vdW-DF-ahcx: a range-separated van der Waals density functional hybrid

Hybrid density functionals replace a fraction of an underlying generalized-gradient approximation (GGA) exchange description with a Fock-exchange component. Range-separated hybrids (RSHs) also effectively screen the Fock-exchange component and thus open the door for characterizations of metals and adsorption at metal surfaces. The RSHs are traditionally based on a robust GGA, such as PBE [PRL $\textbf{77}$, 3865 (1996)], for example, as implemented in the HSE design [JPC $\textbf{118}$, 8207 (2003)]. Here we define a RSH extension to the van der Waals density functional (vdW-DF) method [ROPP $\textbf{78}$, 066501 (2015)], launching vdW-DF-ahcx. We use an analytical-hole (AH) framework [JCP $\textbf{128}$, 194105 (2008)] to characterize the GGA-type exchange in the vdW-DF-cx version [PRB $\textbf{89}$, 075148 (2014)], isolate the short-ranged exchange component, and define the new RSH. We find that the performance vdW-DF-ahcx compares favorably to (dispersion-corrected) HSE for descriptions of bulk (broad molecular) properties. We also find that it provides accurate descriptions of noble-metal surface properties, including CO adsorption.