Can the low symmetry crystal (ligand) field parameters be considered compatible and reliable

摘要: Abstract This paper stems from our recent efforts to clarify the inconsistencies between crystal-field parameter (CFP) data sets reported in literature for various low symmetry transition ion–host systems. Prompted by results of these studies, this we consider intricate properties CF Hamiltonians, hitherto not fully understood. The term ‘low symmetry’ here includes continuous rotational cases, i.e. hexagonal II, tetragonal trigonal monoclinic, and triclinic ones, as well orthorhombic ones. following fundamental aspects are considered: (1) selection axis systems, (2) types CFPs their properties, (3) introduction a new notion nominal system fitted CFP sets, (4) implications Noether's theorem algebraic (5) correlation among (6) degrees freedom reduction number independent CFPs, which special importance (7) extension multiple correlated fitting technique, including quantitative method comparison. Clarification enables us provide general framework aimed at achieving an increased compatibility reliability ions sites crystals. may be especially useful trivalent lanthanides technologically important hosts only limited energy-level available.