General model for molecular interactions in a benzene dimer
Modelling molecular interactions in a benzene dimer is a typical example of a class of problems involving aromatic molecules. Although many studies on the benzene dimer have been carried out both theoretically and experimentally and energetically favorable structures of a benzene dimer have been found, an investigation of all equilibrium structures of a benzene dimer has not so far been done. Previously, the present authors investigated the interaction energy and geometries of a benzene dimer for the special case in which only one rotational angle is used to describe the relative position between two benzene molecules. In general, two rotational angles are necessary to describe the most general relative orientation. Here, we apply the same approach in which the discrete atomic structure of a benzenemolecule is replaced by two continuous rings of atoms, namely an inner carbon ring and an outer hydrogen ring with average constant atomic densities and the molecular interaction forces are calculated from the Lennard-Jones potential function. An analytical expression for the interaction energy is obtained which we use to determine all equilibrium structures of a benzene dimer as well as to determine those domains in which certain configurations are more favorable than others. Our results show that parallel, T-shaped, parallel displaced and tilted structures are all possible configurations of a benzene dimer and they exist at different regions of vertical and offset distances at different energy levels.