3-Angles Under 3-Sphere Approach for Conformational Analysis of 2,6-Dideoxy-2,6-Imino-D-Talonic Acid

Relationships between vicinal ϕ - dihedral θ HnHn+1 - tetrahedral φ Cn angles [deg] under Hopf fibration and Lie algebra theories enable conformational analysis with VISION molecular models on conformational routes that might be followed by six membered ring, i.e. 4 C 1 : 0 H5, 0 H 1 , 2 H 1 , 2 H 3 , 4 H 3 , 4 H 5 , 0 S 2 , 3,0 B, 3 S 1 , B 1,4 , 5 S 1 , 2,5 B, 2 S 0 , B 3,0 , 1 S 3 , 1,4 B, 1 S 5 , B 2,5 of 2,6-dideoxy-2,6-imino-D-talonic acid 1D. Six dihedral angles with cis -, trans-ee , trans-aa stereochemistry calculated from only one vicinal coupling constant 3 J HH [Hz] and torus and invers of torus equations , represented on 3-Sphere, a hypersphere in 4D, are restricted by the stereochemistry of sugar, by the combination of dihedral angles along its shape, tetrahedral angles and at list by the distorted boat B or skew S of relaxed 4 C 1 or 1 C 4 chair conformations. Dihedral angles at anomeric position calculated from vicinal coupling constant are compared with angles calculated from carbon chemical shift with Euler - Conic manifold. On VISION molecular models are simulated first two conformations B 0,3 and B 0,3 as etalon, followed by introduction the calculated exocyclic dihedral angles: 1. from dihedral angles calculated only from vicinal coupling constant 3 J HH [Hz]: S 1 3 (B 0,3) , and B 0,3 (S 2 0 ), S 3 1 ; 2. or from carbon chemical shift δ[ppm] and vicinal coupling constant 3 J HH [Hz]: S 1 3 , B 0,3 , S 2 0 and S 3 1 .