ACADEMIA ROMÂNĂ Revue Roumaine de Chimie http://web.icf.ro/rrch/ Rev. Roum. Chim., 2021, 66(2), 179-183 DOI: 10.33224/rrch.2021.66.2.08 Dedicated to Professor Alexandru T. BALABAN on the occasion of his 90 th anniversary PROGRAM FOR PREDICTION DIHEDRAL ANGLE FROM VICINAL COUPLING CONSTANT WITH 3-SPHERE APPROACH Emerich BARTHA, a Carmen-Irena MITAN, a,* Constantin DRAGHICI, a Miron T. CAPROIU, a Petru FILIP, a Laszlo TARKO a and Robert M. MORIARTY b a Institute of Organic Chemistry “C. D. Nenitescu”, Roumanian Academy, Splaiul Independentei 202B, sect 6, P. P. box 108, Bucharest, 060023, Roumania b University of Illinois at Chicago, Department of Chemistry, Chicago, IL, 60607, U.S.A. Received September 24, 2020 3-Sphere approach is applied on prediction dihedral angle θ HnHn+1 [deg] only from vicinal coupling constant 3 J HnHn+1 [Hz] with Java script, in comparation with angles calculated from the differences between two atoms of carbon chemical shift (Δδ CnCn+1 [ppm]) and Karplus equations. The trigonometric equations 1, 2 ensuring the right sign along the D-, L series rule. INTRODUCTION * Karplus is a general method 1 for the calculation of the dihedral angle (θ HnHn+1 [deg]) from vicinal coupling constant ( 3 J HnHn+1 [Hz]) using the valence bond theory, 2,3 equation optimized and/or particularized by other. 4,5 The degree of non- planarity can be determined accurately from knowledge of the torsional angles 6 using models for pseudorotation. 7 In this paper we proposed 3-sphere approach for prediction of the dihedral angles only from vicinal coupling constant with the hypersphere trigonometric eq. 1, equation which gives information about the sign of the predicted dihedral angle, ensuring a good correlation between dihedral angle and vicinal coupling constant. 3-Sphere approach, a method in three steps: 1. Two characteristic angles are calculated from * Corresponding author: cmitan@yahoo.com NMR data; 2. Construction of the units with seven sets angles; 3. Calculation of the dihedral angles having right stereochemistry and sign with hypersphere equation. 8 The higher number of angles under seven set unit rule is drastically reduced with the prediction program. RESULTS Geometric spatial distribution of two protons with cis- or trans-stereochemistry on HCC’H’ fragment is represented on three concentric cones, where six possible angles (θ nA , n = 1 – 6) have two characteristic angles φ 1 and φ 2 , relative to three arbitrary points P 1 -P 3 (Fig. 1). 3-Sphere is a higher dimensional space, analogue to a sphere with four charts, where each chart is part of the circle to an open interval, and together cover the whole circle. Six dihedral angles can be place in west and east,