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Abstract
An improvement of ligand-field theory has been developed. Based on our theory of pressure-induced shifts and the diagonalization of the complete energy matrix, the unified calculation of the whole energy spectrum and $g$ factors of the ground state at normal pressure and their pressure-induced shifts has been carried out. All the calculated results for $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}{:\mathrm{V}}^{3+}$ are in very good agreement with a great number of experimental data. It is found that the distinct differences in magnitude and/or sign for pressure-induced shifts of various levels are immediately determined by characteristic dependencies of levels on the parameters of interactions, and the pressure-induced shifts of levels can provide definite or crucial criteria for the correctness of assignments and calculations of them.
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