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.