Racah Parameter

When an atom has more than one electron there will be some electrostatic repulsion between those electrons. The amount of repulsion varies from atom to atom, depending upon the number and spin of the electrons and the orbitals they occupy. The total repulsion can be expressed in terms of three parameters ''A'', ''B'' and ''C'' which are known as the Racah parameters after Giulio Racah, who first described them. They are generally obtained empirically from gas-phase spectroscopic studies of atoms.

They are often used in transition-metal chemistry to describe the repulsion energy associated with an electronic term. For example, the interelectronic repulsion of a ³P term is ''A'' + 7''B'', and of a ³F term is ''A'' - 8''B'', and the difference between them is therefore 15''B''.

Definition

The Racah parameters are defined as

$\begin A \\ B\\ C\\ \end = \begin 1 & 0 & -49\\ 0 & 1 & -5 \\ 0 & 0 & 35 \\ \end\begin F_0 \\ F_2\\ F_4\\ \end$

where $F_k$ are Slater integrals

$\begin F_0 \\ F_2\\ F_4\\ \end = \begin F^0 \\ \fracF^2\\ \fracF^4\\ \end$

and $F^k$ are the Slater-Condon parameters

$F^k := \int_0^\infty r_1^2 dr_1 \int_0^\infty r_2^2 dr_2 R^2(r_1) R^2(r_2)\frac$

where $R(r)$ is the normalized radial part of an electron orbital, $r_> = \max\$ and $r_< = \min\$
.

See also

* Tanabe–Sugano diagram
* Nephelauxetic effect

References

External links

Multiplets in Transition Metal Ions
in E. Pavarini, E. Koch, F. Anders, and M. Jarrell (eds.): Correlated Electrons: From Models to Materials, Jülich 2012,

Coordination chemistry
Spectroscopy

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