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The second moment of the sublevels within the initial state | αSLJ  〉 which constitutes a natural and adequate measure of the crystal‐field (CF) effect can be redefined as  where  is the so‐called 2  k   ‐pole CF strength, whereas  A   k    = 〈 αSLJ  ‖  C  ( k )  ‖ αSLJ  〉 the reduced matrix element of the  k  ‐rank spherical tensor operator. Therefore, the CF effect depends on the sum of products of the two factors representing the identical multipole components of two different charge distributions. The term  A   k    expresses the asphericity of the central ion open‐shell, whereas the term  S   k    the asphericity of its surroundings. When these two distributions do not fit each other the observed CF splitting can be unexpectedly weak even for considerable values of the total  and . The tabulated quantities of the  A   k   (| αSLJ  〉), as the 2  k   ‐pole type asphericities, are the intrinsic characteristics of the electron states revealing their multipolar structure and hence their potential susceptibility to CF splitting separately for each effective multipole. For any chosen pair of a central‐ion and CF potential the relevant  A   k    and  S   k    magnitudes, respectively, allow us to predict the scale of the related splitting. We can also compare the CF splitting of various states in the same CF potentials or the splitting of the same state in various CF potentials. Having the model  σ  2  and their experimentally available counterparts we can evaluate the degree of admixing of the free‐ion states. Since the independent quantities  S   k    and  A   k    occur as the scalar product in the formula for  σ  2  the use of the total  S  and  A  notions should be critically considered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Multipole characteristics of the open‐shell electron eigenstates