π–π interactions between benzene and graphene by means of large-scale DFT-D4 calculations

The adsorption of aromatic molecules on graphene is essential for many applications. This study addresses the issues associated with predicting accurate binding energies between graphene and benzene using a series of increasingly larger nanographene (C₂₄H₁₂, C₅₄H₁₈, C₉₆H₂₄, C₁₅₀H₃₀, and C₂₁₆H₃₆). For this purpose, we consider several DFT methods developed for accurately predicting noncovalent interactions, namely, PBE0-D4, ωB97X-D4, PW6B95-D4, and MN15. The C₁₅₀H₃₀ and C₂₁₆H₃₆ nanographene predict binding energies converged to sub-kJ mol⁻¹ with respect to the size of the nanographene. For the largest C₂₁₆H₃₆ nanographene, we obtain binding energies of −37.9 (MN15), −39.7 (ωB97X-D4), −40.7 (PW6B95-D4), and −49.1 (PBE0-D4) kJ mol⁻¹. Averaging these values, we obtain ΔE_e,bind = −41.8 ± 8.6 kJ mol⁻¹, which translates to ΔH_0,bind = −41.0 ± 8.6 kJ mol⁻¹. This theoretical binding energy agrees with the experimental value of −48.2 ± 7.7 kJ/mol within overlapping uncertainties.