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d group-theoretical method is suggested for determining allowed type states of pairs and complexes of impurity ions in ionic crystals. Two cases are discussed in detail. In the first case the energy of the electrostatic interaction Vy,t between electrons of different impurity ions is greater than that of the internal magnetic interactions H F and in the second case VFnt is less than HF. For both cases V&t is assumed to be smaller than the total energy of the internal electrostatic interactions and the energies of a crystal field produced by the remaining ions of the crystal. As an example the I-V order pairs of the equivalent ions Cr3+ in corundum are examined.

The method of effective Hamiltonian (EFH) is applied to the excited state (2E4A2) fine structure of Cr3+–Cr3+ fourth order pairs in ruby. Comparison with experimental data illustrates the importance of both the anisotropic and antisymmetric exchange interactions, and that part of isotropic exchange interaction, which is nondiagonal in the orbital variables. Various microscopical mechanisms responsible for terms in the effective Hamiltonian are discussed.

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