Extension and evaluation of the D4 London-dispersion model for periodic systems

London-dispersion effects are of great relevance to many aspects of materials science and for various condensed matter problems. In this work we present an adaptation and implementation of the DFT-D4 model [Caldeweyher et al., J. Chem. Phys., 2019, 150, 154122] for periodic systems. The main new ingredient are better computed reference polarizabilities for high coordination numbers (including alkaline metals, earth alkaline metals, and d-metals of group 3-5), which are consistently derived from periodic electrostatically embedded cluster calculations. Some technical extensions have been added concerning the coordination number, the partial charges, and the dispersion energy expression. To demonstrate the performance of the improved scheme, several test cases are considered, for which we compare D4 results to those of its predecessor D3(BJ) as well as to several other dispersion corrected methods. The largest improvements are observed for solid state polarizabilities of 16 inorganic salts, where the new D4 model achieves an unprecedented accuracy, surpassing its predecessor as well as other, computationally much more demanding approaches. For cell volumes and lattice energies of two sets of chemically diverse molecular crystals, the accuracy gain is less pronounced compared to the already excellently performing D3(BJ) method. For the challenging adsorption energies of small organic molecules on metallic as well as on ionic surfaces, DFT-D4 provides high accuracy similar to MBD/HI or uncorrected DFT/SCAN approaches. These results suggest the standard application of the proposed periodic D4 model as a physically improved yet computationally efficient dispersion correction for standard DFT calculations as well as low-cost approaches like semi-empirical or even force-field models.