Crystal field spectra of d^3,7 ions. VI. The weak field formalism and covalency

Abstract

When the problem of an ion in a crystal field is solved using the unperturbed atomic wave functions as basis functions, the free ion energies appear explicitly in the diagonal terms of the secular determinant where they can be adjusted as experimental parameters. By fitting the observed crystal field energy levels in this scheme, a set of modified free ion energy levels can be derived for Dq = 0, and it is found that in most cases a single set of electrostatic repulsion parameters F₂ and F₄ describes the energies, provided a Trees correction is applied. The values of F₂ and F₄ obtained in this way from crystal spectra of Cr³⁺ in ruby, yttrium gallium garnet, other oxides, and K₃Cr(CN)₆ and of Co²⁺ in ZnAl₂O₄ are reduced by covalency from their free ion values. The reduction for P₂ is greater than for F₄ because of its greater sensitivity to the outer part of the radial distribution function, where covalency plays its major part. It is concluded that the differential expansion of the t₂ and e orbitals in the crystal field is not great, and that nephelauxetic effects in crystal field spectra should more properly be related to the F₂ and F₄ parameters of Condon and Shortley through the weak field formalism, rather than to Racah's B parameter in the strong field approach. The latter results in unsound conclusions about the effects of covalency. Analysis of the spectra of CrBrs and C0C14" suggests that the d electrons are not adequately described by two electrostatic repulsion parameters and the usual crystal field theory should be applied cautiously.