Prototypical $π$–$π$ dimers re-examined by means of high-level CCSDT(Q) composite ab initio methods

The benzene–ethene and parallel-displaced (PD) benzene–benzene dimers are the most fundamental systems involving π–π stacking interactions. Several high-level ab initio investigations calculated the binding energies of these dimers using the coupled-cluster with singles, doubles, and quasi-perturbative triple excitations [CCSD(T)] method at the complete basis set [CBS] limit using various approaches such as reduced virtual orbital spaces and/or MP2-based basis set corrections. Here, we obtain CCSDT(Q) binding energies using a Weizmann-3-type approach. In particular, we extrapolate the self-consistent field (SCF), CCSD, and (T) components using large heavy-atom augmented Gaussian basis sets [namely, SCF/jul-cc-pV{5,6}Z, CCSD/jul-cc-pV{Q,5}Z, and (T)/jul-cc-pV{T,Q}Z]. We consider post-CCSD(T) contributions up to CCSDT(Q), inner-shell, scalar-relativistic, and Born–Oppenheimer corrections. Overall, our best relativistic, all-electron CCSDT(Q) binding energies are ∆E_e,all,rel = 1.234 (benzene–ethene) and 2.550 (benzene–benzene PD), ∆H₀ = 0.949 (benzene–ethene) and 2.310 (benzene–benzene PD), and ∆H₂₉₈ = 0.130 (benzene–ethene) and 1.461 (benzene–benzene PD) kcal mol⁻¹. Important conclusions are reached regarding the basis set convergence of the SCF, CCSD, (T), and post-CCSD(T) components. Explicitly correlated calculations are used as a sanity check on the conventional binding energies. Overall, post-CCSD(T) contributions are destabilizing by 0.028 (benzene–ethene) and 0.058 (benzene–benzene) kcal mol⁻¹, and thus, they cannot be neglected if sub-chemical accuracy is sought (i.e., errors below 0.1 kcal mol⁻¹). CCSD(T)/aug-cc-pwCVTZ core–valence corrections increase the binding energies by 0.018 (benzene–ethene) and 0.027 (benzene–benzene PD) kcal mol⁻¹. Scalar-relativistic and diagonal Born–Oppenheimer corrections are negligibly small. We use our best CCSDT(Q) binding energies to evaluate the performance of MP2-based, CCSD-based, and lower-cost composite ab initio procedures for obtaining these challenging π–π stacking binding energies.