Java Script programs for calculation dihedral angles from NMR data with manifold equations of 3-Sphere approach: rectangle, Villarceau circles of cyclide (Torus – Dupin Cyclide), polar equations, Euler-Conic. Manifolds are curves or surface in higher dimension used for calculation of dihedral angles under wave character of NMR data, carbon and/or proton chemical shift δ_{Xn}[ppm] and vicinal coupling constant ^{3}J_{HnHn+1}[Hz]. 3-Sphere approach for calculation of the dihedral angles from NMR data in four steps: 1. Prediction, or more exactly calculation of the dihedral angles from vicinal coupling constant with trigonometric equations, 2. Calculation of the dihedral angles from manifold equations; 3. Building units from angle calculated with one of the manifold equations; 4. Calculation the vicinal coupling constant of the manifold dihedral angle. In this paper are presented Java Script programs of step 2 and from step 3 only the Java Script program for calculation of seven sets angles. The bond distances l_{CnCn+1}[A^{0}] between two atoms of carbon are under different polar equations (i.e. limaçons or cardioid, rose or lemniscale), our expectation was to find different manifold equations for calculation the best angle, differences are smaller but can be find sometimes a preferred one for a vicinal coupling constant. 3-Sphere approach has the advantages of calculation from vicinal angle or/and chemical shift the dihedral angle, tetrahedral angle and the bond distance l_{CnCn+1}[A^{0}], with application on conformational and configurational analysis.
Published in | Science Journal of Chemistry (Volume 12, Issue 3) |
DOI | 10.11648/j.sjc.20241203.11 |
Page(s) | 42-53 |
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. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Manifold, Reactangle, Villarceau Circles, Euler-Conic, Hopf Fibration, Lie Algebra, 3-Sphere, Dihedral Angles, Java Script
Entry | ^{3}J_{HH}^{a} [Hz] | H_{n} [ppm] | R_{mH} [π] | θ[deg],^{3}J_{HH}[Hz] | θ^{A}_{ }[deg] | θ[deg], ^{3}J_{HH}[Hz] eq. 17 | θ_{X}^{A} [deg] | |
---|---|---|---|---|---|---|---|---|
1 | 4.1 | 3.08 4.49 4.38 3.22 | 0.3439 | 20.11, 4.18 | 2.907 3.439 | 21.93^{U1C1}, 4.12 22.29^{U1C1}, 4.11 | 33.82 47.30 | 22.35^{U2B1}, 4.11 23.65^{U1E1}, 4.07 |
2 | 5.4 | 0.0203 | -28.83, 5.45 | 49.09 | -24.54^{U1E1}, 5.35 | - | - | |
3 | 0 d, H_{3}, 0.1 | 0.0862 | -94.96^{S1B4}, 1.1^{tan} -92.47^{S1E4}, 0.79^{tan} | 0.203 0.086 0.862 | -24.96^{U1G1}, 5.36 -90.08^{S1B4}, 0.146^{tan} -90.86^{S1B4}, 0.46^{tan} | 0.165 0.029 2.972 | -24.97^{U1G1}, 5.36 -90.029^{S1B4}, 0.086^{tan} -92.97^{S1B4}, 0.86^{tan} | |
4 | 3.1 | 3.71 4.16 4.26 3.58 | 0.1451 | 51.65^{U1A2}, 3.09 | 6.888 1.451 | 51.88^{U2F2}, 3.08 50.24^{U1D2}, 3.15 | 189.82 8.428 | 50.172^{U1A2}, 3.15 51.571^{U1A2}, 3.09 |
5 | 3.9 | 0.0256 | 29.26^{S1E1}, 3.89 | 39.00 0.256 | 25.2^{S1G1}, 4.01 29.74^{S1B1}, 3.88 | - 0.262 | - 29.73^{S1B1}, 3.88 | |
6 | 8.8 | 0.0772 | -166.88^{U1F6}, 8.78^{tan} | 12.941 0.772 | -166.71^{U1A6}, 8.77^{tan} -169.57^{U1B6}, 8.92^{tan} | 167.47 0.597 | -167.16^{U1A6}, 8.8^{tan} -169.63^{U1B6}, 8.93^{tan} | |
7 | 4.8 | 3.11 4.02 4.12 2.89 | 0.1895 | -2.78^{S1A1}, 4.81 | 5.274 1.895 | -1.64^{U1S1A1}, 4.78 -1.89^{S1A1}, 4.79 | 111.290 14.376 | -3.87^{U1S1A1}, 4.84 -1.86^{S1B1}, 4.79 |
8 | 5.2 | 0.0192 | -15.55^{U1G1}, 5.13 -19.66^{U1A1}, 5.23 | 51.999 0.192 | -19.00^{U1G1}, 5.22 -19.93^{U1A1}, 5.24 | - 0.1479 | - -19.95^{U1A1}, 5.24 | |
9 | 0 bs, 0.81 | 0.6585 | -93.57^{S1A4}, 0.94^{tan} | 0.658 6.585 | -90.65^{S1B4}, 0.4^{tan} -93.29^{SD1}, 0.90^{tan} | 1.7346 173.46 | -91.73^{S1B4}, 0.65^{tan} -93.27^{SE4}, 0.90^{tan} |
Entry | ^{3}J_{HH}^{a} [Hz] | C_{n} [ppm] | R_{mC} [π] | θ[deg],^{3}J_{HH}[Hz] | θ^{A}^{ }[deg] | θ_{X}^{A} [deg] | ||
---|---|---|---|---|---|---|---|---|
1 | 4.1 | 55.8 83.5 84.3 65.9 | 0.1480 | 21.48^{U1B1}, 4.13 | 6.756 1.480 | 23.48^{U1B1}, 4.13 20.98^{U1C1}, 4.15 | 182.57 8.763 | 21.71^{U1C1}, 4.13 21.23^{U1B1}, 4.14 |
2 | 5.4 | 0.1481 | -25.74^{S1E1}, 5.37 | 6.75 1.481 | -26.62^{S1E1}, 5.39 -28.51^{S1B1}, 5.44 | 182.25 8.779 | -27.75^{S1B1}, 5.42 -25.61^{S1E1}, 5.37 | |
3 | 0 d, H_{3} | 0.0054 | -90.308^{S1B4}, 0.277^{ tan} | 0.0054 0.0543 | -90.005^{S1B4}, 0.036^{ tan} -90.053^{S1B4}, 0.115^{ tan} | 0.0001 0.0118 | -90.0001^{S1B4}, 0.005^{ tan} -90.0118^{S1B4}, 0.053^{ tan} | |
4 | 3.1 | 57.4 71.5 71.7 66.8 | 0.2198 | 51.35^{U1F2}, 3.108 (-31.98, -53.10^{tan}) | 4.548 2.198 | 50.90^{U1C2}, 3.12 49.26^{U1B2}, 3.19 | 82.751 19.335 | 52.75^{U1B2}, 3.05 50.33^{U1D2}, 3.14 |
5 | 3.9 | 0.0512 | 28.53^{S1E1}, 3.92 | 19.499 0.512 | 28.49^{S1A1}, 3.92 29.48^{S1B1}, 3.88 | - 1.0519 | - 28.94^{S1B1}, 3.90 | |
6 | 8.8 | 0.5568 | -168.49^{U1}^{F6}, 8.87^{tan} | 1.7959 5.5681 | -169.21^{U1}^{F6}, 8.91^{tan} -167.49^{U1}^{F6}, 8.81^{tan} | 3.225 31.004 | -168.71^{U1}^{F6}, 8.88^{tan} -169.49^{U1}^{F6}, 8.92^{tan} | |
7 | 4.8 | 63.7 72.5 74.0 69.3 | 0.5454 | -3.055^{S1B1}, 4.82 (-44.95, 3.06^{tan}) | 1.8333 5.4545 | -1.833^{S1A1}, 4.79 (-44.98, 3.06^{tan}) -2.727^{S1D1}, 4.81 (-44.96, 2.73^{tan}) | 13.444 119.008 | - -1.983^{S1C1}, 4.79 (-44.98, 1.98^{tan}) |
8 | 5.2 | 0.2884 | -16.76^{U1A1}, 5.16 (-43.75, 17.53^{tan}) | 3.4666 2.8846 | -18.84^{U1A1}, 5.21 (-43.42, 19.95^{tan}) -19.03^{U1A1}, 5.22 (-43.38, 20.18^{tan}) | 48.0711 33.2840 | -18.07^{U1B1}, 5.19 (-43.55, 19.04^{tan}) -18.90^{U1A1}, 5.21 (-43.41, 20.02^{tan}) | |
9 | 0 bs, 0.81 | 0.1723 | -90.182^{S1B4}, 0.213^{ tan} | 5.8024 1.7234 | -95.772^{S1B4}, 1.20^{ tan} -91.724^{S1B4}, 0.656^{ tan} | 134.674 11.8804 | -91.953^{S1CB4}, 0.698^{ tan} -95.668^{S1CB4}, 1.187^{ tan} |
RMN | Nuclear Magnetic Resonance |
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APA Style
Mitan, C., Bartha, E., Filip, P., Draghici, C., Caproiu, M., et al. (2024). Java Script Programs for Calculation of Dihedral Angles with Manifold Equations. Science Journal of Chemistry, 12(3), 42-53. https://doi.org/10.11648/j.sjc.20241203.11
ACS Style
Mitan, C.; Bartha, E.; Filip, P.; Draghici, C.; Caproiu, M., et al. Java Script Programs for Calculation of Dihedral Angles with Manifold Equations. Sci. J. Chem. 2024, 12(3), 42-53. doi: 10.11648/j.sjc.20241203.11
@article{10.11648/j.sjc.20241203.11, author = {Carmen-Irena Mitan and Emeric Bartha and Petru Filip and Constantin Draghici and Miron-Teodor Caproiu and Robert Michael Moriarty}, title = {Java Script Programs for Calculation of Dihedral Angles with Manifold Equations }, journal = {Science Journal of Chemistry}, volume = {12}, number = {3}, pages = {42-53}, doi = {10.11648/j.sjc.20241203.11}, url = {https://doi.org/10.11648/j.sjc.20241203.11}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjc.20241203.11}, abstract = {Java Script programs for calculation dihedral angles from NMR data with manifold equations of 3-Sphere approach: rectangle, Villarceau circles of cyclide (Torus – Dupin Cyclide), polar equations, Euler-Conic. Manifolds are curves or surface in higher dimension used for calculation of dihedral angles under wave character of NMR data, carbon and/or proton chemical shift δXn[ppm] and vicinal coupling constant 3JHnHn+1[Hz]. 3-Sphere approach for calculation of the dihedral angles from NMR data in four steps: 1. Prediction, or more exactly calculation of the dihedral angles from vicinal coupling constant with trigonometric equations, 2. Calculation of the dihedral angles from manifold equations; 3. Building units from angle calculated with one of the manifold equations; 4. Calculation the vicinal coupling constant of the manifold dihedral angle. In this paper are presented Java Script programs of step 2 and from step 3 only the Java Script program for calculation of seven sets angles. The bond distances lCnCn+1[A0] between two atoms of carbon are under different polar equations (i.e. limaçons or cardioid, rose or lemniscale), our expectation was to find different manifold equations for calculation the best angle, differences are smaller but can be find sometimes a preferred one for a vicinal coupling constant. 3-Sphere approach has the advantages of calculation from vicinal angle or/and chemical shift the dihedral angle, tetrahedral angle and the bond distance lCnCn+1[A0], with application on conformational and configurational analysis. }, year = {2024} }
TY - JOUR T1 - Java Script Programs for Calculation of Dihedral Angles with Manifold Equations AU - Carmen-Irena Mitan AU - Emeric Bartha AU - Petru Filip AU - Constantin Draghici AU - Miron-Teodor Caproiu AU - Robert Michael Moriarty Y1 - 2024/06/03 PY - 2024 N1 - https://doi.org/10.11648/j.sjc.20241203.11 DO - 10.11648/j.sjc.20241203.11 T2 - Science Journal of Chemistry JF - Science Journal of Chemistry JO - Science Journal of Chemistry SP - 42 EP - 53 PB - Science Publishing Group SN - 2330-099X UR - https://doi.org/10.11648/j.sjc.20241203.11 AB - Java Script programs for calculation dihedral angles from NMR data with manifold equations of 3-Sphere approach: rectangle, Villarceau circles of cyclide (Torus – Dupin Cyclide), polar equations, Euler-Conic. Manifolds are curves or surface in higher dimension used for calculation of dihedral angles under wave character of NMR data, carbon and/or proton chemical shift δXn[ppm] and vicinal coupling constant 3JHnHn+1[Hz]. 3-Sphere approach for calculation of the dihedral angles from NMR data in four steps: 1. Prediction, or more exactly calculation of the dihedral angles from vicinal coupling constant with trigonometric equations, 2. Calculation of the dihedral angles from manifold equations; 3. Building units from angle calculated with one of the manifold equations; 4. Calculation the vicinal coupling constant of the manifold dihedral angle. In this paper are presented Java Script programs of step 2 and from step 3 only the Java Script program for calculation of seven sets angles. The bond distances lCnCn+1[A0] between two atoms of carbon are under different polar equations (i.e. limaçons or cardioid, rose or lemniscale), our expectation was to find different manifold equations for calculation the best angle, differences are smaller but can be find sometimes a preferred one for a vicinal coupling constant. 3-Sphere approach has the advantages of calculation from vicinal angle or/and chemical shift the dihedral angle, tetrahedral angle and the bond distance lCnCn+1[A0], with application on conformational and configurational analysis. VL - 12 IS - 3 ER -