4f occupancy

NfF is the linewidth of a real 4f ->4f° excitation, as in a photoemission experiment which changes the 4f occupation. 

Therefore, the occupied charge fluctuation peak carries most of the weight and the 4f occupation number... 

In this appendix we discuss a very convenient method to calculate electron-phonon coupling effects for stable-moment compounds, i.e., with integer 4f occupation. It is based on diagrammatic perturbation theory and will be used extensively in sect. 2. It is especially suitable for the calculation of finite-frequency phenomena like quadrupolar excitons and their mixing with phonons (sect. 2.7). In this pseudofermion method invented by Abrikosov (1965) and then adapted to CEF problems (Fulde and Peschel 1972) the transition operators = n) (ml that form the standard basis for operators acting within a given CEF system are replaced by pseudofermion operators/ according to Unlike the L... 

The metals Eu and Yb have very different electronic structures from their near neighbors. They are both divalent, and their 4f occupancy, 4f and 4f, is one more than what one would expect from interpolating between their nearest neighbors. The 4f shell appears to be highly stable when it is half-filled or completely filled, to the extent that in these metals one valence electron goes... 

These elements possess well-developed multiplet structure in the soft X-ray spectra of the condensed phase, which can be compared with the spectrum of the fiee atom by performing ab initio Dirac—Fock calculations, the actual 4f occupancy in the solid can be deduced. An example is shown in figs. 4 and 5. The first point to note is that the multiplet structure of the atom survives in the solid, because of the strong localization of the 4f electrons, so that soft X-ray spectroscopy provides a useful probe of the 4f occupancy. To emphasize this point, we show, in fig. 4, a comparison between spectra of Sm vapour and Sm in the solid phase, which reveals the great similarity of structure between them. A multiconfigurational atomic structure calculation (fig. 5 Sarpal et al. 1991) demonstrates that, even in this complex situation, it is possible to deduce from ab initio atomic structure calculations what the 4f occupancy is. 

Many of the early, rigorous investigations of lanthanide-containing molecules have been performed with density-functional methods. They are especially useful for the investigation of photoelectron spectra, however they are certainly not the method of choice when one is interested, e.g., in the energy differences between electronic states arising from an open f shell, especially when configurations with different 4f occupation numbers are involved. 

Fig, 7. Linear behavior of the binding energies of the lanthanide monohydrides for fixed 4f occupation number. Data taken from Dolg and Stoll (1989). 

A more critical quantity seems to be the term energy of the first excited state. The different 4f occupations cause rather large differential relativistic and electron correlation effects. In order to judge the accuracy of the molecular calculations one may first consider a related excitation energy of the atom. The experimental atomic... 

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