Topology on Nature: Isomerization of Five Membered Ring Tetrahedral Angles

Carmen-Irena Mitan; Emerich Bartha; Petru Filip

doi:doi:10.11648/j.sjc.20231104.12

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Topology on Nature: Isomerization of Five Membered Ring Tetrahedral Angles

Carmen-Irena Mitan, Emerich Bartha, Petru Filip

Published in Science Journal of Chemistry (Volume 11, Issue 4)

Received: 22 June 2023 Accepted: 8 July 2023 Published: 21 July 2023

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Abstract

Tetrahedral angles of five membered ring are disclosed from the polyhedron geometry point of view, dodecahedron and icosahedron geometry under Fibonacci number. The number of carbons on carbasugar follows the Fibonacci sequence, each carbon is placed at 0.618034 per turn (222.5[deg]). The Fibonacci golden angle 137.5[deg] with its 0.382 turns is approximately equals with Sunflower (Ferment’s spiral – golden angle 136.18[deg]), icosahedron (138.16[deg]), or icositetrahedron (136.18[deg]). In case of five membered ring iminocyclitols are established four equations 18-21 for calculation the isomers of tetrahedral angles φ_Cn[deg] under Fibonacci approach. As demonstrate by Aston et al in 1941 and confirmed by Pitzer in 1945, the cyclopentene conformation is puckered and the deformation is not static is dynamic, with the puckering displacements progressing pseudorotation. In case of five membered ring iminocyclitols with α-D ribitol (1-5) and β-L ribitol (6-8) stereochemistry the wave character of the NMR data on 3-sphere approach – Hopf fibration versus Lie algebra – point out the existence of the pseudorotation through the values of tetrahedral angles φ_Cn[deg] around the five membered ring in close relationships with dihedral angles θ_HnHn+1[deg] and vicinal angles ϕ[deg], angles result from vicinal coupling constant ³J_HnHn+1[Hz]. Hűckel theories under Hopf fibration and polyhedron geometry confirming the existence of tetrahedral angles able to fluctuate around the ring. The Fibonacci approach highlighting the existence of the pseudorotation through three characteristics number: 1.6, 1.9, 1.5 calculated from carbon chemical shift δ_Cn[ppm] with equations 18-21. The main question, is that only a problem of geometry? or with some exception three indubitable isomers must be considered responsible for puckered five membered ring structure on its pseudo rotational itinerary. If you are exciting about this question follow the demonstration about the implication of topology on nature.

Published in	Science Journal of Chemistry (Volume 11, Issue 4)
DOI	10.11648/j.sjc.20231104.12
Page(s)	146-154
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), 2024. Published by Science Publishing Group

Keywords

Tetrahedral Angle, Isomerization, Pseudorotation, Fibonacci Number, Golden Ratio, Golden Triangle, Polyhedron Geometry, 3-Sphere

References

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Carmen-Irena Mitan, Emerich Bartha, Petru Filip. (2023). Topology on Nature: Isomerization of Five Membered Ring Tetrahedral Angles. Science Journal of Chemistry, 11(4), 146-154. https://doi.org/10.11648/j.sjc.20231104.12

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ACS Style

Carmen-Irena Mitan; Emerich Bartha; Petru Filip. Topology on Nature: Isomerization of Five Membered Ring Tetrahedral Angles. Sci. J. Chem. 2023, 11(4), 146-154. doi: 10.11648/j.sjc.20231104.12

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AMA Style

Carmen-Irena Mitan, Emerich Bartha, Petru Filip. Topology on Nature: Isomerization of Five Membered Ring Tetrahedral Angles. Sci J Chem. 2023;11(4):146-154. doi: 10.11648/j.sjc.20231104.12

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@article{10.11648/j.sjc.20231104.12,
  author = {Carmen-Irena Mitan and Emerich Bartha and Petru Filip},
  title = {Topology on Nature: Isomerization of Five Membered Ring Tetrahedral Angles},
  journal = {Science Journal of Chemistry},
  volume = {11},
  number = {4},
  pages = {146-154},
  doi = {10.11648/j.sjc.20231104.12},
  url = {https://doi.org/10.11648/j.sjc.20231104.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjc.20231104.12},
  abstract = {Tetrahedral angles of five membered ring are disclosed from the polyhedron geometry point of view, dodecahedron and icosahedron geometry under Fibonacci number. The number of carbons on carbasugar follows the Fibonacci sequence, each carbon is placed at 0.618034 per turn (222.5[deg]). The Fibonacci golden angle 137.5[deg] with its 0.382 turns is approximately equals with Sunflower (Ferment’s spiral – golden angle 136.18[deg]), icosahedron (138.16[deg]), or icositetrahedron (136.18[deg]). In case of five membered ring iminocyclitols are established four equations 18-21 for calculation the isomers of tetrahedral angles φCn[deg] under Fibonacci approach. As demonstrate by Aston et al in 1941 and confirmed by Pitzer in 1945, the cyclopentene conformation is puckered and the deformation is not static is dynamic, with the puckering displacements progressing pseudorotation. In case of five membered ring iminocyclitols with α-D ribitol (1-5) and β-L ribitol (6-8) stereochemistry the wave character of the NMR data on 3-sphere approach – Hopf fibration versus Lie algebra – point out the existence of the pseudorotation through the values of tetrahedral angles φCn[deg] around the five membered ring in close relationships with dihedral angles θHnHn+1[deg] and vicinal angles ϕ[deg], angles result from vicinal coupling constant 3JHnHn+1[Hz]. Hűckel theories under Hopf fibration and polyhedron geometry confirming the existence of tetrahedral angles able to fluctuate around the ring. The Fibonacci approach highlighting the existence of the pseudorotation through three characteristics number: 1.6, 1.9, 1.5 calculated from carbon chemical shift δCn[ppm] with equations 18-21. The main question, is that only a problem of geometry? or with some exception three indubitable isomers must be considered responsible for puckered five membered ring structure on its pseudo rotational itinerary. If you are exciting about this question follow the demonstration about the implication of topology on nature.},
 year = {2023}
}

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TY  - JOUR
T1  - Topology on Nature: Isomerization of Five Membered Ring Tetrahedral Angles
AU  - Carmen-Irena Mitan
AU  - Emerich Bartha
AU  - Petru Filip
Y1  - 2023/07/21
PY  - 2023
N1  - https://doi.org/10.11648/j.sjc.20231104.12
DO  - 10.11648/j.sjc.20231104.12
T2  - Science Journal of Chemistry
JF  - Science Journal of Chemistry
JO  - Science Journal of Chemistry
SP  - 146
EP  - 154
PB  - Science Publishing Group
SN  - 2330-099X
UR  - https://doi.org/10.11648/j.sjc.20231104.12
AB  - Tetrahedral angles of five membered ring are disclosed from the polyhedron geometry point of view, dodecahedron and icosahedron geometry under Fibonacci number. The number of carbons on carbasugar follows the Fibonacci sequence, each carbon is placed at 0.618034 per turn (222.5[deg]). The Fibonacci golden angle 137.5[deg] with its 0.382 turns is approximately equals with Sunflower (Ferment’s spiral – golden angle 136.18[deg]), icosahedron (138.16[deg]), or icositetrahedron (136.18[deg]). In case of five membered ring iminocyclitols are established four equations 18-21 for calculation the isomers of tetrahedral angles φCn[deg] under Fibonacci approach. As demonstrate by Aston et al in 1941 and confirmed by Pitzer in 1945, the cyclopentene conformation is puckered and the deformation is not static is dynamic, with the puckering displacements progressing pseudorotation. In case of five membered ring iminocyclitols with α-D ribitol (1-5) and β-L ribitol (6-8) stereochemistry the wave character of the NMR data on 3-sphere approach – Hopf fibration versus Lie algebra – point out the existence of the pseudorotation through the values of tetrahedral angles φCn[deg] around the five membered ring in close relationships with dihedral angles θHnHn+1[deg] and vicinal angles ϕ[deg], angles result from vicinal coupling constant 3JHnHn+1[Hz]. Hűckel theories under Hopf fibration and polyhedron geometry confirming the existence of tetrahedral angles able to fluctuate around the ring. The Fibonacci approach highlighting the existence of the pseudorotation through three characteristics number: 1.6, 1.9, 1.5 calculated from carbon chemical shift δCn[ppm] with equations 18-21. The main question, is that only a problem of geometry? or with some exception three indubitable isomers must be considered responsible for puckered five membered ring structure on its pseudo rotational itinerary. If you are exciting about this question follow the demonstration about the implication of topology on nature.
VL  - 11
IS  - 4
ER  -

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Author Information

Carmen-Irena Mitan

Organic Chemistry, Institute of Organic and Supramolecular Chemistry, Bucharest, Roumania
Emerich Bartha

Organic Chemistry, Institute of Organic and Supramolecular Chemistry, Bucharest, Roumania
Petru Filip

Organic Chemistry, Institute of Organic and Supramolecular Chemistry, Bucharest, Roumania

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APA Style

Carmen-Irena Mitan, Emerich Bartha, Petru Filip. (2023). Topology on Nature: Isomerization of Five Membered Ring Tetrahedral Angles. Science Journal of Chemistry, 11(4), 146-154. https://doi.org/10.11648/j.sjc.20231104.12

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ACS Style

Carmen-Irena Mitan; Emerich Bartha; Petru Filip. Topology on Nature: Isomerization of Five Membered Ring Tetrahedral Angles. Sci. J. Chem. 2023, 11(4), 146-154. doi: 10.11648/j.sjc.20231104.12

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AMA Style

Carmen-Irena Mitan, Emerich Bartha, Petru Filip. Topology on Nature: Isomerization of Five Membered Ring Tetrahedral Angles. Sci J Chem. 2023;11(4):146-154. doi: 10.11648/j.sjc.20231104.12

Copy | Download

@article{10.11648/j.sjc.20231104.12,
  author = {Carmen-Irena Mitan and Emerich Bartha and Petru Filip},
  title = {Topology on Nature: Isomerization of Five Membered Ring Tetrahedral Angles},
  journal = {Science Journal of Chemistry},
  volume = {11},
  number = {4},
  pages = {146-154},
  doi = {10.11648/j.sjc.20231104.12},
  url = {https://doi.org/10.11648/j.sjc.20231104.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjc.20231104.12},
  abstract = {Tetrahedral angles of five membered ring are disclosed from the polyhedron geometry point of view, dodecahedron and icosahedron geometry under Fibonacci number. The number of carbons on carbasugar follows the Fibonacci sequence, each carbon is placed at 0.618034 per turn (222.5[deg]). The Fibonacci golden angle 137.5[deg] with its 0.382 turns is approximately equals with Sunflower (Ferment’s spiral – golden angle 136.18[deg]), icosahedron (138.16[deg]), or icositetrahedron (136.18[deg]). In case of five membered ring iminocyclitols are established four equations 18-21 for calculation the isomers of tetrahedral angles φCn[deg] under Fibonacci approach. As demonstrate by Aston et al in 1941 and confirmed by Pitzer in 1945, the cyclopentene conformation is puckered and the deformation is not static is dynamic, with the puckering displacements progressing pseudorotation. In case of five membered ring iminocyclitols with α-D ribitol (1-5) and β-L ribitol (6-8) stereochemistry the wave character of the NMR data on 3-sphere approach – Hopf fibration versus Lie algebra – point out the existence of the pseudorotation through the values of tetrahedral angles φCn[deg] around the five membered ring in close relationships with dihedral angles θHnHn+1[deg] and vicinal angles ϕ[deg], angles result from vicinal coupling constant 3JHnHn+1[Hz]. Hűckel theories under Hopf fibration and polyhedron geometry confirming the existence of tetrahedral angles able to fluctuate around the ring. The Fibonacci approach highlighting the existence of the pseudorotation through three characteristics number: 1.6, 1.9, 1.5 calculated from carbon chemical shift δCn[ppm] with equations 18-21. The main question, is that only a problem of geometry? or with some exception three indubitable isomers must be considered responsible for puckered five membered ring structure on its pseudo rotational itinerary. If you are exciting about this question follow the demonstration about the implication of topology on nature.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Topology on Nature: Isomerization of Five Membered Ring Tetrahedral Angles
AU  - Carmen-Irena Mitan
AU  - Emerich Bartha
AU  - Petru Filip
Y1  - 2023/07/21
PY  - 2023
N1  - https://doi.org/10.11648/j.sjc.20231104.12
DO  - 10.11648/j.sjc.20231104.12
T2  - Science Journal of Chemistry
JF  - Science Journal of Chemistry
JO  - Science Journal of Chemistry
SP  - 146
EP  - 154
PB  - Science Publishing Group
SN  - 2330-099X
UR  - https://doi.org/10.11648/j.sjc.20231104.12
AB  - Tetrahedral angles of five membered ring are disclosed from the polyhedron geometry point of view, dodecahedron and icosahedron geometry under Fibonacci number. The number of carbons on carbasugar follows the Fibonacci sequence, each carbon is placed at 0.618034 per turn (222.5[deg]). The Fibonacci golden angle 137.5[deg] with its 0.382 turns is approximately equals with Sunflower (Ferment’s spiral – golden angle 136.18[deg]), icosahedron (138.16[deg]), or icositetrahedron (136.18[deg]). In case of five membered ring iminocyclitols are established four equations 18-21 for calculation the isomers of tetrahedral angles φCn[deg] under Fibonacci approach. As demonstrate by Aston et al in 1941 and confirmed by Pitzer in 1945, the cyclopentene conformation is puckered and the deformation is not static is dynamic, with the puckering displacements progressing pseudorotation. In case of five membered ring iminocyclitols with α-D ribitol (1-5) and β-L ribitol (6-8) stereochemistry the wave character of the NMR data on 3-sphere approach – Hopf fibration versus Lie algebra – point out the existence of the pseudorotation through the values of tetrahedral angles φCn[deg] around the five membered ring in close relationships with dihedral angles θHnHn+1[deg] and vicinal angles ϕ[deg], angles result from vicinal coupling constant 3JHnHn+1[Hz]. Hűckel theories under Hopf fibration and polyhedron geometry confirming the existence of tetrahedral angles able to fluctuate around the ring. The Fibonacci approach highlighting the existence of the pseudorotation through three characteristics number: 1.6, 1.9, 1.5 calculated from carbon chemical shift δCn[ppm] with equations 18-21. The main question, is that only a problem of geometry? or with some exception three indubitable isomers must be considered responsible for puckered five membered ring structure on its pseudo rotational itinerary. If you are exciting about this question follow the demonstration about the implication of topology on nature.
VL  - 11
IS  - 4
ER  -

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