Abstract
Two-fold helical assemblies of points, lines and faces were analyzed by the multipoint approximation method on the basis of three-dimensional space geometry. The analysis has led to the new concept that assemblies generated from a rotational operation by 180 degrees exhibit supramolecular chirality with distinguishable right- or left-handedness, termed as supramolecular tilt chirality, in contrast with the conventional theory in crystallography. This concept has enabled us to determine handedness of two-fold helical assemblies of various organic molecules and macromolecules. Such helical assemblies with three-axial chirality are bundled in various manners through three-stepwise and three-direction processes by using weak interactions. The bundling manners explain formation of chiral crystals starting from achiral molecules, guiding us toward an interpretation of chirality recognition mechanism in host-guest systems. This methodology can unify various kinds of chirality in molecules, supramolecules, macromolecules, and daily life materials on the basis of four-point chirality recognition in three-dimensional space geometry.
