On a Distinguished Quality of the Im B kq/Re B kq Parameter Ratios in the Multipole Expansions of the Crystal Field Potentials

Abstract

It is demonstrated that for crystal field potentials having complex parameterizations characterized by low symmetry and large number of independent parameters, the formulas for the Im B k q /Re B k q ratios, i.e., for the parameters of the same k and | q|, correspond to a more general superposition model requiring the local metal-ligand symmetry to be ν instead of C ∞ν if the scaling factors alone are treated phenomenologically. A formal expression revealing the mutual interplay of both the distance and the nonaxial scaling factors has been obtained which allows the ratios Im B k q /Re B k q to be estimated more adequately. The generalization is substantial indeed; the corresponding number of independent intrinsic parameters of kth degree rises from one to k + 1. The distinguished quality of these ratios allows them to be treated in a distinguished way during the fitting of the potentials to experimental data. The proper fitting is then easier, since the number of independent parameters can be reduced.