Abstract
A multi-point approximation method clarifies supramolecular chirality of twofold rotational or helical assemblies as well as bundles of the one-dimensional (1D) assemblies. While one-point approximation of materials claims no chirality generation of such assemblies, multi-point approximations do claim possible generation in the 1D assemblies of bars and plates. Such chirality derives from deformations toward three-axial directions around the helical axes. The chiral columns are bundled in chiral ways through symmetry operations. The preferable right- or left-handed columns are bundled together to yield chiral crystals with right- or left-handedness, respectively, indicating that twofold helix symmetry operations cause chiral crystals composed of achiral components via a three-stepwise and three-directional process.
Highlights
IntroductionSince the discovery of cholic acid inclusion compounds [1,2,3], our research has been devoted to supramolecular chirality in crystals of chiral molecules, such as steroids [4,5,6,7,8,9,10] and alkaloids [11,12,13,14,15,16,17,18]
We solved the overlooked problem of chirality generation through twofold rotations, leading to the idea that achiral molecules can create chiral 21 columns which are bundled via chiral bottom-up process to yield chiral crystals
It is attractive that each step of the process involves generation of supramolecular chirality, and that over 70% of the Cambridge Structural Database (CSD) involve the twofold helices
Summary
Since the discovery of cholic acid inclusion compounds [1,2,3], our research has been devoted to supramolecular chirality in crystals of chiral molecules, such as steroids [4,5,6,7,8,9,10] and alkaloids [11,12,13,14,15,16,17,18]. The evoking idea was that even achiral groups and molecules can afford twofold helical assemblies with supramolecular chirality [20,21]. One can find only a single notation (21) for twofold helices (Figure 1c), in contrast to a pair of notations (31 and 32) for threefold helices (Figure 1d) Such a discrepancy between the fact and the theory prompted us to reconsider a root of molecular and supramolecular chirality, facing with the discrepancy which lies between twofold rotation operations in space groups and chirality generation in space geometry. This article deals with a geometric elucidation for generating supramolecular chirality in twofold helical assemblies of achiral components. We focus hitherto overlooked supramolecular chirality of twofold rotational or helical (21) molecular assemblies and their bundles in organic crystals. The final part is briefly concerned with a linkage between molecular and supramolecular chirality in the hierarchical structure of universe
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