Forms of crystal field Hamiltonians – A critical review

Our survey reveals that various disparate forms, both compact and expanded ones, of crystal field (CF) Hamiltonians, HCF, expressed in the Wybourne notation have been used in the literature. It turns out that the disparities in the symbolic explicit forms of HCF are especially important for monoclinic and triclinic site symmetry. The extent of the inconsistencies identified in selected papers has prompted us to embark on a systematic critical review of the HCF forms employed in optical spectroscopy and related areas. Most crucial results of this survey are presented here. Comparative analysis has been carried out to establish the interrelations between CF parameters (CFPs) expressed in disparate forms. The usage of inconsistent or confusing HCF forms has implications also for CFP conversions between the Stevens and Wybourne notations as well as for theoretical modeling of CFPs. This review reveals that comparison of CFP data taken from various sources should be carried out with special care, especially for low symmetry cases.

Research highlights
► Inconsistent sequence of operators in crystal field Hamiltonians [CFHs] is identified.
► This affects signs of some low-symmetry CF parameters [CFPs].
► Comparison of CFPs should be carried out with special care.
► Conventions on the forms of CFHs and CFP notations should be adopted.