3-Sphere Torsional Angles and Six Membered Ring Conformation

Emerich Bartha; Carmen-Irena Mitan; Petru Filip

doi:doi:10.11648/j.ajqcms.20230701.12

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3-Sphere Torsional Angles and Six Membered Ring Conformation

Emerich Bartha, Carmen-Irena Mitan, Petru Filip

Published in American Journal of Quantum Chemistry and Molecular Spectroscopy (Volume 7, Issue 1)

Received: 16 March 2023 Accepted: 4 April 2023 Published: 24 April 2023

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Abstract

The conformation of six membered ring, 1,3,4-tri-o-acetyl-2-azido-6-bromo-2,6-dideoxy-D-galactose α-1 and β-1, and 2,6-dideoxy-2,6-imino- D-talonic acid 2D and L-talonic acid 2L, is analyzed inscribing two five membered ring on six membered ring. Altona’s five membered ring conformational parameters, phase angles of the pseudorotation P₁, P₂ [deg] and angle of deviation from planarity θ_m [deg] = f(P [deg]), are calculated with Java Script program using 3-Sphere torsional angles. The correlation between Altona map and six membered ring Stoddart’s diagram conformations was confirmed with VISION molecular models. 3-Sphere torsional angles θ_nn+1 [deg] for all cis, trans-ee, -aa stereochemistry are disclosed from trigonometric point of view, Hopf fibration confirmed by Lie algebra. The cis, trans stereochemistry on two units with six sets angles ensure relationships between dihedral θ_HnHn+1 [deg]/vicinal angles ϕ [deg] (θ^Bn + A = θ^An, θ^An = θ_HnHn+1, θ^Bn = ϕ), and between dihedral θ_HnHn+1 [deg]/torsional angles θ_nn+1 [deg] (θ_nn+1 = A +/- θ_HnHn+1); in first case A = 150 for trans-aa^6,1 and A = 90 for trans-aa^5,2 and trans-ee stereochemistry, in last case A = 180 [deg] for cis and trans-aa stereochemistry and A = 120 [deg] for trans-ee stereochemistry. The number of dihedral angles with positive and negative sign results from 3-sphere approach for only one vicinal coupling constant ³J_HnHn+1 [Hz] are restricted by the VISION molecular models.

Published in	American Journal of Quantum Chemistry and Molecular Spectroscopy (Volume 7, Issue 1)
DOI	10.11648/j.ajqcms.20230701.12
Page(s)	9-15
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

3-Sphere, Hopf Fibration, Lie Algebra, 6 Membered Ring Conformation, Altona Map, Stoddart’s Diagrams, Carbasugar

References

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[2]	A. Navarro-Vazquez, J. C. Cobas, F. J. Sardina, A graphical tool for the prediction of vicinal proton-proton 3JHH coupling constants, J. Chem. Inf. Comput. Sci. 2004, 44, 1690; doi.10.1021/ci049913f.
[3]	E. Bartha, C.-I. Mitan, C. Draghici, M. T. Caproiu, P. Filip, R. Moriarty, Program for prediction dihedral angle from vicinal coupling constant with 3-sphere approach, Rev. Roum. Chim. 2021, 66, 178-183; DOI: 10.33224/rrch.2021.66.2.08 (Eng).
[4]	C.-I. Mitan, E. Bartha, P. Filip, C. Draghici, M. T. Caproiu, R. M. Moriarty, Two isomers with trans-aa5,2 stereochemistry are calculated with 3-sphere trigonometric equations approach at circle inversion motion from NMR data. ACS National Meeting in Chicago, IL, August 21- 25, 2022, CARB 3717658, 22 august 2022; doi.org/10.1021/scimeetings.2c00523.
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[10]	C.-I. Mitan, E. Bartha, P. Filip, C. Draghici, M. T. Caproiu, R. M. Moriarty, NMR data on conformational analysis of five and six membered ring under 3-sphere approach. Vicinal constant coupling 3JHH on relationships between dihedral angles and tetrahedral angles. “Sustainability in a changing world” ACS National Meeting in Chicago, IL, August 21- 25, 2022, CARB 3717557, 22 august 2022; doi.org/10.1021/scimeetings.2c00876.
[11]	X. Biarnés, A. Ardeval, A. Planas, C. Rovira, A. Laio, M. Parrinello, The conformational free energy landscape of β-glucopyranose. Implications for substrate preactivation in β-glucoside hydrolases, J. Am. Chem. Soc. 2007, 129, 10686; Doi: 10.1021/ja068411a.
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[18]	C.-I. Mitan, E. Bartha, P. Filip, C. Draghici, M. T. Caproiu, R. M. Moriarty, Dihedral angles calculated with 3-sphere approach as integer in conformational analysis on D-, L- ribitol series, Rev. Roum. Chim. 2022, 66 (21), 941, DOI: 10.33224/rrch.2021.66.12.07 (Eng).
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APA Style

Emerich Bartha, Carmen-Irena Mitan, Petru Filip. (2023). 3-Sphere Torsional Angles and Six Membered Ring Conformation. American Journal of Quantum Chemistry and Molecular Spectroscopy, 7(1), 9-15. https://doi.org/10.11648/j.ajqcms.20230701.12

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ACS Style

Emerich Bartha; Carmen-Irena Mitan; Petru Filip. 3-Sphere Torsional Angles and Six Membered Ring Conformation. Am. J. Quantum Chem. Mol. Spectrosc. 2023, 7(1), 9-15. doi: 10.11648/j.ajqcms.20230701.12

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AMA Style

Emerich Bartha, Carmen-Irena Mitan, Petru Filip. 3-Sphere Torsional Angles and Six Membered Ring Conformation. Am J Quantum Chem Mol Spectrosc. 2023;7(1):9-15. doi: 10.11648/j.ajqcms.20230701.12

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@article{10.11648/j.ajqcms.20230701.12,
  author = {Emerich Bartha and Carmen-Irena Mitan and Petru Filip},
  title = {3-Sphere Torsional Angles and Six Membered Ring Conformation},
  journal = {American Journal of Quantum Chemistry and Molecular Spectroscopy},
  volume = {7},
  number = {1},
  pages = {9-15},
  doi = {10.11648/j.ajqcms.20230701.12},
  url = {https://doi.org/10.11648/j.ajqcms.20230701.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajqcms.20230701.12},
  abstract = {The conformation of six membered ring, 1,3,4-tri-o-acetyl-2-azido-6-bromo-2,6-dideoxy-D-galactose α-1 and β-1, and 2,6-dideoxy-2,6-imino- D-talonic acid 2D and L-talonic acid 2L, is analyzed inscribing two five membered ring on six membered ring. Altona’s five membered ring conformational parameters, phase angles of the pseudorotation P1, P2 [deg] and angle of deviation from planarity θm [deg] = f(P [deg]), are calculated with Java Script program using 3-Sphere torsional angles. The correlation between Altona map and six membered ring Stoddart’s diagram conformations was confirmed with VISION molecular models. 3-Sphere torsional angles θnn+1 [deg] for all cis, trans-ee, -aa stereochemistry are disclosed from trigonometric point of view, Hopf fibration confirmed by Lie algebra. The cis, trans stereochemistry on two units with six sets angles ensure relationships between dihedral θHnHn+1 [deg]/vicinal angles ϕ [deg] (θBn + A = θAn, θAn = θHnHn+1, θBn = ϕ), and between dihedral θHnHn+1 [deg]/torsional angles θnn+1 [deg] (θnn+1 = A +/- θHnHn+1); in first case A = 150 for trans-aa6,1 and A = 90 for trans-aa5,2 and trans-ee stereochemistry, in last case A = 180 [deg] for cis and trans-aa stereochemistry and A = 120 [deg] for trans-ee stereochemistry. The number of dihedral angles with positive and negative sign results from 3-sphere approach for only one vicinal coupling constant 3JHnHn+1 [Hz] are restricted by the VISION molecular models.},
 year = {2023}
}

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TY  - JOUR
T1  - 3-Sphere Torsional Angles and Six Membered Ring Conformation
AU  - Emerich Bartha
AU  - Carmen-Irena Mitan
AU  - Petru Filip
Y1  - 2023/04/24
PY  - 2023
N1  - https://doi.org/10.11648/j.ajqcms.20230701.12
DO  - 10.11648/j.ajqcms.20230701.12
T2  - American Journal of Quantum Chemistry and Molecular Spectroscopy
JF  - American Journal of Quantum Chemistry and Molecular Spectroscopy
JO  - American Journal of Quantum Chemistry and Molecular Spectroscopy
SP  - 9
EP  - 15
PB  - Science Publishing Group
SN  - 2994-7308
UR  - https://doi.org/10.11648/j.ajqcms.20230701.12
AB  - The conformation of six membered ring, 1,3,4-tri-o-acetyl-2-azido-6-bromo-2,6-dideoxy-D-galactose α-1 and β-1, and 2,6-dideoxy-2,6-imino- D-talonic acid 2D and L-talonic acid 2L, is analyzed inscribing two five membered ring on six membered ring. Altona’s five membered ring conformational parameters, phase angles of the pseudorotation P1, P2 [deg] and angle of deviation from planarity θm [deg] = f(P [deg]), are calculated with Java Script program using 3-Sphere torsional angles. The correlation between Altona map and six membered ring Stoddart’s diagram conformations was confirmed with VISION molecular models. 3-Sphere torsional angles θnn+1 [deg] for all cis, trans-ee, -aa stereochemistry are disclosed from trigonometric point of view, Hopf fibration confirmed by Lie algebra. The cis, trans stereochemistry on two units with six sets angles ensure relationships between dihedral θHnHn+1 [deg]/vicinal angles ϕ [deg] (θBn + A = θAn, θAn = θHnHn+1, θBn = ϕ), and between dihedral θHnHn+1 [deg]/torsional angles θnn+1 [deg] (θnn+1 = A +/- θHnHn+1); in first case A = 150 for trans-aa6,1 and A = 90 for trans-aa5,2 and trans-ee stereochemistry, in last case A = 180 [deg] for cis and trans-aa stereochemistry and A = 120 [deg] for trans-ee stereochemistry. The number of dihedral angles with positive and negative sign results from 3-sphere approach for only one vicinal coupling constant 3JHnHn+1 [Hz] are restricted by the VISION molecular models.
VL  - 7
IS  - 1
ER  -

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Author Information

Emerich Bartha

Department of Chemistry, “C. D. Nenitescu” Institute of Organic and Supramolecular Chemistry, Bucharest, Romania
Carmen-Irena Mitan

Department of Chemistry, “C. D. Nenitescu” Institute of Organic and Supramolecular Chemistry, Bucharest, Romania
Petru Filip

Department of Chemistry, “C. D. Nenitescu” Institute of Organic and Supramolecular Chemistry, Bucharest, Romania

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Plain Text BibTeX RIS

APA Style

Emerich Bartha, Carmen-Irena Mitan, Petru Filip. (2023). 3-Sphere Torsional Angles and Six Membered Ring Conformation. American Journal of Quantum Chemistry and Molecular Spectroscopy, 7(1), 9-15. https://doi.org/10.11648/j.ajqcms.20230701.12

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ACS Style

Emerich Bartha; Carmen-Irena Mitan; Petru Filip. 3-Sphere Torsional Angles and Six Membered Ring Conformation. Am. J. Quantum Chem. Mol. Spectrosc. 2023, 7(1), 9-15. doi: 10.11648/j.ajqcms.20230701.12

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AMA Style

Emerich Bartha, Carmen-Irena Mitan, Petru Filip. 3-Sphere Torsional Angles and Six Membered Ring Conformation. Am J Quantum Chem Mol Spectrosc. 2023;7(1):9-15. doi: 10.11648/j.ajqcms.20230701.12

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@article{10.11648/j.ajqcms.20230701.12,
  author = {Emerich Bartha and Carmen-Irena Mitan and Petru Filip},
  title = {3-Sphere Torsional Angles and Six Membered Ring Conformation},
  journal = {American Journal of Quantum Chemistry and Molecular Spectroscopy},
  volume = {7},
  number = {1},
  pages = {9-15},
  doi = {10.11648/j.ajqcms.20230701.12},
  url = {https://doi.org/10.11648/j.ajqcms.20230701.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajqcms.20230701.12},
  abstract = {The conformation of six membered ring, 1,3,4-tri-o-acetyl-2-azido-6-bromo-2,6-dideoxy-D-galactose α-1 and β-1, and 2,6-dideoxy-2,6-imino- D-talonic acid 2D and L-talonic acid 2L, is analyzed inscribing two five membered ring on six membered ring. Altona’s five membered ring conformational parameters, phase angles of the pseudorotation P1, P2 [deg] and angle of deviation from planarity θm [deg] = f(P [deg]), are calculated with Java Script program using 3-Sphere torsional angles. The correlation between Altona map and six membered ring Stoddart’s diagram conformations was confirmed with VISION molecular models. 3-Sphere torsional angles θnn+1 [deg] for all cis, trans-ee, -aa stereochemistry are disclosed from trigonometric point of view, Hopf fibration confirmed by Lie algebra. The cis, trans stereochemistry on two units with six sets angles ensure relationships between dihedral θHnHn+1 [deg]/vicinal angles ϕ [deg] (θBn + A = θAn, θAn = θHnHn+1, θBn = ϕ), and between dihedral θHnHn+1 [deg]/torsional angles θnn+1 [deg] (θnn+1 = A +/- θHnHn+1); in first case A = 150 for trans-aa6,1 and A = 90 for trans-aa5,2 and trans-ee stereochemistry, in last case A = 180 [deg] for cis and trans-aa stereochemistry and A = 120 [deg] for trans-ee stereochemistry. The number of dihedral angles with positive and negative sign results from 3-sphere approach for only one vicinal coupling constant 3JHnHn+1 [Hz] are restricted by the VISION molecular models.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - 3-Sphere Torsional Angles and Six Membered Ring Conformation
AU  - Emerich Bartha
AU  - Carmen-Irena Mitan
AU  - Petru Filip
Y1  - 2023/04/24
PY  - 2023
N1  - https://doi.org/10.11648/j.ajqcms.20230701.12
DO  - 10.11648/j.ajqcms.20230701.12
T2  - American Journal of Quantum Chemistry and Molecular Spectroscopy
JF  - American Journal of Quantum Chemistry and Molecular Spectroscopy
JO  - American Journal of Quantum Chemistry and Molecular Spectroscopy
SP  - 9
EP  - 15
PB  - Science Publishing Group
SN  - 2994-7308
UR  - https://doi.org/10.11648/j.ajqcms.20230701.12
AB  - The conformation of six membered ring, 1,3,4-tri-o-acetyl-2-azido-6-bromo-2,6-dideoxy-D-galactose α-1 and β-1, and 2,6-dideoxy-2,6-imino- D-talonic acid 2D and L-talonic acid 2L, is analyzed inscribing two five membered ring on six membered ring. Altona’s five membered ring conformational parameters, phase angles of the pseudorotation P1, P2 [deg] and angle of deviation from planarity θm [deg] = f(P [deg]), are calculated with Java Script program using 3-Sphere torsional angles. The correlation between Altona map and six membered ring Stoddart’s diagram conformations was confirmed with VISION molecular models. 3-Sphere torsional angles θnn+1 [deg] for all cis, trans-ee, -aa stereochemistry are disclosed from trigonometric point of view, Hopf fibration confirmed by Lie algebra. The cis, trans stereochemistry on two units with six sets angles ensure relationships between dihedral θHnHn+1 [deg]/vicinal angles ϕ [deg] (θBn + A = θAn, θAn = θHnHn+1, θBn = ϕ), and between dihedral θHnHn+1 [deg]/torsional angles θnn+1 [deg] (θnn+1 = A +/- θHnHn+1); in first case A = 150 for trans-aa6,1 and A = 90 for trans-aa5,2 and trans-ee stereochemistry, in last case A = 180 [deg] for cis and trans-aa stereochemistry and A = 120 [deg] for trans-ee stereochemistry. The number of dihedral angles with positive and negative sign results from 3-sphere approach for only one vicinal coupling constant 3JHnHn+1 [Hz] are restricted by the VISION molecular models.
VL  - 7
IS  - 1
ER  -

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