Supramolecular, Hierarchical, and Energetical Interpretation of Organic Crystals: Generation of Supramolecular Chirality in Assemblies of Achiral Molecules

Abstract

Recent progress in personal computers and computational methods has enabled us to practically perform quantitative evaluation of intermolecular interaction energies of organic molecules consisting of more than one hundred carbon atoms using density functional theory (DFT) calculations with dispersion correction. The calculations prompted us to make a systematic method for defining dimeric molecular assemblies in organic crystals. Based on Z-matrix involving dummy atoms, we designed a rectangular triangle model where a molecule positions through three kinds of rotations. This model clarified generation of position-dependent chirality along an axis. Symmetry operations, such as translation, two-fold rotation, two-fold helix, and so on, connect the identical triangles to generate position-dependent supramolecular chirality of the assemblies. The intermolecular interaction energies of the dimers evaluated by the supermolecule method depend on assemble modes of the dimers, leading us to the interpretation for hierarchical structures in crystals as well as generation of supramolecular chirality from achiral molecules in the crystals.