Research Article
Stereochemistry of D, L-ribitol Iminocyclitols Between 4 and 2 Dimensions
Carmen-Irena Mitan*
,
Emerich Bartha
Issue:
Volume 14, Issue 5, October 2026
Pages:
142-151
Received:
8 September 2026
Accepted:
16 September 2026
Published:
29 September 2026
DOI:
10.11648/j.sjc.20261405.11
Downloads:
Views:
Abstract: The transformation from 4D to 3D and 2D exemplified recently with Lie algebra and Hopf fibration on cis, trans-ee, trans-aa stereochemistry, now is demonstrated with hypersphere trigonometric equations for calculation dihedral angles θHnHn+1 [deg] from carbon chemical shift δCn [ppm], then the vicinal angle ϕ [deg] and the other five possible dihedral angles θHnHn+1 [deg] for one known vicinal coupling constant 3JHnHn+1 [Hz]. Cis, trans-ee and trans-aa stereochemistry placed on six sets angles on two units have trans-ee4, 1 stereochemistry under 2D dimension on unit S and trans-ee3, 2 stereochemistry particularized with algebraic equations on unit U under 4D. Both trans-ee stereochemistry representing a great example for continuum transformation for hypersphere to torus. B2 root system θ = 150 [deg] as alternative model for building unit under Hopf fibration, along A2 root system θ = 120 [deg] unit will be disclosed, the second one ensuring also relationships between dihedral θHnHn+1[deg] and vicinal angles ϕ[deg]. Three pair of sets angles representative for five membered rings simulated for a vicinal coupling constant, sets A, B - dihedral and vicinal angles, set C used to build unit U2 with set A and B calculated with 3α + 2β, and pair of sets A and B of unit S1 calculated with 3α + 3β.
Abstract: The transformation from 4D to 3D and 2D exemplified recently with Lie algebra and Hopf fibration on cis, trans-ee, trans-aa stereochemistry, now is demonstrated with hypersphere trigonometric equations for calculation dihedral angles θHnHn+1 [deg] from carbon chemical shift δCn [ppm], then the vicinal angle ϕ [deg] and the other five possible dihed...
Show More
