On the application of group theory to molecular excitons

In this paper a group theoretical approach was employed for the classification and construction of molecular exciton wavefunctions for two important crystal structures (naphthalene--anthracene and benzene), utilizing the representation theory of finite groups. The generally valid scheme requires only cyclic boundary conditions (being explicitly imposed on all space group operations, including rotations and reflections). Even though these symmetry considerations are insufficient to determine crystal wavefunctions belonging to a general k vector, it is still possible to write a simple expression for such wavefunctions. This is achieved for cases where the nonvanishing exciton transfer integrals are confined to molecular interactions along symmetry axes and/or planes.