Two hybrid van der Waals density functionals (vdW-DFs) are constructed using 25%, Fock exchange with i) the consistent-exchange vdW-DF-cx functional and ii) with the vdW-DF2 functional. The ability to describe covalent and non-covalent binding properties of molecules are assessed. For properties related to covalent binding, atomization energies (G2-1 set), molecular reaction energies (G2RC set), as well as ionization energies (G21IP set) are benchmarked against experimental reference values. We find that hybrid-vdW-DF-cx yields results that are rather similar to those of the standard non-empirical hybrid PBE0 [JCP 110, 6158 (1996)]. Hybrid vdW-DF2 follows somewhat different trends, showing on average significantly larger deviations from the reference energies, with a MAD of 14.5 kcal/mol for the G2-1 set. Non-covalent binding properties of molecules are assessed using the S22 benchmark set of non-covalently bonded dimers and the X40 set of dimers of small halogenated molecules, using wavefunction-based quantum chemistry results for references. For the S22 set, hybrid-vdW-DF-cx performs better than standard vdW-DF-cx for the mostly hydrogen-bonded systems. Hybrid-vdW-DF2 offers a slight improvement over standard vdW-DF2. Similar trends are found for the X40 set, with hybrid-vdW-DF-cx performing particularly well for binding involving the strongly polar hydrogen halides, but poorly for systems with tiny binding energies. Our study of the X40 set reveals both the potential of mixing Fock exchange with vdW-DF, but also highlights shortcomings of the hybrids constructed here. The solid performance of hybrid-vdW-DF-cx for covalent-bonded systems, as well as the strengths and issues uncovered for non-covalently bonded systems, makes this study a good starting point for developing even more precise hybrid vdW-DFs.
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