Condon-Shortley theory

Firstly, these /8 parameters are rather ill-defined but most immediately, the qualitative trends between the values has been shown merely to reflect a greater reduction in Fi than in from the corresponding free-ion values. In short these parameter trends furnish little or no evidence for differential orbital expansion. Further, even if such differentiation is really there - by which we presumably mean within a conventional m.o. sheme - it must manifest itself only within the numerical values of (and ligand field parameters). While working within a (f basis, therefore, there is no inconsistency whatever by recognizing the non-spherical hgand field within Fl.f. of (1-5) at the same time as representing the interelectron repulsions - l/r,y of (1-5) - in the usual free-ion Condon-Shortley theory. 

The Slater-Condon-Shortley theory is a first-order perturbation treatment based upon irreducible tensorial sets of 1-orbitals (2). 

E. XT. Condon and G. H. Shortley, Theory of Atomic Spectra, Cambridge University Press, 1935 M. E. Bose, Elementary Theory of Angular Momentum, John Wiley and Sons, Inc., New York, 1957 A. Edmonds, Angular Momentum in Quantum Mechanics, Princeton University Press, 1957. 

The energy levels of the free Cr3+-ion (d ) are quite well known (4). A quantitative description with the Slater-Condon-Shortley method (5) using the Racah-parameters B and C ) and the L—S-coupling parameter A does not lead to a satisfactory agreement between theory and experiment this can be achieved only by assuming different C/R-ratios for different doublet-levels (Table 1). The depression of the P-level is especially remarkable. The deviations from the three-parameter theory are less pronounced for Ni + or Co + (2), for example. 

E. U. Condon and G. H. Shortley, Theory of Atomic Spectra (Cambridge University Press, 1935). 

It should be remembered that terms such as < ,HF M fry> will vanish as a consequence of the Slater-Condon-Shortley rules, and if we were to use perturbation theory to calculate the Ct etc. we would find C[Pg.78]

Condon EU, Shortley GH (1951) The theory of atomic spectra. Cambridge University Press, Cambridge, UK... 

Condon, E. U., Shortley, G. H. Theory of atomic spectra. Chaps. 7 and 8. Cambridge University Press 1935. 

A brief review is given here of the spectroscopic vector model of an atom or ion. In crystal-field theory, the wave function of the isolated ion is taken as the unperturbed state, and the perturbing effect of the electric and magnetic fields is computed. Thus crystal field theory uses the language, nomenclature, and methods employed in the theory of atomic spectra. A complete discussion of these methods can be found in books by Condon and Shortley (5) and by Griffith (/). 

The monograph of Condon and Shortley [2] was a major work of reference for a whole generation of spectroscopists [20]. It treats an atom in the central-field approximation and it does not require deep knowledge of the theory of groups. 

Condon and Shortley wrote the book(4) on atomic theory and I will use their equations for the radial components of the relativistic wave function for an electron in a central field(5). Thus 1 quote... 

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