Slater-Condon parameter

Apart from minor exceptions all other parameters are given the same values as in standard INDO (electroneguivities, Slater-Condon parameters, bonding parameters) or CNDO/S (one-centre repulsion integrals) methods. Two-centre repulsion integrals are usually evaluted by the Ohno-Klopman formula. 

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... 

Note The Slater-Condon parameters of Di Sipio et al. (75), derived from experimental data, lead to B values in reasonable agreement with those listed above for M+ and M2+ ions, but give appreciably larger values for M°. Fitting of the data of Table 22 on this basis would lead to appreciably smaller values of zeff than the listed values, especially where these are relatively low. 

Note Where the 5d values are derived from 3d results based on empirical Slater-Condon parameters, the same caveat applies as for the 4 d elements. [C. f. also Ref. (7)]. 

A theoretical analysis reveals [93] that the (reduced) Slater-Condon parameters should obey a relationship F° > 49F2 > 441F4. Moreover, F° > 49F4 and F2 > 5F4 should be fulfilled, which implies a relationship between the Racah parameters A Bcomplex formation, the relaxed parameters (A A = Aion - complex) obey a similar relationship, i.e., A A g> A B < AC. 

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 ... 

The energies of the d-d-excitations in this model are obtained by diagonalizing the matrix of the Hamiltonian constructed in the basis of rid-electronic wave functions (nd is the number of d-electrons). Matrix elements of the Hamiltonian are expressed through the parameters describing the crystal field and those of the Coulomb repulsion of d-electrons, which are Slater-Condon parameters Fk, k = 0,2,4, or the Racah parameters A, B, and C. In the simplest version of the CFT these quantities are considered empirical parameters and determined by fitting the calculated excitation energies to the experimental ones. 

The last ratio is independent of the parameters, a and 3 and may regarded as a purely group theoretical (kinematic) result. The same result is obtained dynamically without group theory through the Slater-Condon parameters which are integrals of e2/rjj over analytic hydrogenic orbitals. The chain has been interpreted as the sum of a p orbital-p orbital and a spin orbital-spin orbital magnetic dipole interaction. This inteipretation is clearly nonphysical. 

The electron repulsion integrals can be disposed of at once since these integrals in the pure d orbital basis reduce exactly to combinations of the usual Slater-Condon parameters, F k = 0, 2, 4) or Racah parameters A, B, C for the [Pg.15]

The general expression for the energy matrices of the fn configuration in terms of Slater-Condon parameters (F ) is normally written as a linear combination of the Fk integrals as... 

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... 

Electron-electron interaction is significant in studies where spin-orbital degeneracy, or near degeneracy, is present. The atomic d-orbitals have a common radial factor and their 15 distinct products give rise to 120 density-density integrals. These are expressed in terms of three basic ones, F0, F2, and F4 in the Slater-Condon formulation. The 100 spin-orbital densities are linear combination of the orbital ones and the 100 by 100 interaction integral matrix has a rank of 15 and is expressed by the Slater-Condon parameters. 

Here, the elements of the first operator are (in Slater-Condon parameters) taken from Ref. [11) p. 53 and translated into Racah parameters... 

The empirical values of the Slater-Condon parameters have been compiled by several authors for the p-block and rf-block elements (see e.g. [4] for a review). 

---