Periodic implementation of the random phase approximation with numerical atomic orbitals and dual reciprocal space grids

The random phase approximation (RPA) has emerged as a prominent first-principles method in material science, particularly to study the adsorption and chemisorption of small molecules on surfaces. However, its widespread application is hampered by its relatively high computational cost. Here, we present a well-parallelised implementation of the RPA with localised atomic orbitals and pair-atomic density fitting, which is especially suitable for studying two-dimensional systems. Through a dual $\textbf{k}$-grid scheme, we achieve fast and reliable convergence of RPA correlation energies to the thermodynamic limit. We demonstrate the efficacy of our implementation through an application to the adsorption of CO on MgO(001) using PBE input orbitals (RPA@PBE) Our calculated adsorption energy in in good agreement with previously published RPA@PBE studies, but, as expected, overestimates the experimentally available adsorption energies as well as recent CCSD(T) results.