3-Spherical Conformational Insights into Iminocyclitols with 1-α-D-Ribose and 1-β-L-Ribose Stereochemistry Under Homotopic Behaviour of Nuclear Magnetic Resonance Data

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, <i>i.e.</i> dihedral θ<sub>HnHn+1</sub> [deg] – tetrahedral φ<sub>Cn</sub> [deg] – phase angle of the pseudorotation P [deg] calculated from NMR data, vicinal coupling constant <sup>3</sup><i>J</i><sub>HH</sub> [Hz] and carbon chemical shift δ<sub>C</sub> [ppm]. This approach gave for 1-α-methyl-1,4-imino-1,4-dideoxy-D-ribitol 2 two conformers E<sub>3</sub> and <sup>3</sup>T<sub>2</sub> having different dihedral θ<sub>HnHn+1</sub> [deg] and tetrahedral φ<sub>Cn</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 ⇆ J<sup>-1</sup> 0.238). Two methods for calculation of tetrahedral angles φ<sub>Cn</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 θ<sub>HnHn+1</sub> [deg] relative to endocyclic torsional angles θ<sub>n,n</sub><sub>+1</sub> [deg] from Altona-Sundaralingan model have been evaluated. In addition, the corresponding angle of deviation from planarity θ<sub>m</sub> [deg] has been determined.