3-Sphere Torsional Angles and Six Membered Ring Conformation

Abstract

The conformation of six membered ring, 1,3,4-tri-o-acetyl-2-azido-6-bromo-2,6-dideoxy-D-galactose α-1 and β-1, and 2,6-dideoxy-2,6-imino- D-talonic acid 2D and L-talonic acid 2L, is analyzed inscribing two five membered ring on six membered ring. Altona’s five membered ring conformational parameters, phase angles of the pseudorotation P₁, P₂ [deg] and angle of deviation from planarity θ_m [deg] = f(P [deg]), are calculated with Java Script program using 3-Sphere torsional angles. The correlation between Altona map and six membered ring Stoddart’s diagram conformations was confirmed with VISION molecular models. 3-Sphere torsional angles θ_nn+1 [deg] for all <i>cis</i>, <i>trans</i>-ee, -<i>aa</i> stereochemistry are disclosed from trigonometric point of view, Hopf fibration confirmed by Lie algebra. The <i>cis</i>, <i>trans</i> stereochemistry on two units with six sets angles ensure relationships between dihedral θ_HnHn+1 [deg]/vicinal angles ϕ [deg] (θ^Bn + A = θ^An, θ^An = θ_HnHn+1, θ^Bn = ϕ), and between dihedral θ_HnHn+1 [deg]/torsional angles θ_nn+1 [deg] (θ_nn+1 = A +/- θ_HnHn+1); in first case A = 150 for <i>trans-aa</i>^6,1 and A = 90 for <i>trans-aa</i>^5,2 and <i>trans-ee</i> stereochemistry, in last case A = 180 [deg] for <i>cis</i> and <i>trans-aa</i> stereochemistry and A = 120 [deg] for <i>trans-ee</i> stereochemistry. The number of dihedral angles with positive and negative sign results from <i>3-sphere approach</i> for only one vicinal coupling constant ³<I>J</I>_HnHn+1 [Hz] are restricted by the VISION molecular models.