Twofold Helical Molecular Assemblies in Organic Crystals: Chirality Generation and Handedness Determination

Abstract

Conventionally, twofold helical molecular assemblies in organic crystals have been considered from space groups but not from space geometry, leading to an obscure understanding of their chirality generation. The reason is that identical twofold helical assemblies are obtained by twofold screw operations with clockwise or anticlockwise rotations by 180°, while enantiomeric twofold helical assemblies are observed even from achiral molecules. On the basis of three-dimensional space geometry, we succeeded in exposing chirality which has been hidden for a long time. The key for the success consists of the following two methods: one is multipoint approximation with lines and faces for representing materials and the other is tilt alignments along a helical axis for discriminating chirality and handedness. These methods proved generation of real chirality in twofold helical assemblies of organic molecules and further led us to the fact that the twofold helices exhibit three-axial chirality toward right-to-left, up-to-down, and in-to-out directions. Such helices are bundled together in various ways to provide crystals with the corresponding space groups. The bundling of only one-handed preferred helices affords one-handed crystals, explaining chiral crystallization of achiral molecules from a geometrical viewpoint.