The maximal axial components in the equivalent parametrizations of crystal‐field Hamiltonians

Within the limits of every class of equivalent parametrizations of the crystal‐field Hamiltonian there exists always such a parametrization(s) for which the magnitude of the axial parameter B k 0 of a 2 k ‐pole component, where k = 2, 4, 6, reaches a well–defined maximal value, max | B k 0 | ≤ $ \left [ {\sum \limits _{m}} \, | B_{km}|^2 \right ] ^{1/2} $ . This extreme constitutes a convenient discriminant of all these parametrizations, provided the B k 0 sign is recognized. Such discriminants, the same for all the equivalent parametrizations, distinguish the space directions which can be used as the z ‐axis of the common reference frame. A method of calculation of max | B k 0 | as well as the angles between the distinguished z ‐axes of the appropriately rotated reference frame for the individual crystal‐field multipoles is given. It allows to identify and explicitly verify the equivalence of the ℋ CF parametrizations, and in consequence, to perform their standardization. The proposed method concerns particularly triclinic crystal‐field potentials for which no other distinguished orientation of the reference frame seems to exist. A number of available crystal‐field parametrizations of the low‐symmetry crystal‐field potentials ( C 2 , C s ), obtained from fitting spectroscopic data, have been analyzed from the postulated discriminant point of view. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)