Crystal field spectra of d3,7 ions. VI. The weak field formalism and covalency

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.