Relationships between torsional angles and ring-puckering coordinates Part IV.Application to four-membered rings

Abstract

The dependence of the intracyclic torsion angles, φ j and bond angles θ j upon the puckering amplitudes Φ and q has been analyzed for a set of ab initio geometries of four-membered rings (CH 2) 3X as well as for a set of X-ray structures of derivatives. The coefficients in the corresponding expressions have been estimated both theoretically, from the bond angles and bond lengths of planar reference conformations, and by parameterization. The coefficients in equations φ j (Φ), φ j(q), and Φ(q) calculated for the ab initio structures from the planar ring geometries are in good agreement with those obtained by parameterization. Likewise, the results from the analysis of X-ray structures are in reasonable agreement with the ab initio ones. The torsion angles φ j are described more accurately by using the Φ amplitudes than the q ones. However, the bond angles θ j are described with similar accuracy using Φ or q. For the X-ray structures the description of the θ j angles is not very good, the r.m.s. deviations σ being greater than 1° due mainly to substituent and/or packing effects. However, for the sum of the bond angles in each ring the deviation σ is smaller than 0.1 °. A planar ring geometry has been estimated for each X-ray structure from the θ j angles which has been used to calculate the coefficients in the corresponding equation φ j (Φ). The deviation σ for φ j decreases to 0.03° when using these individual equations against the value of 0.2° obtained when, for parameterizing φ j (Φ), the same planar ring is used for all derivatives of each parent compound.