Racah parameters of interelectronic repulsion

State. In order to obtain knowledge about the potential energy curves for the alternative spin states and hence about the respective non-adiabatic energy difference between the two minimum positions, help by reliable calculations was needed. DFT was our method of choice here [2,12], our experience is, that one may confidently use DFT results, if only Franck-Condon transitions from the ground state to lower excited states and polyhedron structures at or near to those for the ground state are utilised - and also, that the calculations are performed in the presence of a charge-compensating solvent medium. One has further to note, that the Racah parameters of interelectronic repulsion cannot be reproduced by DFT sufficiently well - they usually come out too small in comparison to the experimental values. 

Racah parameters of interelectronic repulsion in f shell parameter in spin-pairing treatment... 

Table I. The Wavenumbers of the Two Absorption Maxima Corresponding to the Two First Spin-Allowed Transitions for Octahedral 3

Once it was realized that there is an almost invariant ratio between the parameters of interelectronic repulsion in the f shell, both in the Slater-Condon-Shortley parametrization 1 0.75 0.5, and in the treatment of Racah... 

The SCS treatment for 4f electrons was thoroughly analyzed by Racah (1949), introducing three ingeniously chosen parameters of interelectronic repulsion, one of which is = D. This analysis is now being continued by Brorson and Schaffer (1987) for 3d electrons in both spherical and lower symmetries (i.e. compounds). 

Several of the numbers in eq. (15) may readily be uncertain by a factor of two, but for our purpose, the most important feature is Xz close to a half. This qualitative result pervades ligand field calculations, and it is almost surprising that Hartree-Fock radial 4f functions only overestimate the parameters of interelectronic repulsion by 30-40%, and it is close to unbelievable that the relative distances of terms in Ln(III) are better described by Slater-Condon-Shortley-Racah parameters than d and p in monatomic entities. 

In some papers, only the spin-allowed bands have been used in the analysis for d3 and d8 systems, this obviates the need to consider the Racah parameter C. Where the spin-forbidden bands have been included, C has sometimes been allowed to find a value which best fits the experimental data, along with the other parameters others have assumed a fixed value of the ratio B/C, such as 0.2S. The treatment of interelectron repulsion introduces some uncertainty into the orbital splitting parameters. Although it is well-known that the d-d spectra of Oh chromophores cannot be perfectly fitted within a model which allows only one value of B (1-3,... 

The ligand-field parameter A and the Racah-parameter of the interelectronic repulsion B are calculated from the energetic positions of two of the ligand-field bands. 

The most straightforward modifications of simple- crystal field-theory-that make allowance for orbital overlap involve using all parameters of interelectronic interactions as variables rather than taking them equal to the values found for the free ions. Of these parameters, three are of decisive importance, namely, the spin-orbit coupling constant, A, and the interelectronic repulsion parameters, which may be the Slater integrals, F , or certain usually more convenient linear combinations of these called the Racah parameters, B and C. 

Assignment of (he observed bands to these transitions, provides an estimate of B, the Racah interelectron repulsion parameter. Its value (Table 23.6) is invariably below that of the fiee-ion (1030cm ) because (he expansion of d-electron charge on complexation reduces the inteielectronic repulsions. 

A2g transitions, respectively. Besides being able to correlate jS with oscillator strength,/, of transitions the values may be employed 42) to evaluate the effective charges on the Cr(III) ions in various complexes. Fig. 4 provides plots of the effective metal charge vs. /3, the nephelauxetic parameter and B, the Racah interelectronic repulsion parameter for chromium(III). Jorgensen... 

Fig. 4. Effective metal charge, Z, in chromium(III) complexes as a function of the nephel-auxetic parameter, P, and the Racah interelectronic repulsion parameter, B...

The interelectronic repulsion Racah B parameters were also derived from the crystal field spectra of Mg-Ni olivines. (Hu et al., 1990). The compositional variations given by... 

Ligands can be arranged in order according to the extent to which they reduce interelectronic repulsion, as gauged by the Racah B parameter or nephelauxetic P ratio. This order constitutes the nephelauxetic (or cloudexpanding) series, a limited version of which is... 

The nephelauxetic effect is described quantitatively by parameter, f, which is equal to the ratio of the interelectron repulsion parameters (either Slater s integrals, Fk, or Racah parameters, Ek) in the complex and in the free ion. We may write... 

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