Exploring Atom-Pairwise and Many-Body Dispersion Corrections for the BEEF-vdW Functional

The Bayesian error estimation functional (BEEF-vdW) is widely used in surface science and catalysis, because it provides a balanced description of molecular, surface and solid state systems, along with reliable error estimates. However, the nonlocal van-der-Waals density functional (vdW-DF2) employed in BEEF-vdW {can be computationally costly and displays relatively low accuracy for molecular systems.} Therefore, this work explores whether atom-pairwise and many-body dispersion treatments represent viable alternatives to using the vdW-DF2 functional with BEEF-vdW. To this end, we investigate the performance of commonly used atom-pairwise corrections (\emph{i.e.} the Tkatchenko-Scheffler, TS, and the exchange-hole dipole moment, XDM, approaches) and many-body dispersion (MBD) treatments for molecular, surface and solid-state systems. The results indicate that atom pairwise methods such as TS and particularly XDM provide a good balance of cost and accuracy across all systems.