3-Sphere, a hypersphere in 4 dimensions approach, applied for calculating stereochemical parameters of iminocyclitol 1 – 5 with Hopf fibration and Lie algebra is described. Three angles have been considered, ii.e./i dihedral θsubHnHn+1/sub deg – tetrahedral φsubCn/sub deg – phase angle of the pseudorotation P deg calculated from NMR data, vicinal coupling constant sup3/supiJ/isubHH/sub Hz and carbon chemical shift δsubC/sub ppm. This approach gave for 1-α-methyl-1,4-imino-1,4-dideoxy-D-ribitol 2 two conformers Esub3/sub and sup3/supTsub2/sub having different dihedral θsubHnHn+1/sub deg and tetrahedral φsubCn/sub deg angles with same vicinal angles ϕ deg. Notably, phase angle of pseudorotation P deg placed the conformations on the south side for D-ribitols 1 - 3 and on the north side for L-ribitol 4, excepting trifluoroacetate salt of L-ribitol 5. The wave character of NMR data introduced few homotopic switches, the transformation from torus to inverse of torus, the relationship between angles of set A and set B, the transformation from Planck constants h to h-bar, along with the transformation from Joule to Calorie (J 4.1868 ⇆ Jsup-1/sup 0.238). Two methods for calculation of tetrahedral angles φsubCn/sub deg, energy-graph and Euler conic with two ways for representing the angles, polyhedron and unit models are analyzed. The conformational parameters, phase angle of the pseudorotation P deg established with VISION molecular model and exocyclic 3-Sphere dihedral angles θsubHnHn+1/sub deg relative to endocyclic torsional angles θsubn,n/subsub+1/sub deg from Altona-Sundaralingan model have been evaluated. In addition, the corresponding angle of deviation from planarity θsubm/sub deg has been determined.
Mitan et al. (Mon,) studied this question.