Slater parameter

Usually, for both theoretical and semi-empirical determination of energy spectra, radial integrals that do not depend on term energy of the configuration are used. More exact values of the energy levels are obtained while utilizing the radial wave functions, which depend on term. Therefore, there have been attempts to account for this dependence in semi-empirical calculations. Usually the Slater parameters are multiplied by the energy dependent coefficient... 

On the other hand, electrostatic models regard the ligands or the whole crystal as polarizable units and thereby lead to weaker Coulomb and spin-orbit interactions. In a dielectric screening model (DSM) from Morrison et al. (1967) the f element is placed within an empty sphere with radius Rs which is embedded into an infinite medium with dielectric constant e. This leads to a reduction AFk of the Slater parameters (Newman, 1973) ... 

Experimental results for the Slater parameter reductions of Nd3+, Pr34-, and U3+ (Troster et al 1995) in LaCl under pressure up to 8 GPa in comparison with results from the dielectric screening model. All values in cm 1 3... 

Troster et al. (1995) also considered the DS model, whereby the radius R.s was assumed to be proportional to a mean metal ion - chloride ion distance Rm. As ambient pressure values they used ratios Rs/Rm of 0.417 for Nd3+, 0.424 for Pr3+, and 0.500 for U3+. With these values the absolute changes of the Slater parameters have been calculated up to 8 GPa as shown in table 4. 

Similar to the rare-earth trichlorides, also different ternary MYX compounds have been studied thoroughly under high pressure. The results for the pressure-induced changes of the Slater parameter F2 and the spin-orbit coupling parameter of these and other compounds are presented in table 5. Due to the difficulties with the DS model, the evaluation of the parameter shifts has been performed only in terms of the two covalency models. Assuming small changes for the free-ion parameters, the relative changes were approximated by ... 

According to table 5, in all cases except for some Eu3+ compounds, the decrease for F2 is larger than for . Thus, the SRC model plays the dominant role. In the case of some Eu3+ compounds on the contrary, the spin-orbit coupling parameter decrease more strongly than the Slater parameter, which leads to the conclusion that the CFC model is dominating here. 

An interesting improvement of the SRC model has been discussed by Wang and Bulou (1995). They considered simplified expansion factors used in the Hartree-Fock radial wave-functions for the f-electrons. With these factors it was possible to introduce a k dependence for the pressure-induced change of different Slater parameters. This procedure would remove the weak point of the model which could not account for the observed -dependence of the parameters under pressure. 

The first term in eq. (1) Ho represents the spherical part of a free ion Hamiltonian and can be omitted without lack of generality. F s are the Slater parameters and ff is the spin-orbit interaction constant /<- and A so are the angular parts of electrostatic and spin-orbit interactions, respectively. Two-body correction terms (including Trees correction) are described by the fourth, fifth and sixth terms, correspondingly, whereas three-particle interactions (for ions with three or more equivalent f electrons) are represented by the seventh term. Finally, magnetic interactions (spin-spin and spin-other orbit corrections) are described by the terms with operators m and p/. Matrix elements of all operators entering eq. (1) can be taken from the book by Nielsen and Koster (1963) or from the Argonne National Laboratory s web site (Hannah Crosswhite s datafiles) http //chemistry.anl.gov/downloads/index.html. In what follows, the Hamiltonian (1) without Hcf will be referred to as the free ion Hamiltonian. 

Jorgensen elsewhere in this volume discusses how the Slater parameters appropriate to the multiplet splitting deviate from those associated with the optical multiplet spectra of the 4fn 1 ions in salts. 

Fig 6. Theoretical XPS valence band spectra of PO/ obtained by using (a) Slater parameters ... 

Fig. 20 Plots of Slater parameters Fk against atomic number for Cs2NaLnCl6, from Pr (2=59) to Tm (2=69). (Data from [35, 72, 207, 213, 216, 223, 229, 270])...

A more likely explanation is that the intensities are reduced for the same reason that the Slater parameters are reduced (Osborn 1989), i.e., because the 4f wavefunctions are hybridised with other configurations of higher energy. The f electrons partially occupy more delocalised levels so reducing their mutual electrostatic repulsion from the Hartree-Fock estimates (see sect. 2.1.2). In a metallic environment, there may be additional hybridisation with the band states, implying a correlation between the Slater parameter shifts and the intensity reductions. 

The attraction of the second spectrum of lanthanum for atomic spectroscopists has been mentioned in section 2.1. The analyses of the two-electron configurations 4f5d and 4f carried out by Condon and Shortley (1931) achieved great importance by being the only lanthanide spectrum described in detail in their subsequent monograph (Condon and Shortley 1935). The least-squares fits to the experimental data provided by Russell and Meggers (1932) yielded Slater parameters given (in cm ) by... 

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