Fractal nature of benzene stacking interactions

Benzene and other aromatic groups, as planar groups with [Formula: see text] electrons cloud, tend to form stacking interactions which have an important role in various chemical and biological processes. In order to have a better insight in the nature of these interactions, we have performed a fractal analysis on patterns of electron density and electrostatic potential for two benzenes in stacking interaction. The calculated fractal dimension follows the trend of the calculated interaction energy for the interplanar distances of 4.0 to 6.0 Å, which partially coincides with the strongest attractive stacking interactions. The fractal dimension vs. energy dependences were fitted with the logistic curve, and the fitting coefficient was 0.96 up to 1.00.

For the benzene stacking interaction energy, with a range of conformations and distances between two benzenes, DFT calculations at the B3LYP+D3/aug-cc-pVDZ level were performed with the TURBOMOLE software. The fractal analysis for electron density and electrostatic potential has been done by python scripting.