Abstract
Current interest in spin relaxation arising from molecular reorientation in liquids or from quantum-rotational tunnelling of molecular spin-cluster ions in solids, within the framework of Liouville, or spin-spatial product, formalisms serves to highlight the value of the symmetric group and its subduced symmetries in understanding MQ-NMR and related fields, such as single-particle inelastic neutron scattering. Combinatorial generalized wordlengths, are realizations of Rota's view of Cayley algebra of bracketed fields defining scalar invariants of spin systems, and are used in conjuctions with invariance hierarchies under the simple and direct product group algebras to generate the partitional and Γ/ Γ (( S 7)↓D 5) structures associated with the Hilbert and Liouville MQ-NMR spin bases implicit in the [A] 7/[AX] 7 cluster problems. Realization of the irreps involves consideration of the combinatorics associated with higher primes and utilising the known inner tensor products of these higher S n groups. The results derived provide insight into the higher quantum aspects of the evolution and spin dynamics of model systems, such as IF 7 and the cage molecular ion [ 11BH] 7 2−; from such properties the density operators may be expanded over the partitions or subduced irreps which leads to partitioned forms for the matrix representation of the Liouville operator. The symmetry factoring may be coupled with selective q considerations thus allowing a subset of the full spin problem to yield the significant information content of a spin problem without the necessity to consider the higher dimensioned q or [ λ ] subspaces; a conceptual parallel with the motivation underlying some of the experimental MQ-NMR work originating from the Berkeley group may be discerned.
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