The Accuracy of Density Functional Theory in the Description of Cation-π and π-Hydrogen Bond Interactions

Cation-pi and pi-hydrogen bond interactions are ubiquitous in protein folding, molecular recognition, and ligand-receptor associations. As such systems are routinely studied at the DFT level, it becomes essential to understand the underlying accuracy of the plethora of density functionals currently available for the description of these interactions. For that purpose, we carried out theoretical calculations on two small model systems (benzene-Na+ and benzene H2O) that represent a paradigm for those intermolecular interactions and systematically tested 46 density functionals against the results of high-level post-HF methods, ranging from MP2 to extrapolated CCSD(T)/CBS. A total of 13 basis sets were also tested to examine the convergence of the interaction energy with basis set size. The convergence was surprisingly fast, with deviations below 0.2 kcal/mol for double-xi polarized basis sets with diffuse functions. Concerning functional benchmarking, the Truhlar group functionals were particularly well suited for the description of the pi-hydrogen bond interactions. In the case of cation-pi interactions, there was not a clear correlation between accuracy and functional sophistication. Despite the large number of functionals predicting interaction energies within chemical accuracy (five for pi-hydrogen bond and 20 for cation-pi interactions), not a single functional has shown chemical accuracy in both cases. Moreover, if we calculate the average error for these two interactions, only two density functionals resulted in an average error below 1.0 kcal/mol (M06 and HCTH, with average errors of 0.6 and 0.8 kcal/mol). The obtained results serve as a guide for future computer simulations on this kind of system.