Twofold and Threefold Sinusoidal Patterns in Coupled Molecular Motions of 184,025 Structures of Phenylethane, Nitroethane, and Carboxylate Derivatives.

Scatter plot analyses for 14,169 phenylethanes of the substructure C β -C α H 2 -Ph with three open coordination positions at C β and 150,568 phenylethanes of C β -C α HX-Ph with an additional open coordination position X at C α have been performed, based on searches in the Cambridge Structural Database. The correlation of rotation angle ψ = C β -C α -C i -C o with a pyramidalization angle θ = C o -C o' -C i -C α in a 360° rotation about the bond C α -C i reveals a sinusoidal pattern with three maxima and minima, whereas the correlation of rotation angle ψ with bond angle ω = C β -C α -C i and bond length d = C β -C α results in sinusoidal patterns with two maxima and minima. A total of 3993 nitro derivatives of the substructure C β -C α HX-NO 2 confirm the results and show that atoms C i /C o /C o' in the phenyl compounds can be replaced by atoms N/O/O' without any change in the two- and threefold patterns. In 15,295 methyl acetates of the substructure C β -C α HX-C'(═O)OMe, pyramidalization of the group C α C'(═O)OMe results in a chiral flat tetrahedron with four different corners. ( R θ )/( S θ ) selectivity in the configuration of the tetrahedron is induced by the bonds C α -C β , C α -H, and C α -X, emanating from the tetrahedral center C α . It is surprising that bonds as different as C α -C β , C α -H, and C α -X (X = H, C, N, O, S, etc.) give almost the same induction intensities.