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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. 

The focal-point approximation can be used to estimate a high-accuracy, slow quantum chemistry computation by combining several lower-accuracy, faster computations. We examine the performance of focal-point methods by combining second-order Møller–Plesset perturbation theory (MP2) with coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] for the calculation of harmonic frequencies and that of fundamental frequencies using second-order vibrational perturbation theory (VPT2). In contrast to standard CCSD(T), the focal-point CCSD(T) method approaches the complete basis set (CBS) limit with only triple-ζ basis sets for the coupled-cluster portion of the computation. The predicted harmonic and fundamental frequencies were compared with the experimental values for a set of 20 molecules containing up to six atoms. The focal-point method combining CCSD(T)/aug-cc-pV(T + d)Z with CBS-extrapolated MP2 has mean absolute errors vs experiment of only 7.3 cm−1 for the fundamental frequencies, which are essentially the same as the mean absolute error for CCSD(T) extrapolated to the CBS limit using the aug-cc-pV(Q + d)Z and aug-cc-pV(5 + d)Z basis sets. However, for H2O, the focal-point procedure requires only 3% of the computation time as the extrapolated CCSD(T) result, and the cost savings will grow for larger molecules.