Modelling the interaction in a benzene dimer

The interaction between aromatic rings is a fundamental problem in material science and biochemistry. These interactions are generally found to stabilise protein molecules and the double helical structure of DNA, and they also play an important role in the recognition processes in biological and non-biological systems. However, the complexity and variety in the structures and components of aromatic compounds are major obstacles to investigating their interactions. In this study, the simplest case of aromatic interactions, which is the interaction between two benzene rings, is modelled using a continuous approximation. Assuming a constant atomic surface density and modelling the structure of a benzene molecule as a combination of two rings, namely an inner carbon ring and an outer hydrogen ring, the van der Waals interaction between any two benzene rings can be obtained as the sum of four interactions. The major result obtained here is an analytical expression for the potential energy which can then be used to predict equilibrium configurations for two interacting benzene molecules. Moreover, we find that at sufficiently large distances between the two benzene molecules, the orientational angle φ at which the interaction energy is a minimum can be approximated by the arctan of the ratio of two separation distances in two mutually perpendicular directions.