The coupled representation matrix of the pair hamiltonian

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Abstract
A complete treatment of the spin hamiltonian for a pair of exchange coupled metal ions is given. The results obtained through the use of the Wigner-Eckart theorem are unrestricted with respect to the relative orientation of the single-ion tensors, and appropriate for both the S 1 = S 2 and S 1 ≠ S 2 cases. The necessary constants are derived so that matrix elements within a given spin multiplet can be treated by ordinary operator algebra with the coupled representation state vectors, |SM>, as a basis set. Explicit algebraic formulae for matrix elements between spin multiplets are presented for the first time. Symmetry restrictions are discussed in general and illustrated for the simple case of two ions related by an inversion centre, pair symmetry Ci .