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

Abstract

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°r otation 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.

Pyramidalization at the sp2‐Hybridized ipso‐Carbon Atom of Phenyl Compounds

“…A CSD search for ethylbenzene compounds C β −C α H 2 −C 6 H 5 with three open positions for variation at C β had given 14,169 structures, [9] including independent molecules in the unit cell. Figure 8A shows the distribution of the structures with respect to the rotation angle ψ from 0° to ±180° in a bar chart.…”

“…had been observed in previous publications, generated by the threefold potential of the three single bonds at the α-carbon atom C α , carrying all kinds of substituents. [7][8][9] It is to be expected that all compounds, in which a sp 3 -hybridized center X 3 E is attached to a sp 2hybridized center E'Y 2 by bond EÀ E', the periodic pyramidalization of the sp 2 -hybridized center E' in a potential with three maxima, three minima, and six zero-crossings during rotation about bond EÀ E' is an integral part of the intramolecular motions. Whereas the symmetry plane in conformations of type B (Figure 14) prevents pyramidalization of the sp 2 -hybridized center, conformations of type A enforce it.…”

“…[18][19][20] Figure 8B shows the scatter plot of the pyramidalization angles θ of 14,169 structures C β À C α H 2 À C 6 H 5 versus the rotation angle ψ. [9] The open circle rotation/pyramidalization curve ψ/θ av in Figure 7B is obtained by plotting the rotation angle ψ versus the 10°section averages θ av of the pyramidalization angle. The intensity differences in the scatter plot do not affect the ψ/θ av curve, because the averages of more or fewer points are the same.…”

“…Further investigations into the pyramidalization of sp 2 ‐hybridized centers followed sporadically [4] . In a recent series of papers [5–9] we showed that the sp 2 ‐hybridized carbon atom C*, surrounded by three different substituents E 1 , E 2 , and E 3 , is an element of chirality, which induces remarkable diastereoselectivities in chiral conformations of all kind of molecules, as shown for scatter plot analyses of 84,572 carboxylates, 55,941 carboxamides, and 59,498 ketones on the Cover Picture of J. Org. Chem .…”

“…We investigate the pyramidalization on the theoretical side by DFT calculations of toluene, t-butylbenzene, and ethylbenzene and on the experimental side by a scatter plot analysis of 14,169 structures of ethylbenzene compounds C β À C α H 2 À C 6 H 5 with three open positions for variation at C β , accumulated in the Cambridge Structural Database CSD. We had briefly reported on compounds with the substructure C β À C α H 2 À C 6 H 5 , [9] We include the results here, because they complement our analysis.…”