived by using a minimal basis set. 

---