By J. Mulak
Because it effects from the very nature of items, the round symmetry of the encompassing of a website in a crystal lattice or an atom in a molecule can by no means ensue. hence, the eigenfunctions and eigenvalues of any sure ion or atom need to range from these of spherically symmetric respective loose ions. during this method, the main simplified thought of the crystal box impression or ligand box impression in terms of person molecules could be brought.
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Extra info for Effective Crystal Field Potential
Covalency, 7. screening, 8. polarization 37 In the metallic systems some specific mechanisms resulting from the presence of conduction electrons and broadening the energy levels ought to be additionally allowed for. The three fundamental contributions have been quantitatively (or rather semi-quantitatively) defined in the theory by Dixon and Wardlaw . These are: 1. screening the ionic cores potentials with the conduction electrons, 2. contribution of so-called virtual bound states, 3. hybridization of localized and delocalized electron states.
In the case of axial symmetry, but only its z-axis orientation with respect to the final system, two angles: c~ = r and /3 = 0 are sufficient. They are nothing else than the spherical coordinates of the initial z-axis in the final coordinate system. It corresponds to the three Euler angles according to the relation (c~,/3, 7) = (r 0, 0) and the geometrical 21 sense of the angles has been defined previously at description of the Jones transformation. 26) What is needed now is knowledge of the elements in the middle column of the D(k)(r 0, 0) matrix only which are easily available from tables of the spherical harmonics [28, 39].
30) where the coefficients c~ for relating extended 0~ and normalized r k Stevens q operators (()'~ - c~O~ and correspondingly/}'k - ( l l c ~ ) S ~ ) are listed by Rudowicz [34, 37]. 4 T h e n u m b e r of i n d e p e n d e n t c r y s t a l field p a r a m e t e r s Now, it is timely to answer the basic q u e s t i o n - how does the number of independent crystal field parameters depend on the surroundings symmetry. The expansion of 7~CF into the spherical tensor operator series is not subjected, a priori, to any limitation as for the range of variability of k and q indices.