Accuracy of basis-set extrapolation schemes for DFT-RPA correlation energies in molecular calculations

We construct a reference benchmark set for atomic and molecular random-phase-approximation (RPA) correlation energies in a density functional theory (DFT) framework at the complete basis set limit. This set is used to evaluate the accuracy of some popular extrapolation schemes for RPA all-electron molecular calculations. The results indicate that for absolute energies accurate results, clearly outperforming raw data, are achievable with two-point extrapolation schemes based on quintuple- and sextuple-zeta basis sets. Moreover, we show that results in good agreement with the benchmark can also be also obtained by using a semiempirical extrapolation procedure based on quadruple- and quintuple-zeta basis sets. Finally, we analyze the performance of different extrapolation schemes for atomization energies.