Conic projection as manifold enable calculation dihedral θsubHnHn+1/subdeg angles from differences between two atoms of carbon ΔδsubCnCn+1/subppm in three steps or from only one atom of carbon δsubCn/subppm in close relationships with tetrahedral φsubCn/subdeg angles under 3-Sphere approach. Hopf fibration and Lie algebra ensuring calculation dihedral θsubHnHn+1/subdeg angles from vicinal ϕdeg angle, angle results from vicinal coupling constant sup3/supiJ/isubHH/subHz. Real Hopf fibration for calculation dihedral θsubHnHn+1/subdeg angle in real space, and Rsup16/sup octonionic Hopf fibration, double of quaternionic Rsup7/sup, for all icis/i, itrans-ee/i, itrans-aa/i stereochemistry, unreal space relative to calculated dihedral θsubHnHn+1/subdeg angle. Continue “deformation”, homotopic behaviour h ⇆ hsup-1/sup characteristic for wave NMR data, probably a point of swich on Möbius band, in case of radius r of the cone inscribes on sphere at tangent point, calculated from height of cone h or inverse of height hsup-1/sup, the tan function of h is equal with sin function of hsup-1/sup. Dihedral θsubHnHn+1/subdeg and tetrahedral φsubCn/subdeg angles are from the trigonometric point of view under sin and tan function, or iviceversa/i, homotopic behavior of NMR data under conic projection demonstrating that. Because the dihedral θsubHnHn+1/subdeg angles are not found in first unit, for few vicinal coupling constants sup3/supiJ/isubHH/subHz, the rule accepted until now are explored taking in consideration other sets for building unit along the set C, respectively D, E and F, G, or vicinal angle ϕdeg with its three possible dihedral θsubHnHn+1/subdeg angles in close relationships with tetrahedral φsubCn/subdeg angles under seven sets unit. Building units through sets U or S calculated from isin/i or itan/i functions until calculated angles are almost equals with angles of unit Usub1/sub or Ssub1/sub, required long time for calculation.
Mitan et al. (Thu,) studied this question.