Abstract
A tensorial formalism adapted to the case of octahedral molecules or molecular ions with half-integer angular momenta is proposed as an extension of the usual formalism for the group chain O(3) ⊃ O h . We use the chain SU(2) ⊗ C I ⊃ O S h , where O S h is the octahedral group with its spinorial representations. Coupling coefficients (3 j − m, isoscalar factors, etc.) and formulas for the computation of matrix elements of tensor operators are derived for this chain. A deduction of coupling coefficients (3 C − σ, 6 C, .) and similar formulas is proposed for the non-simply reducible group O S itself.
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