Graph theoretical approach to evaluate molecular interactions in crystal

Abstract

We have applied the graph theory to estimation of interactions between electronic excitations in molecular crystals. Intramolecular and intermolecular excitations have been considered. The intermolecular interactions contain molecular integrals extended over two or three molecules, which we have called dimer or trimer. The intermolecular interactions, such as \pi-\pi stacking, is regarded as connections between neighboring molecules. To take up all dimers and trimers in molecular crystal, we have treated the connections between molecules as edges of a graph. The adjacency matrix of the graph and related quantity are utilized to count all dimers and trimers systematically. The absorption spectrum of TiOPc crystal in which we have defined three types of intermolecular excitations is presented.