3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-<I>N</I>-dehydro-L-ribitol

Robert Michael Moriarty; Carmen-Irena Mitan; Emerich Bartha; Petru Filip; Rajesh Naithani; Timothy Block

doi:doi:10.11648/ajqcms.20240801.11

Research Article |

| Peer-Reviewed

3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol

Robert Michael Moriarty, Carmen-Irena Mitan^*, Emerich Bartha, Petru Filip, Rajesh Naithani, Timothy Block

Published in American Journal of Quantum Chemistry and Molecular Spectroscopy (Volume 8, Issue 1)

Received: 9 January 2024 Accepted: 20 January 2024 Published: 1 February 2024

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

The conformation of 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol 1, phase angles of the pseudorotation of five (C³) and six (C₁⁴) membered rings, was analyzed with dihedral angles θ_HnHn+1[deg] calculated only from vicinal coupling constants ³J_HH[Hz] with 3-Sphere approach and VISION molecular models. The dimension space around the six and five membered ring are established based on hypersphere equations results from calculation of the dihedral angles from carbon chemical shift. Higher biological activity was observed to date at iminocyclitols having dihedral or vicinal angles calculated in 2D. Tetrahedral angles in close relationships with dihedral angles are calculated from carbon and / or proton chemical shift with manifold equations, conic and rectangle geometries. Equations for calculation of the tetrahedral angles φ_Cn[deg] only from vicinal coupling constant ³J_HnHn+1[deg] or from chemical shift δ_Cn[ppm] are analyzed for five and established for six membered ring, resulting general rules for calculation of tetrahedral angles. Conic as manifold in case of six membered ring enable calculation of dihedral angle θ_HnHn+1[deg] from tetrahedral angle φ_Cn[deg] starting with tetrahedral angle on unit, and in case of five membered ring based on opposite relationship between dihedral and tetrahedral (sin versus tan function), unit start with dihedral angles. Rectangle as manifold enable calculation for both the tetrahedral angle from dihedral angle starting with dihedral angle on unit, for six membered ring using two or three units with three sets angles and in case of five membered ring only one unit with seven set angles. The bond distances l_CnCn+1[A⁰] of five and six membered ring are calculated from 3-Sphere-dihedral angles θ_HnHn+1[deg].

Published in	American Journal of Quantum Chemistry and Molecular Spectroscopy (Volume 8, Issue 1)
DOI	10.11648/ajqcms.20240801.11
Page(s)	1-12
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-Dihedral Angles, Phase Angle of the Pseudorotation, Tetrahedral Angles, Bond Distances

References

[1]	C.-I. Mitan, E. Bartha, F. Petru, C. Draghici, M.-T. Caproiu, R. M. Moriarty, Manifold inversion on prediction dihedral angle from vicinal coupling constant with 3-sphere approach, Rev. Roum. Chim. 2023, 68, 185; DOI: 10.33224/rrch.2023.68.3-4.08.
[2]	C.-I. Mitan, E. Bartha, C. Draghici, M. T. Caproiu, P. Filip, R. M. Moriarty, Hopf fibration on relationship between dihedral angle θ_HnHn+1[deg] and vicinal angle ϕ[deg], angles calculated from NMR data with 3-sphere approach and Java Script, Science Journal of Chemistry 2022, 10, 21. SciencePG: DOI: 10.11648/j.sjc.20221001.13.
[3]	E. Bartha, C.-I. Mitan, C. Draghici, M. T. Caproiu, P. Filip, R. Moriarty, Rectangle as manifold on relationships between vicinal constant couplings ³J_HH, ¹H and ¹³C-chemical shifts and dihedral angles, Rev. Roum. Chim. 2022, 67(3), 167 – 172. DOI: 10.33224/rrch.2022.67.3.05.
[4]	C.-I. Mitan, E. Bartha, P. Filip, Relationship between tetrahedral and dihedral on hypersphere coordinates, Rev. Roum. Chim. 2023, 68(5-6), 261; DOI: 10.33224/rrch.2023.68.5-6.09.
[5]	C.-I. Mitan, E. Bartha, P. Filip, Tetrahedral angles of six membered ring calculated from NMR data with 3-sphere approach, Rev. Roum. Chim. 2023, 68(5-6), 273; DOI: 10.33224/rrch.2023.68.5-6.10.
[6]	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.
[7]	W. Zou, D. Izotov, D. Cremer, New way of describing static and dynamic deformations of the Jahn-Teller in ring molecules, J. Phys. Chem. A. 2011, 115, 8731; dx.doi.org/10.1021/jp2041907.
[8]	A. Wu, D. Cremer, New approach for determining the conformational features of pseudorotating ring molecules utilizing calculated and measured NMR spin-spin coupling constants, J. Phys. Chem. A 2003, 107, 1797: doi.org/10.1021.jp022277m.
[9]	W. J. Adams, H. J. Geise, L. S. Bartell, Structure, equilibrium conformation, and pseudorotation in cyclopentene. An electron diffraction study, J. Am. Chem. Soc.1970, 92, 5013; doi.org/10.1021/ja10720a001.
[10]	P. Herzyk, A. Rabczenko, A new description of equilateral five-membered rings during pseudorotation, J. Chem. Soc. Perkin. Trans. II, 1983, 213; doi.org/10.1039/P29830000213.
[11]	D. Cremer, Calculation of puckered rings with analytical gradients, J. Phys. Chem. 1990, 94, 5502; doi.org/10.1021/j100377a017.
[12]	A. H. Hill, P. J. Reilly, Puckering coordinates of monocyclic rings by triangular decomposition, J. Chem. Inf. Model 2007, 47, 1031; doi.org/10.1021/ci600492e.
[13]	C. B. Barnett, K. J. Naidoo, Calculating ring pucker free energy surfaces from reaction coordinate forces, AIP Conference Proceedings 2009, 214, 1102; doi.org/10.1063/1.3108377.
[14]	C. B. Barnett, K. J. Naidoo, Ring puckering: A metric for evaluation the occuracy of AM1, PM3, PM3CARB-1, and SCC-DFTB carbohydrate QM/MM simulations, J. Phys. Chem. B 2010, 114, 17142; doi.org/10.1021/jp107620h.
[15]	D. Wu, The puckering free energy surface of proline, AIP Advances 2013, 3, 032141; doi.org/10.10631/1.4799082.
[16]	A. Wu, D. Cremer, A. A. Auer, Extension of the Karplus relationship for NMR Spin Spin cupling constants to nonplanar ring systems: Pseudorotation of cyclopentene, J. Gauss, J. Phys. Chem. A 2002, 106, 657; doi.org/10.1021/jp0131601.
[17]	R. C. Lord, T. C. Rounds, T. Ueda, For infrared spectra of ring coumponds. X. Hindered pseudorotation in six membered rings: Estimation of the barrier height for half chair inversion in dioxane and 2,3-dihydropyrane, J. Chem. Phys.1972, 2572; doi.org/10.1063/1.1678625.
[18]	J. Jang, J. Lanne, Calculation of kinetic energy functions for the ring-twisting and ring-bending vibrations at tetralin and related molecules, J. Mol. Str. 2006, 798, 27; doi.org/10.1016/j.molstruc.2006.07.024.
[19]	K. Kitamura, A. Wakahara, H. Mizuno, Y. Baba, K. I. Tomita, Conformationally ‘concerted’ changes in nucleotide structures. A new description using circular correlation and regression analyses, J. Am. Chem. Soc.1981, 103, 3899; doi.org/10.1021/ja00403a048.
[20]	C. Altona, M. Sundaralingam, Conformational analysis of the sugar ring in nucleosides and nucleotides, A new description using the concept of pseudorotation, J. Am. Chem. Soc. 1972, 94, 8205: doi.org/10.1021/ja00778a043.
[21]	K. Nauwelaerts, E. Lescrinier, G. Sclep, P. Herdewijn, Cyclohexenyl nucleis acids: conformationally flexible oligonucleotides, Nucleic Acids Research 2005, 33; doi: 10.1093/nar/gki 538.
[22]	E. Bartha, C.-I. Mitan, P. Filip 3-Sphere Torsional Angles and Six Membered Ring Conformation, American Journal of Quantum Chemistry and Molecular Spectroscopy 2023, 7(1), 9. SciencePG: doi: 10.116481j.ajqcms.20230701.12.
[23]	R. M. Moriarty, C.-I. Mitan, B. Gu, T. Block, Hypersphere and Antiviral Activity of three Alkyl Chain Imnocyclitols with D and L Ribitol Stereochemistry, American Journal of Heterocyclic Chemistry 2023, 9(1), 9-24. SciencePG: doi: 10.116481/jajhc20230901.12, ISSN: 2575-7059(Print), ISSN: 2575-5722 (online).
[24]	C.-I. Mitan, E. Bartha, P. Filip, Hypersphere coordinates on calculation of the dihedral angles from carbon chemical shift, Bulletin of Romanian Chemical Engineering Society 2022, 9(2), 151; ISSN 2360-4697.
[25]	R. M. R. M. Moriarty, C.-I. Mitan, N. Branza-Nichita, K. R. Phares, D. Parrish, exo-Imino to endo-Iminocyclitol Rearrangement. A General Route to Five-Membered Antiviral Azasugars, Org. Lett. 2006, 8, 3465.
[26]	C.-I. Mitan, E. Bartha, P. Filip, M.-T. Caproiu, C. Draghici, R. M. Moriarty, Graph Flux Intensity and Electromagnetic Wave on 3-sphere Approach, Science Journal of Chemistry 2023, 11, 212; SciencePG: doi: 10.11648/j.sjc.20231106.1226.
[27]	Z. B. Maksic, M. Randic, Carbon-Carbon and Carbon-Hydrogen bond length bond overlap correlations, J. Am. Chem. Soc. 1070, 92, 424; doi.org/10.1021/ja00705a627.

Cite This Article

Plain Text BibTeX RIS

APA Style

Moriarty, R. M., Mitan, C., Bartha, E., Filip, P., Naithani, R., et al. (2024). 3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol. American Journal of Quantum Chemistry and Molecular Spectroscopy, 8(1), 1-12. https://doi.org/10.11648/ajqcms.20240801.11

Copy | Download

ACS Style

Moriarty, R. M.; Mitan, C.; Bartha, E.; Filip, P.; Naithani, R., et al. 3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol. Am. J. Quantum Chem. Mol. Spectrosc. 2024, 8(1), 1-12. doi: 10.11648/ajqcms.20240801.11

Copy | Download

AMA Style

Moriarty RM, Mitan C, Bartha E, Filip P, Naithani R, et al. 3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol. Am J Quantum Chem Mol Spectrosc. 2024;8(1):1-12. doi: 10.11648/ajqcms.20240801.11

Copy | Download

@article{10.11648/ajqcms.20240801.11,
  author = {Robert Michael Moriarty and Carmen-Irena Mitan and Emerich Bartha and Petru Filip and Rajesh Naithani and Timothy Block},
  title = {3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol},
  journal = {American Journal of Quantum Chemistry and Molecular Spectroscopy},
  volume = {8},
  number = {1},
  pages = {1-12},
  doi = {10.11648/ajqcms.20240801.11},
  url = {https://doi.org/10.11648/ajqcms.20240801.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.ajqcms.20240801.11},
  abstract = {The conformation of 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol 1, phase angles of the pseudorotation of five (C3) and six (C14) membered rings, was analyzed with dihedral angles θHnHn+1[deg] calculated only from vicinal coupling constants 3JHH[Hz] with 3-Sphere approach and VISION molecular models. The dimension space around the six and five membered ring are established based on hypersphere equations results from calculation of the dihedral angles from carbon chemical shift. Higher biological activity was observed to date at iminocyclitols having dihedral or vicinal angles calculated in 2D. Tetrahedral angles in close relationships with dihedral angles are calculated from carbon and / or proton chemical shift with manifold equations, conic and rectangle geometries. Equations for calculation of the tetrahedral angles φCn[deg] only from vicinal coupling constant 3JHnHn+1[deg] or from chemical shift δCn[ppm] are analyzed for five and established for six membered ring, resulting general rules for calculation of tetrahedral angles. Conic as manifold in case of six membered ring enable calculation of dihedral angle θHnHn+1[deg] from tetrahedral angle φCn[deg] starting with tetrahedral angle on unit, and in case of five membered ring based on opposite relationship between dihedral and tetrahedral (sin versus tan function), unit start with dihedral angles. Rectangle as manifold enable calculation for both the tetrahedral angle from dihedral angle starting with dihedral angle on unit, for six membered ring using two or three units with three sets angles and in case of five membered ring only one unit with seven set angles. The bond distances lCnCn+1 [A0] of five and six membered ring are calculated from 3-Sphere-dihedral angles θHnHn+1[deg].
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - 3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol
AU  - Robert Michael Moriarty
AU  - Carmen-Irena Mitan
AU  - Emerich Bartha
AU  - Petru Filip
AU  - Rajesh Naithani
AU  - Timothy Block
Y1  - 2024/02/01
PY  - 2024
N1  - https://doi.org/10.11648/ajqcms.20240801.11
DO  - 10.11648/ajqcms.20240801.11
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  - 1
EP  - 12
PB  - Science Publishing Group
SN  - 2994-7308
UR  - https://doi.org/10.11648/ajqcms.20240801.11
AB  - The conformation of 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol 1, phase angles of the pseudorotation of five (C3) and six (C14) membered rings, was analyzed with dihedral angles θHnHn+1[deg] calculated only from vicinal coupling constants 3JHH[Hz] with 3-Sphere approach and VISION molecular models. The dimension space around the six and five membered ring are established based on hypersphere equations results from calculation of the dihedral angles from carbon chemical shift. Higher biological activity was observed to date at iminocyclitols having dihedral or vicinal angles calculated in 2D. Tetrahedral angles in close relationships with dihedral angles are calculated from carbon and / or proton chemical shift with manifold equations, conic and rectangle geometries. Equations for calculation of the tetrahedral angles φCn[deg] only from vicinal coupling constant 3JHnHn+1[deg] or from chemical shift δCn[ppm] are analyzed for five and established for six membered ring, resulting general rules for calculation of tetrahedral angles. Conic as manifold in case of six membered ring enable calculation of dihedral angle θHnHn+1[deg] from tetrahedral angle φCn[deg] starting with tetrahedral angle on unit, and in case of five membered ring based on opposite relationship between dihedral and tetrahedral (sin versus tan function), unit start with dihedral angles. Rectangle as manifold enable calculation for both the tetrahedral angle from dihedral angle starting with dihedral angle on unit, for six membered ring using two or three units with three sets angles and in case of five membered ring only one unit with seven set angles. The bond distances lCnCn+1 [A0] of five and six membered ring are calculated from 3-Sphere-dihedral angles θHnHn+1[deg].

VL  - 8
IS  - 1
ER  -

Copy | Download

Author Information

Robert Michael Moriarty

Department of Chemistry, University of Illinois at Chicago, Chicago, US

Contact Email
Carmen-Irena Mitan

Department of Chemistry, University of Illinois at Chicago, Chicago, US; Department of Chemistry, “C.D. Nenitescu”, Institute of Organic and Supramolecular Chemistry, Bucharest, Romania

Contact Email
Emerich Bartha

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

Contact Email
Petru Filip

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

Department of Chemistry, University of Illinois at Chicago, Chicago, US
Timothy Block

Drexel Institute for Biotechnology and Virology Research, College of Medicine, Drexel University, Doylestown, US

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Moriarty, R. M., Mitan, C., Bartha, E., Filip, P., Naithani, R., et al. (2024). 3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol. American Journal of Quantum Chemistry and Molecular Spectroscopy, 8(1), 1-12. https://doi.org/10.11648/ajqcms.20240801.11

Copy | Download

ACS Style

Moriarty, R. M.; Mitan, C.; Bartha, E.; Filip, P.; Naithani, R., et al. 3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol. Am. J. Quantum Chem. Mol. Spectrosc. 2024, 8(1), 1-12. doi: 10.11648/ajqcms.20240801.11

Copy | Download

AMA Style

Moriarty RM, Mitan C, Bartha E, Filip P, Naithani R, et al. 3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol. Am J Quantum Chem Mol Spectrosc. 2024;8(1):1-12. doi: 10.11648/ajqcms.20240801.11

Copy | Download

@article{10.11648/ajqcms.20240801.11,
  author = {Robert Michael Moriarty and Carmen-Irena Mitan and Emerich Bartha and Petru Filip and Rajesh Naithani and Timothy Block},
  title = {3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol},
  journal = {American Journal of Quantum Chemistry and Molecular Spectroscopy},
  volume = {8},
  number = {1},
  pages = {1-12},
  doi = {10.11648/ajqcms.20240801.11},
  url = {https://doi.org/10.11648/ajqcms.20240801.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.ajqcms.20240801.11},
  abstract = {The conformation of 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol 1, phase angles of the pseudorotation of five (C3) and six (C14) membered rings, was analyzed with dihedral angles θHnHn+1[deg] calculated only from vicinal coupling constants 3JHH[Hz] with 3-Sphere approach and VISION molecular models. The dimension space around the six and five membered ring are established based on hypersphere equations results from calculation of the dihedral angles from carbon chemical shift. Higher biological activity was observed to date at iminocyclitols having dihedral or vicinal angles calculated in 2D. Tetrahedral angles in close relationships with dihedral angles are calculated from carbon and / or proton chemical shift with manifold equations, conic and rectangle geometries. Equations for calculation of the tetrahedral angles φCn[deg] only from vicinal coupling constant 3JHnHn+1[deg] or from chemical shift δCn[ppm] are analyzed for five and established for six membered ring, resulting general rules for calculation of tetrahedral angles. Conic as manifold in case of six membered ring enable calculation of dihedral angle θHnHn+1[deg] from tetrahedral angle φCn[deg] starting with tetrahedral angle on unit, and in case of five membered ring based on opposite relationship between dihedral and tetrahedral (sin versus tan function), unit start with dihedral angles. Rectangle as manifold enable calculation for both the tetrahedral angle from dihedral angle starting with dihedral angle on unit, for six membered ring using two or three units with three sets angles and in case of five membered ring only one unit with seven set angles. The bond distances lCnCn+1 [A0] of five and six membered ring are calculated from 3-Sphere-dihedral angles θHnHn+1[deg].
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - 3-Sphere Approach on 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol
AU  - Robert Michael Moriarty
AU  - Carmen-Irena Mitan
AU  - Emerich Bartha
AU  - Petru Filip
AU  - Rajesh Naithani
AU  - Timothy Block
Y1  - 2024/02/01
PY  - 2024
N1  - https://doi.org/10.11648/ajqcms.20240801.11
DO  - 10.11648/ajqcms.20240801.11
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  - 1
EP  - 12
PB  - Science Publishing Group
SN  - 2994-7308
UR  - https://doi.org/10.11648/ajqcms.20240801.11
AB  - The conformation of 9-O-(10,11-di-O-benzyl-12,14-O-benzylidene-α-D-galactopyranosyl)-1-butyl-2,3-O-isopropylidene-1,4-dideoxy-1,4-imino-1-N-dehydro-L-ribitol 1, phase angles of the pseudorotation of five (C3) and six (C14) membered rings, was analyzed with dihedral angles θHnHn+1[deg] calculated only from vicinal coupling constants 3JHH[Hz] with 3-Sphere approach and VISION molecular models. The dimension space around the six and five membered ring are established based on hypersphere equations results from calculation of the dihedral angles from carbon chemical shift. Higher biological activity was observed to date at iminocyclitols having dihedral or vicinal angles calculated in 2D. Tetrahedral angles in close relationships with dihedral angles are calculated from carbon and / or proton chemical shift with manifold equations, conic and rectangle geometries. Equations for calculation of the tetrahedral angles φCn[deg] only from vicinal coupling constant 3JHnHn+1[deg] or from chemical shift δCn[ppm] are analyzed for five and established for six membered ring, resulting general rules for calculation of tetrahedral angles. Conic as manifold in case of six membered ring enable calculation of dihedral angle θHnHn+1[deg] from tetrahedral angle φCn[deg] starting with tetrahedral angle on unit, and in case of five membered ring based on opposite relationship between dihedral and tetrahedral (sin versus tan function), unit start with dihedral angles. Rectangle as manifold enable calculation for both the tetrahedral angle from dihedral angle starting with dihedral angle on unit, for six membered ring using two or three units with three sets angles and in case of five membered ring only one unit with seven set angles. The bond distances lCnCn+1 [A0] of five and six membered ring are calculated from 3-Sphere-dihedral angles θHnHn+1[deg].

VL  - 8
IS  - 1
ER  -

Copy | Download