Racah parameters

Racah parameters The parameters used to express quantitatively the inter-electronic repulsion between the various energy levels of an atom. Generally expressed as B and C. The ratios between B in a compound and B in the free ion give a measure of the nephelauxetic effect. ... 

This term describes a shift in energy by Acim rn, for an orbital with quantum numbers I — 2, mi and that is proportional to the average orbital angular momentum (/z) for the TOj-spin subsystem and the so-called Racah parameters Bm, that in turn can be represented by the Coulomb integrals and The operator that corresponds to this energy shift is given by... 

Figure 1.1 shows that the stability sequence revealed by chemical reactions and chemical synthesis corresponds to thermodynamic stabilities. An explanation requires a theory that will explain both. To get it we apply the theory of atomic spectra [9]. The energy of the 4f electrons in an ion with the configuration [Xe]4P, F(4P), can be written [nU+E Q-p(4f )] where U, a negative quantity, is the energy of each 4f electron in the field of the positively charged xenon core, and Frep(4P) represents the repulsion between the n 4f electrons. In Table 1.1, rep(4P) is expressed as a function of the Racah parameters and E. The... 

Schetinger MRC, Morsch VM, Bohrer D (2003) Aluminium Interaction with Nucleotides and Nucleotidases and Analytical Aspects of Determination 104 99-138 Schmidtke HH (2003) The Variation of Slater-Condon Parameters Fk and Racah Parameters B and C with Chemical Bonding in Transition Group Complexes 106 19-35 Schubert DM (2003) Borates in Industrial Use 105 1-40... 

In our previous survey (7) of the hexafluoro complexes of the 3d series we discussed in some detail the information which may be derived from a consideration of the value of the nephelauxetic ratio, / (=i compiex/5gas). To obtain this parameter it is clearly necessary to have available values of the free-ion Racah parameter, B, and for the 4 d elements these may be obtained either from the compilation of Di Sifiio et al. (75) or by use of the Jorgensen-Racah relationship (76, 77). 

Table 21. Free-ion values of the Racah parameter, B, for Ad and 5d elements...

From this equation, we see that the Racah parameter for the metal ion in a complex, B, is the value for the gaseous ion reduced by a correction (expressed as Bhk) for the cloud-expanding effect. As should be expected, the effect is a function of the nature of the particular metal ion and ligand. As a result, analysis of the spectrum for a complex must be made to determine both Dq and B (which is actually B for the complex). Table 18.7 shows values of the nephelauxetic parameters for ligands and metal ions. 

Fig. 5 Regions of stability of either one or the other spin state as a function of the ligand-field strength. The region of spin crossover compounds is indicated by the shaded area. For the calculation, the values of the Racah parameters were taken to be 75% of the free ion values. This corresponds to a typical reduction for iron(II) coordination compounds of the type under consideration... 

Based on the bond length dependence of lODq, the fact that II does not vary to any great extent, and that in a complex the Racah parameters of electron-electron repulsion are typically reduced to 70 to 80% of their free ion values, the zero-point energy difference, A °hl= 0hs- °ls> between the high-spin and the low-spin state can be estimated as a function of 10DqHS as well as of lODq15 (see Fig. 5). For 10DqHS< 10,000 cm, A °Hl< 0, that is, the... 

Racah parameter for interelectronic repulsion Transition temperature (at 50% HS, 50% LS)... 

The energy matrices contain one-electron terms (which can be written down in terms of the AOM e parameters) and two-electron terms, expressed as multiples of the Racah parameters B and C. Values of the and Racah parameters which provide the best fit to the experimental data are then found. Most work has been done on the tetragonal (D4h) chromophores M X where the N atoms (equatorial) are provided by amine ligands. Only three AOM parameters can be determined since there are only three independent orbital splitting parameters eff(N), e0(X) and en.(X) can be found if ew(N) is taken to be zero, saturated amines having no orbitals available for jr-overlap. 

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 was parameterised in terms of ea only, and values of this parameter, together with the spin-orbit coupling constant X, the orbital reduction factor k and the Racah parameter B were obtained by fitting the d-d spectra, zero-field splittings, principal magnetic susceptibilities and e.s.r. g-values. 

EXAMPLE 6.4 Using the Sugano-Tanabe diagram of Figure 6.8, estimate the energy for the lowest energy transition in V MgF2 (AE —2500 cm ) and infer details about the emission of this laser material. The Racah parameters for the free ions are B = 755 cm and C = 3257 cm f... 

Indeed, this is not far off the peak wavelength (about 850 nm) experimentally observed for the " Aag " Tag absorption band (Moulton, 1985). The agreement is good, especially when we take into account that we are using free ion Racah parameters, which can be slightly modified in the crystal, and a Sugano-Tanabe diagram with a nonexact CIB value. 

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