Benchmark coupled-cluster lattice energy of crystalline benzene and assessment of multi-level approximations in the many-body expansion.

The many-body expansion (MBE) is promising for the efficient, parallel computation of lattice energies in organic crystals. Very high accuracy should be achievable by employing coupled-cluster singles, doubles, and perturbative triples at the complete basis set limit [CCSD(T)/CBS] for the dimers, trimers, and potentially tetramers resulting from the MBE, but such a brute-force approach seems impractical for crystals of all but the smallest molecules. Here, we investigate hybrid or multi-level approaches that employ CCSD(T)/CBS only for the closest dimers and trimers and utilize much faster methods like Møller-Plesset perturbation theory (MP2) for more distant dimers and trimers. For trimers, MP2 is supplemented with the Axilrod-Teller-Muto (ATM) model of three-body dispersion. MP2(+ATM) is shown to be a very effective replacement for CCSD(T)/CBS for all but the closest dimers and trimers. A limited investigation of tetramers using CCSD(T)/CBS suggests that the four-body contribution is entirely negligible. The large set of CCSD(T)/CBS dimer and trimer data should be valuable in benchmarking approximate methods for molecular crystals and allows us to see that a literature estimate of the core-valence contribution of the closest dimers to the lattice energy using just MP2 was overbinding by 0.5 kJ mol-1, and an estimate of the three-body contribution from the closest trimers using the T0 approximation in local CCSD(T) was underbinding by 0.7 kJ mol-1. Our CCSD(T)/CBS best estimate of the 0 K lattice energy is -54.01 kJ mol-1, compared to an estimated experimental value of -55.3 ± 2.2 kJ mol-1.