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
Cβ-CαH2-Ph with three
open coordination positions at Cβ and 150,568 phenylethanes
of Cβ-CαHX-Ph with an additional
open coordination position X at Cα have been performed,
based on searches in the Cambridge Structural Database. The correlation
of rotation angle ψ = Cβ–Cα–Ci–Co with a pyramidalization
angle θ = Co–Co′–Ci–Cα in a 360° rotation about
the bond Cα–Ci reveals a sinusoidal
pattern with three maxima and minima, whereas the correlation of rotation
angle ψ with bond angle ω = Cβ–Cα–Ci and bond length d = Cβ–Cα results in sinusoidal
patterns with two maxima and minima. A total of 3993 nitro derivatives
of the substructure Cβ-CαHX-NO2 confirm the results and show that atoms Ci/Co/Co′ 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 Cβ-CαHX-C′(O)­OMe, pyramidalization
of the group CαC′(O)­OMe results in
a chiral flat tetrahedron with four different corners. (Rθ)/(Sθ) selectivity
in the configuration of the tetrahedron is induced by the bonds Cα–Cβ, Cα–H,
and Cα–X, emanating from the tetrahedral center
Cα. It is surprising that bonds as different as Cα–Cβ, Cα–H,
and Cα–X (X = H, C, N, O, S, etc.) give almost
the same induction intensities.