Characterization of supramolecular hidden chirality of hydrogen-bonded networks by advanced graph set analysis.

Supramolecular hidden chirality of hydrogen-bonded (HB) networks of primary ammonium carboxylates was exposed by advanced graph set analysis from a symmetric viewpoint in topology. The ring-type HB (R-HB) networks are topologically regarded as faces, and therefore exhibit prochirality and positional isomerism due to substituents attached on the faces. To describe the symmetric properties of the faces, additional symbols, Re (right-handed or clockwise), Si (left-handed or anticlockwise), and m (mirror), were proposed. According to the symbols, various kinds of faces were classified based on the symmetry. This symmetry consideration of the faces enables us to precisely evaluate supramolecular chirality, especially its handedness, of 0D-cubic, 1D-ladder and 2D-sheet HB networks that are composed of the faces. The 1D-ladder and 2D-sheet HB networks generate chirality by accumulating the chiral faces in 1D and 2D manners, respectively, whereas 0D-cubic HB networks generate chirality based on combinations of eight kinds of faces, similar to the chirality of dice.