Eur. Phys. J. B 11, 177-185 (1999)
https://doi.org/10.1007/s100510050927

Group-embeddings for NMR spin dual symmetries, to λ_SA|-Π: Determinate [¹⁰BH]^2-₁₂ (SU(m≤12)xS₁₂↓I) natural subduction via symbolic S_n combinatorial generators: Complete sets of bijective maps, CNP-weights

Mathematical Chemistry and Theory Group, Department of Chemistry, Queen's University, Kingston-ON, Canada, K7L 3N6

Corresponding author: ^a Temmef@chem.queensu.ca

Received: 4 December 1998
Published online: 15 September 1999

Abstract

Modelling of the properties of high-spin isotopomers, as polyhedra- on-lattice-points which yield various symbolic-computational -encodings of nuclear permutation (upto some specific SU(m) branching level), is important in deriving the spin-ensemble weightings of clusters, or cage-molecules. The mathematical determinacies of these, obtained here for higher m-valued SU group embeddings, are compared with that of an established group embedding, in order to collate the spin physics of with that for -analogue. The most symmetrical form of anion provides a pertinent example of the physics discussed in [CITE]. Retention of determinacy in the two cases is correlated to the completeness of the 1:1 bijective maps for natural embeddings of automorphic dual group NMR spin symmetries. The Kostka transformational coefficients of a suitable model ( module, Schur fn.) play a important role. Our findings demonstrate that determinacy persists (to branching levels) more readily for embeddings derived from (automorphic) finite groups dominated by odd-permutational class algebras, such as the above , or the case discussed in [16a,15,3d], compared to other examples -(e.g. as respectively, in press, and in [17b]): , . Generality of the symbolic algorithmic difference approach is stressed throughout and the corresponding dodecahedral maps are outlined briefly -for the wider applicability of SF-difference mappings, or of comparable -symbolic methods, (e.g.) via [CITE].