We outline double coset and restricted character cycle index methods which generate the equivalence classes of NMR spin functions and the irreducible representations in the representation spanned by spin functions in any equivalence class. Elegant operator methods are developed by which the projection operators of NMR groups can be obtained in terms of the projection operators of composing groups. Thus, the projection operators of NMR groups of many molecules can be obtained without the knowledge of their character tables. Projection operators thus obtained are applied on the set of spin functions in an equivalence class of NMR spin functions (rather than the whole set of spin functions) which are generated by double coset methods to obtain symmetryhyphen;adapted NMR spin functions in the composite particle representation. Methods are illustrated with several examples of molecules containing as many as 230NMR spin functions. The methods developed here are quite general so that they can be applied to NMR of nuclei with multispin states and they do not require the character tables of NMR groups. The techniques outlined here are illustrated with 2, 2, 3, 3hyphen;tetramethyl butane for which the symmetryhyphen;adapted NMR spin couplings are obtained in the composite particle representation. The NMR Hamiltonian matrix of this molecule which is of order 218times;218is factored into 26times;26matrix by the composite particle treatment. This is further factored into 8 1times;1 matrices and 6 4times;4, 4 2times;2, and 3 8times;8 matrices in the symmetryhyphen;adapted basis.
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