Convergence of the many-body expansion with respect to distance cutoffs in crystals of polar molecules: Acetic acid, formamide, and imidazole

The many-body expansion, where one computes the total energy of a supersystem as the sum of the dimer, trimer, tetramer, etc., subsystems, provides a convenient approach to compute the lattice energies of molecular crystals. We investigate approximate methods for computing the non-additive three-body contributions to the crystal lattice energy of the polar molecules acetic acid, imidazole, and formamide, comparing to coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] level benchmarks. Second-order Møller-Plesset perturbation theory (MP2), if combined with a properly damped Axilrod-Teller-Muto dispersion potential, displays excellent agreement with CCSD(T) at a substantially reduced cost. Errors between dispersion-corrected MP2 and CCSD(T) are less than 1 kJ mol-1 for all three crystals. However, the three-body energy requires quite large distance cutoffs to converge, up to 20 Å or more.