On a complementary scale of crystal-field strength

Abstract

A new measure of the crystal-field strength, complementary to the conventional one, is defined. It is based on the rotational invariants |B_{k0}|_{av} or |\sum_{k}B_{k0}|_{av}, k=2,4,6, of the crystal-(ligand)-field (CF) Hamiltonian H_{CF} parametrizations, i.e. on the axial CF parameters modules averaged over all reference frame orientations. They turn out to be equal to |H_{CF}^{(k)}|_{av} and |H_{CF}|_{av}, respectively. While the traditional measure is established on the parametrization modules or on the second moment of the CF energy levels, the introduced scale employs rather the first moment of the energy modules and has better resolving power. The new scale is able to differentiate the strength of various iso-modular parametrizations according to the classes of rotationally equivalent parametrizations. Using both the compatible CF strength measures one may draw more accurate conclusions about the Stark levels arrays and particularly their total splitting magnitudes.