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 [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.