Mixed Gaussian and plane wave basis set implementation of the random phase approximation and of <i>σ</i> -functionals within the program package CP2K

The reliability of the random phase approximation (RPA) and of σ-functional methods in conjunction with the mixed Gaussian and plane wave (GPW) basis set scheme as implemented in the CP2K package is investigated. First, based on the results for thermochemical properties of molecules and structural properties of crystalline solids, we establish reliable computational setups for practical calculations. Next, we compare the results obtained with these setups to those from standard GPW basis set approaches. For molecules, the results of RPA and σ-functional calculations within the GPW scheme are slightly worse, though still comparable, to those obtained using the standard Gaussian basis set scheme, provided a large enough orbital basis set is employed in the GPW calculations. Furthermore, the GPW calculations using σ-functionals are clearly more accurate than RPA calculations and even more so than those of conventional Kohn-Sham methods in the prediction of reaction energies and barrier heights for main group chemistry. For crystalline solids, the RPA and σ-functional methods significantly outperform the conventional Perdew-Burke-Ernzerhof (PBE) method in determining lattice constants. However, only the RPA method provides improved results for bulk moduli, while the σ-functional method yields errors comparable to those of the PBE method. A comparison of the results of the plane wave basis set calculations with the projector augmented wave method shows reasonable consistency for lattice constants and bulk moduli.