Random-phase approximation vs Møller–Plesset perturbation theory for many-body energy contributions of hydrogen-bonded molecular solids

The fragment-based approach is a promising strategy for applying correlated-wavefunction methods to lattice energies of molecular solids. A key requirement is the efficient inclusion of the long-distance and nonadditive contributions to the many-body expansion (MBE) of the lattice energy. This is especially important in crystals of polar molecules, where MBE converges slowly with distance. In this context, we compare the simplest coupled-cluster approach-the random-phase approximation (RPA)-against the well-established methodology of Møller-Plesset (MP) perturbation theory. Using the examples of solid ammonia, methanol, and formic acid, we show that the RPA with singles corrections based on the Kohn-Sham (KS) Perdew-Burke-Ernzerhof (PBE) orbitals yields near-benchmark accuracy for the two-body contributions. However, for any PBE-based variant of RPA, the three- and four-body contributions suffer from artifacts. For the nonadditive terms, the Hartree-Fock (HF) orbitals appear necessary. In fact, we find that the HF-based RPA with additional corrections recovers the nonadditive interactions about as accurately as the more expensive MP2.5 method. This is a departure from the typical KS-based RPA and an indication that the HF-based RPA can serve as an alternative to the usual MP methods in accurate approximations of the crystal lattice energy.