The theory of coupled Cr3+pairs of D3hsymmetry

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Abstract
In order to interpret the optical spectra of Cs3Cr2Cl9, (I.W. Johnston et al., ibid., vol.14, p.1297, 1981), it has been necessary to develop a theory suitable for describing pairs of Cr3+ ions which have D3h symmetry. The pair is regarded as rather like a rigid molecule. The theory begins with a very general Hamiltonian and then derives an effective Hamiltonian, the eigenvalues of which give the energy levels in a restricted energy range (the region of the 2T1 levels of isolated Cr3+). The intention has been to concentrate on features which should help in characterising the observed spectra and it is shown that there are no splittings, such as might be anticipated on crystal-field arguments, nor are there any first-order spin-orbit splittings. Also, certain interval relations are obtained and it is shown that approximately spin-only Zeeman splittings should be found for some of the levels.