Java Script Programs for Calculation of Dihedral Angles with Manifold Equations

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 δ<sub>Xn</sub>[ppm] and vicinal coupling constant <sup>3</sup><I>J</I><sub>HnHn+1</sub>[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<sub>CnCn+1</sub>[A<sup>0</sup>] between two atoms of carbon are under different polar equations (<i>i.e.</i> 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<sub>CnCn+1</sub>[A<sup>0</sup>], with application on conformational and configurational analysis.