3-Sphere Tetrahedral Angles and Phase Angle of the Pseudorotation P[deg] of C<sub>1</sub>-CH<sub>3</sub>-α-D Ribitol Iminocyclitol

Abstract

3-Sphere dihedral angles θ<sub>HnHn+1</sub>[deg] calculated from NMR data, from vicinal coupling constant <sup>3</sup><I>J</I><sub>HnHn+1</sub>[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 <sup>3</sup><I>J</I><sub>HnHn+1</sub>[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 <i>cis</i> stereochemistry, and only negative sign for <i>trans</i> stereochemistry, in accord with D-ribitol stereochemistry. The sign of the endocyclic <i>trans-ee</i> torsional angle is positive, relative to <i>trans-aa</i> and <i>cis</i> stereochemistry with same sign as exocyclic angle, as visualized on VISION molecular models. Tetrahedral angles φ<sub>Cn</sub>[deg] in close relationship with dihedral angles θ<sub>HnHn+1</sub>[deg] are calculated only from vicinal coupling constant <sup>3</sup><I>J</I><sub>HnHn+1</sub>[Hz] in attempt to corelate the change in conformation with tetrahedral values φ<sub>Cn</sub>[deg] and bond lengths l[A<sup>0</sup>], 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 <i>versus</i> sin/cos units.