D-orbital theory for an octahedral-site-symmetry crystal and pressure-induced spectral shifts in ruby.

Abstract

A d orbital for the transition-metal ion in an octahedral-site-symmetry crystal is proposed by considering the ligand-charge penetration. The expanded radial d-orbital wave function in the crystal is expressed as a function of the bond length. With this d orbital the nephelauxetic decrease of Racah parameters B, C, spin-orbit-coupling parameter ξ d , and their pressure-induced reductions can be described quantitatively with a simple point-charge model. The theory is applied to calculate the d-d transitions (R, R', Y, B, and U) in ruby and their pressure-induced shifts. The calculated results are in good agreement with experimental data