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.
| Published in | Science Journal of Chemistry (Volume 14, Issue 5) |
| DOI | 10.11648/j.sjc.20261405.11 |
| Page(s) | 142-151 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2026. Published by Science Publishing Group |
Hypersphere Coordinates, Hopf Fibration, A2 Root System - Lie Algebra, B2 Root System - Hasic, Stereochemistry, Dihedral Angles
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APA Style
Mitan, C., Bartha, E. (2026). Stereochemistry of D, L-ribitol Iminocyclitols Between 4 and 2 Dimensions. Science Journal of Chemistry, 14(5), 142-151. https://doi.org/10.11648/j.sjc.20261405.11
ACS Style
Mitan, C.; Bartha, E. Stereochemistry of D, L-ribitol Iminocyclitols Between 4 and 2 Dimensions. Sci. J. Chem. 2026, 14(5), 142-151. doi: 10.11648/j.sjc.20261405.11
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Download@article{10.11648/j.sjc.20261405.11,
author = {Carmen-Irena Mitan and Emerich Bartha},
title = {Stereochemistry of D, L-ribitol Iminocyclitols Between 4 and 2 Dimensions},
journal = {Science Journal of Chemistry},
volume = {14},
number = {5},
pages = {142-151},
doi = {10.11648/j.sjc.20261405.11},
url = {https://doi.org/10.11648/j.sjc.20261405.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjc.20261405.11},
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.},
year = {2026}
}
TY - JOUR T1 - Stereochemistry of D, L-ribitol Iminocyclitols Between 4 and 2 Dimensions AU - Carmen-Irena Mitan AU - Emerich Bartha Y1 - 2026/09/29 PY - 2026 N1 - https://doi.org/10.11648/j.sjc.20261405.11 DO - 10.11648/j.sjc.20261405.11 T2 - Science Journal of Chemistry JF - Science Journal of Chemistry JO - Science Journal of Chemistry SP - 142 EP - 151 PB - Science Publishing Group SN - 2330-099X UR - https://doi.org/10.11648/j.sjc.20261405.11 AB - 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. VL - 14 IS - 5 ER -
Department of Organic Chemistry, Institute of Organic and Supramolecular Chemistry “Costin D. Nenitescu”, Bucharest, Romania
Department of Organic Chemistry, Institute of Organic and Supramolecular Chemistry “Costin D. Nenitescu”, Bucharest, Romania
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