Research Article
Java Script Programs for Calculation of Dihedral Angles with Manifold Equations
Carmen-Irena Mitan*
,
Emeric Bartha,
Petru Filip,
Constantin Draghici,
Miron-Teodor Caproiu,
Robert Michael Moriarty
Issue:
Volume 12, Issue 3, June 2024
Pages:
42-53
Received:
1 May 2024
Accepted:
20 May 2024
Published:
3 June 2024
DOI:
10.11648/j.sjc.20241203.11
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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.
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 p...
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Research Article
3-Sphere Tetrahedral Angles and Phase Angle of the Pseudorotation P[deg] of C1-CH3-α-D Ribitol Iminocyclitol
Petru Filip,
Carmen Irena Mitan*,
Emerich Bartha
Issue:
Volume 12, Issue 3, June 2024
Pages:
54-62
Received:
13 May 2024
Accepted:
30 May 2024
Published:
19 June 2024
Abstract: 3-Sphere dihedral angles θHnHn+1[deg] calculated from NMR data, from vicinal coupling constant 3JHnHn+1[Hz] with right sign and stereochemistry, are used for simulation of the conformation of the five membered ring with VISION molecular models and Gausian09W. For a vicinal angle ϕ[deg], angle result from vicinal coupling constant 3JHnHn+1[Hz], result three possible dihedral angles with negative and positive sign. Different phase angles of the pseudorotation results from combination of dihedral angles (exocyclic angles) with positive and negative sign in case of cis stereochemistry, and only negative sign for trans stereochemistry, in accord with D-ribitol stereochemistry. The sign of the endocyclic trans-ee torsional angle is positive, relative to trans-aa and cis stereochemistry with same sign as exocyclic angle, as visualized on VISION molecular models. Tetrahedral angles φCn[deg] in close relationship with dihedral angles θHnHn+1[deg] are calculated only from vicinal coupling constant 3JHnHn+1[Hz] in attempt to corelate the change in conformation with tetrahedral values φCn[deg] and bond lengths l[A0], once the iminocyclitol push out from planarity one or two atoms of carbon, and once again to confirm the method for calculation of tetrahedral angles of five membered ring, sin/tan versus sin/cos units.
Abstract: 3-Sphere dihedral angles θHnHn+1[deg] calculated from NMR data, from vicinal coupling constant 3JHnHn+1[Hz] with right sign and stereochemistry, are used for simulation of the conformation of the five membered ring with VISION molecular models and Gausian09W. For a vicinal angle ϕ[deg], angle result from vicinal coupling constant 3JHnHn+1[Hz], resu...
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