Relative stability of complexes of six-carbon-rings with variable numbers of double bonds: DFT and ab initio results

Protein-ligand interactions, including enzyme-drug interactions, often depend on a variety of non-covalent bonds. Ring-ring interactions, though generally weaker than other non-covalent interactions, are important both in the binding of ligands to proteins, and also in the specific 3-D orientation of the ligand molecule in the protein binding site. We calculated the counterpoise-corrected interaction energies and relative stabilities of complexes of six-membered carbon rings using MP2/aug-cc-pvdz. These two-ring complexes, each with three, two, one, or no double bonds per ring, serve as models for the above mentioned protein-ligand binding. Using MP2/aug-cc-pvdz as a standard, we also evaluated the accuracy of MP2 with smaller basis sets. Further we compared Hartree-Fock and several DFT methods with MP2 in order to see if these less resource-intensive methods could achieve and accuracy comparable to MP2. We find that smaller basis sets within the MP2 theory reproduce accurate trends and relative energies of complexes compared to aug-cc-pvdz, and the HCTH407 DFT method can reproduce accurate relative energies for most of the complexes studied here. We also compute HCTH407-level polarizabilities of the rings and examine the relationship between these values and the interaction energies.