RESUMEN
The random-phase approximation (RPA) includes a subset of higher than second-order correlation-energy contributions, but stays in the same complexity class as the second-order Møller-Plesset perturbation theory (MP2) in both Gaussian-orbital and plane-wave codes. This makes RPA a promising ab initio electronic structure approach for the binding energies of molecular crystals. Still, some issues stand out in practical applications of RPA. Notably, compact clusters of nonpolar molecules are poorly described, and the interaction energies strongly depend on the reference single-determinant state. Using the many-body expansion of the binding energy of a crystal, we investigate those issues and the effect of beyond-RPA corrections. We find the beneficial effect of quartic-scaling exchange and non-ring coupled-cluster doubles corrections. The nonadditive interactions in compact trimers of molecules are improved by using the self-consistent Hartree-Fock orbitals instead of the usual Kohn-Sham states, but this kind of orbital input also leads to underestimated dimer energies. Overall, a substantial improvement over the RPA with a renormalized singles approach is possible at a modest quartic-scaling cost, which encourages further research into additional RPA corrections.
RESUMEN
The relative energies of different phases or polymorphs of molecular solids can be small, less than a kilojoule/mol. A reliable description of such energy differences requires high-quality treatment of electron correlations, typically beyond that achievable by routinely applicable density functional theory (DFT) approximations. At the same time, high-level wave function theory is currently too computationally expensive. Methods employing an intermediate level of approximations, such as Møller-Plesset (MP) perturbation theory and the random phase approximation (RPA), are potentially useful. However, their development and application for molecular solids has been impeded by the scarcity of necessary benchmark data for these systems. In this work, we employ the coupled-cluster method with singles, doubles, and perturbative triples to obtain a reference-quality many-body expansion of the binding energy of four crystalline hydrocarbons with a varying π-electron character: ethane, ethene, and cubic and orthorhombic forms of acetylene. The binding energy is resolved into explicit dimer, trimer, and tetramer contributions, which facilitates the analysis of errors in the approximate approaches. With the newly generated benchmark data, we test the accuracy of MP2 and non-self-consistent RPA. We find that both of the methods poorly describe the non-additive many-body interactions in closely packed clusters. Using different DFT input states for RPA leads to similar total binding energies, but the many-body components strongly depend on the choice of the exchange-correlation functional.
