The standardization idea previously applied for an orthorhombic Hamiltonian is now extended to the monoclinic crystal-field Hamiltonian (HCF). Relations are given which allow for transformations of the three admissible forms of monoclinic HCF between themselves to achieve the ratio of B22/B02 confined to the standard range (0,±1). Thereby correlations between the apparently different crystal-field parameter (CFP) sets of various authors can be established. Algebraic symmetry of the characteristic equation of HCF for monoclinic C2, C1h(Cs), and C2h symmetry is considered by the method proposed earlier using altran. Magnitudes, signs, and/or relative signs of the CF parameters which can be determined from fitting the optical spectra of fn ions at sites of the above symmetry are established for the reduced approach (with one [B−qk]=0). Some misinterpretations on the complete approach, which yields ambiguous and unreliable results in general, as well as on the approximated approach are clarified. An extensive survey has revealed several cases of usage of the inappropriate complete approach. Based on the theoretical considerations a multipole correlated fitting technique has been proposed. The results of this paper are expected to greatly facilitate fitting of the optical spectra of fn ions as well as dn ions at sites of low symmetry.

The idea that the ratio E/D ≡ λ can be confined by a proper choice of the axis system to the range (0,±1/3) serves as a basis for the standardization of the spin Hamiltonian and the ligand field Hamiltonian for orthorhombic symmetry. Due to recent results on the transformation of the Stevens operators Oqk, relations are given which allow for extension of the standardization to the spin Hamiltonian for paramagnetic centers with spin S≥2. Several EPR studies of 3dn and 4 f n ions in crystals are reconsidered. The results prove the usefulness of the clear choice of the parameters Bqk suggested by the standardization idea. Application of the standardization in the area of the ligand field theory, which seems rather novel, is also considered. Crystal-field parameters for several rare earth ions in garnets are recalculated. An arbitrary choice from among the equivalent sets of the crystal-field parameters used in the review by Morrison and Leavitt (1982) should be replaced by a transformation to the ‘‘standard’’ set.

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