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 ∆Ee,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.
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We note that at the DSD-PBEP86–D3BJ/Def2-QZVPPD level of theory, we obtain a small imaginary frequency of 3.9 cm−1 for the TT dimer, which is attributed to numerical instability. At the DSD-PBEP86-D3BJ/Def2-TZVPPD level of theory, we obtain all real frequencies for the TT dimer.
