Estimation and prediction of ellipsoidal molecular shapes in organic crystals based on ellipsoid packing

Crystal structure prediction has been one of the fundamental and challenging problems in materials science. It is computationally exhaustive to identify molecular conformations and arrangements in organic molecular crystals due to complexity in intra- and inter-molecular interactions. From a geometrical viewpoint, specific types of organic crystal structures can be characterized by ellipsoid packing. In particular, we focus on aromatic systems which are important for organic semiconductor materials. In this study, we aim to estimate the ellipsoidal molecular shapes of such crystals and predict them from single molecular descriptors. First, we identify the molecular crystals with molecular centroid arrangements that correspond to affine transformations of four basic cubic lattices, through topological analysis of the dataset of crystalline polycyclic aromatic molecules. The novelty of our method is that the topological data analysis is applied to arrangements of molecular centroids intead of those of atoms. For each of the identified crystals, we estimate the intracrystalline molecular shape based on the ellipsoid packing assumption. Then, we show that the ellipsoidal shape can be predicted from single molecular descriptors using a machine learning method. The results suggest that topological characterization of molecular arrangements is useful for structure prediction of organic semiconductor materials.