A critical comparison of CH∙∙∙π versus π∙∙∙π interactions in the benzene dimer: obtaining benchmarks at the CCSD(T) level and assessing the accuracy of lower scaling methods
In this study, we have established CCSD(T)/CBS (Complete Basis Set) limits for 3 stationary points on the benzene dimer potential energy surface, corresponding to the π∙∙∙π (parallel displaced or PD(C 2h ), minimum) and CH∙∙∙π (T-shaped or T(C 2v ), transition state) and tilted T-shaped (or TT(Cs), minimum) bonding scenarios considering both the structure and binding energy. The CCSD(T)/CBS binding energies are -2.65 ± 0.02 (PD), -2.74 ± 0.03 (T), and -2.83 ± 0.01 kcal mol -1 (TT). To this end, the CH∙∙∙π is ~0.2 kcal mol -1 stronger than the π∙∙∙π interaction, whereas the tilting of the CH donating benzene molecule with respect to the other benzene is worth 0.1 kcal mol -1 . As previously discussed in the literature, the MP2 level of theory does not provide a close match for either the energy or structure, yet the SCS-MP2 yields structures in excellent agreement with respect to the CCSD(T) result. It is found that the SCS-MI-MP2 also gives optimized structures very close to SCS-MP2 (within ~0.01 Å of the benchmark). Despite the closer match in structure, the spin-biased MP2 methods (SCS-, SCS-MI-, and SOS-MP2) incorrectly predict the relative stabilities of the isomers. That said, none of the spin biased MP2 methods offers a good compromise between energy and structure for the systems examined. Finally, the CCSD(T)/CBS benchmarks were used to assess the performance of 13 DFT functionals selected from different rungs of Jacob's ladder. Several functionals such as TPSS-D3, B3LYP-D3, B97-D, B97-D3, and B2PLYP-D3 provided a good description of the binding energies for both CH∙∙∙π and π∙∙∙π interactions, yielding values within 6% of the CCSD(T)/CBS benchmark values. Unlike the MP2 methods, these functionals correctly predict the relative stability of the PD(C 2h ) and T(C 2v ) dimers. Further, we find that there is no systematic improvement as Jacob's ladder is ascended (increased complexity of functional). The best functionals that result in a good compromise between structure and energy accuracy are B97-D3 and B2PLYP-D3 for both the CH∙∙∙π and π∙∙∙π interaction. Despite the impressive performance of these functionals, a challenge that remains is ensuring the transferability of these density functionals in accurately describing the interaction between dimers of larger aromatic molecules, the latter requiring high-level benchmarks for these systems.