Slater-Condon parameters, effective

Using the Slater-Condon parameters all symmetry allowable two-electron one-center integrals, which brought about a modification of the matrix elements of the Fock operator, are taken into account. This allows one to write down the matrix elements of the effective Fock operator ... 

Effective Hamiltonians and effective operators are used to provide a theoretical justification and, when necessary, corrections to the semi-empirical Hamiltonians and operators of many fields. In such applications, Hq may, but does not necessarily, correspond to a well defined model. For example. Freed and co-workers utilize ab initio DPT and QDPT calculations to study some semi-empirical theories of chemical bonding [27-29] and the Slater-Condon parameters of atomic physics [30]. Lindgren and his school employ a special case of DPT to analyze atomic hyperfine interaction model operators [31]. Ellis and Osnes [32] review the extensive body of work on the derivation of the nuclear shell model. Applications to other problems of nuclear physics, to solid state, and to statistical physics are given in reviews by Brandow [33, 34], while... 

The absorption spectra of the bimetallic compounds showed intense 4f-4f bands along with a small nephelauxetic effect. The observed small nephelauxetic effect may be due to lowering of Slater-Condon (Fk) and Racah (Ek) interaction parameters which is in agreement with the ionic nature of the compounds in water and trifluoroacetic acid [234]. 

As with ligand-field absorption spectra, the Nephelauxetic effect [41, 42] will also impact L-edge XAS data. For L-edge spectra, the effect of a reduction in interelectron repulsion is also to reduce the ffee-ion state splitting and make the spectra somewhat more orbital like. This is demonstrated by the sequence of simulated low-spin Fe(III) L-edge X-ray absorption spectra shown in Fig. 13, where the e - e repulsion is reduced systematically from [i = 100% to 60%. This starts from 80% of the Hartree-Fock calculated values of the Slater Condon Shortley parameters for e - e repulsion. 

In further refinement, one could consider additional pressure effects on C for some ions. (One might expect that the Slater-Condon-Shortley parameter would be more affected by pressure than F. ) Alternatively one might assume with Stout that the higher energy Cg) levels are more spread out by the crystal field than the 2 levels. One could then calculate the covalency parameter e for these as a function of pressure. 

The parameters and Cf correspond to Slater-Condon electrostatic and spin-orbit integrals, respectively, and / and Aso represents matrix elements for the angular parts of these electrostatic and spin-orbit interactions. The integrals as used in the effective-operator approach are different from those used in the Hartree-Fock (HF) approach because they absorb some effects of configuration interaction that are not included in the... 

The spectra of these ions have not been interpreted experimentally but the Slater-Condon method was applied to the sequence As I — Ag XV for predicting energy levels and radiative transition probabilities within the ground configuration 4s 4p. Slater and spin-orbit parameters are from Hartree-Fock calculations, corrected for relativistic effects and scaled to fit the known elements [3]. The predicted levels are (energy in cm ) ... 

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