Symmetry substructures for MQ-NMR of [A]20 spin clusters of dodecahedranes, [13CH]20 or [13CD]20, metallic M @M20 and [H2O]+ @[H2O]20 exo-cage cluster molecules and their higher-n SO(3) ×l n spin algebras, within the context of mapping,l n -ITP algebras and number partitions

Abstract

Atoms, Molecules~o " = , " and Clusters ~t PhysikD © Springer-Vertag 1993 Symmetry substructures for MQ-NMR of [A]zo spin clusters of dodecahedranes, 1 3CH]2o or 1 3CD]2o, metallic M @Mzo and [HzO] + @[H20]z o exo-cage cluster molecules and their higher-n SO(3)x 50. spin algebras, within the context of mapping, 6P,,-ITP algebras and number partitionsAbstract. For both higher n and Ii >_ 1 spin clusters, combinatorics provides powerful arguments with which to investigate the substructural forms of cluster spin algebras; this is especially so for SO(3)x 6e, symmetries for 12 < n < 60 where Z[!i I character tabulations become extensive. Bijective enumerative mappings over the combinatorial p-tuples (number partitions) afford insight into the general function tip, n) as well as into {IIM (I 1 -I,,) [2]) }M-structure of spin algebras, even where the full details of the explicit ZI~ E (~,) characters are not readily available. Both simply-reducible and higher aspects of Y,-inner tensor product (ITP) algebras are derived from dimensionality considerations, as part of combinatorial hooklength formalisms for Z[lXl).The Ii< 3/2 forms of [A],, clusters for n < 20, (for p < 3, 4) of multiple-quantum NMR (MQ-NMR) are considered here as part of current interest in giant cage-clusters. In addition, the SU2 substructural hierarchy over Liouville space is derived for [A]z0(Y20 ) (Ii= 1/2) spin cluster of the cagecluster molecule dodecahedrane; aspects of Iz=l spin cluster over {I/M(...))} space are derived as high temperature model of the exo-cage of [H20]+@[H20]20 cluster ion; 20-fold higher-I~ clusters provide models for M @M2o metal-clusters and further applications of Jzonumber partitions.