A promising approach to developing improved potential functions for modeling macromolecular interactions consists of combining protein structural analysis, quantum mechanical calculations on small molecule models, and molecular mechanics potential decomposition. Here we apply this approach to the interactions of pairs of ring-containing amino acids in proteins. We find reasonable qualitative agreement between molecular mechanics and quantum chemistry calculations, both over one-dimensional projections of the binding free energy landscape for amino acid homodimers and over a set of homodimers and heterodimers from experimentally observed protein crystal structures. The molecular mechanics landscapes are a sum of charge-charge and Lennard-Jones contributions; short-range quantum mechanical effects such as charge transfer appear not to be significant in ring side chain interactions. We also find a reasonable degree of correlation between the molecular mechanics energy landscapes and the distributions of dimer geometries observed in protein structures, suggesting that the intrinsic dimer interaction energies do contribute to packing of side chains in proteins rather than being overwhelmed by the numerous interactions with other protein atoms and solvent. These results demonstrate that interactions involving aromatic residues and proline can be fairly well modeled using current molecular mechanics force fields, but there is still room for improvement, particularly for interactions involving proline and tyrosine.