Using the experimental energy levels of Gd3+ in six hexagonal crystals as a basis, we discuss modifications to the electrostatic-approximation crystal-field model caused by nonlinear shielding, nephelauxetic, and covalency-induced molecular orbital effects. The crystal-field fit improves when levels belonging to different irreducible representations (crystal quantum numbers) are fitted separately and when levels of different spectroscopic terms are fitted separately. Nephelauxetic and covalency effects are related for the same crystal structure and are strongly structure dependent. Nonlinear shielding and/or term-dependent configuration-interaction effects are shown to be important but not simply related to the host structure.
R. L. SCHWIESOW, "Departures from the Electrostatic Crystal-Field Model for Gd3+ in Six Hexagonal Crystals," J. Opt. Soc. Am. 62, 649-653 (1972)