Assessment of three-body dispersion models against coupled-cluster benchmarks for crystalline benzene, carbon dioxide, and triazine

To study the contribution of three-body dispersion to crystal lattice energies, we compute the three-body contributions to the lattice energies for crystalline benzene, carbon dioxide, and triazine using various computational methods. We show that these contributions converge quickly as the intermolecular distances between the monomers grow. In particular, the smallest value among the three pairwise intermonomer closest-contact distances, R_min, shows a strong correlation with the three-body contribution to the lattice energy, and, here, the largest of the closest-contact distances, R_max, serves as a cutoff criterion to limit the number of trimers to be considered. We considered all trimers up to R_max=15Å. The trimers with R_min<4Å contribute 90.4%, 90.6%, and 93.9% of the total three-body contributions for crystalline benzene, carbon dioxide, and triazine, respectively, for the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] method. For trimers with R_min>4Å, the second-order Møller-Plesset perturbation theory (MP2) supplemented with the Axilrod-Teller-Muto (ATM) three-body dispersion correction reproduces the CCSD(T) values for the cumulative three-body contributions with errors of less than 0.1 kJ mol^-1. Moreover, three-body contributions are converged within 0.15 kJ mol^-1 by R_max=10Å. From these results, it appears that in molecular crystals where dispersion dominates the three-body contribution to the lattice energy, the trimers with R_min>4Å can be computed with the MP2+ATM method to reduce the computational cost, and those with R_max>10Å appear to be basically negligible.