Assessment of random phase approximation and second-order Møller-Plesset perturbation theory for many-body...

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.