Supramolecular tilt chirality in crystals of steroids and alkaloids.

The concept of supramolecular chirality has assumed increasing importance in association with the development of supramolecular chemistry over the last two decades. In chiral crystals, 2 1 helical molecular assemblies are frequently observed as key motifs. Helical handedness of the 2 1 assemblies, however, has not been determined from the mathematical or crystallographical viewpoints. In this context, we have proposed two new concepts, three-axial chirality and tilt chirality. On the basis of the concepts, we describe supramolecular chirality and determine the handedness of 2 1 assemblies that are composed of relatively complicated molecules with multiple stereogenic centers such as brucine, bile acids, and cinchona alkaloids as well as those of simple molecules.