Repulsion, inter-electronic

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. ... 

The hydrogen atom and one-electron ions are the simplest systems in the sense that, having only one electron, there are no inter-electron repulsions. However, this unique property leads to degeneracies, or near-degeneracies, which are absent in all other atoms and ions. The result is that the spectrum of the hydrogen atom, although very simple in its coarse structure (Figure 1.1) is more unusual in its fine structure than those of polyelectronic atoms. For this reason we shall defer a discussion of its spectrum to the next section. 

Data for some typical complexes are given in Table 26.5. The assignments are made, producing values of the inter-electronic repulsion parameter B as well as of the crystal-field splitting, 0Dq. 

However, in the case of the electronic orbital model there is no way in which the inter-electronic repulsions can be physically reduced. This form of distinction has not been sufficiently emphasized by philosophers. I believe that the nature of the orbital model shows that not all theoretical models can be lumped together as in the work of Achinstein [1968]. 

Inter-electron Repulsion and Irregularities in the Chemistry of Transition Series... 

Table 1.1 The inter-electronic repulsion energies, rep(f"), and the ionization energies, l[f), off configurations according to the theory of atomic spectra.

The second class of reaction is that of processes in which the 4f electrons are conserved. The obvious examples are the complexing reactions of tripositive lanthanide ions. Here the irregularities due to changes in inter-electronic repulsion almost entirely disappear. We then get the slight smooth energy change whose consequences were so familiar to 19 century chemists, who struggled vdth the separation problem. 

Calls for an explanation were answered by Jorgensen and elaborated by Nugent [26]. When a lanthanide ion moves from the aqueous to the organic phase, the nephelauxetic effect leads to a small decrease in inter-electronic repulsion within the 4f shell. This decrease varies irregularly with atomic number and is responsible for the irregularities in Fig. 1.3. 

Table 1.2 The excess inter-electronic repulsion for T configurations (column 4), relative to a smoothly varying baseline function, g(n), drawn through the formulae for f, f and f. ...

The energetics of the dihydrogen molecule-ion, H2+, and the dihydrogen molecule were outlined to give a calculation of the inter-electronic repulsion energy in the latter. 

As will be elaborated later, to deal with the spectra of transition metal ions with more than one electron in the empty (or hole in the filled) d10 shell, it is necessary to take into account inter-electronic repulsion energies within the d manifold. On the basis of CFT, of course, the parameters... 

The inter-electron repulsion integrals are often written in a contracted form as follows Jtj = (ii jj ), and Kij = (i j I ij ) It is conventionally understood that the first two indices within the bracket refer to the orbitals involving electron 1, and the second two indices to the orbitals involving electron 2. In general the functions are real and the stars are omitted. 

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