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Two hybrid van der Waals density functionals (vdW-DFs) are constructed using25%, 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-covalentbinding properties of molecules are assessed. For properties related tocovalent binding, atomization energies (G2-1 set), molecular reaction energies(G2RC set), as well as ionization energies (G21IP set) are benchmarked againstexperimental reference values. We find that hybrid-vdW-DF-cx yields resultsthat are rather similar to those of the standard non-empirical hybrid PBE0 [JCP110, 6158 (1996)]. Hybrid vdW-DF2 follows somewhat different trends, showing onaverage significantly larger deviations from the reference energies, with a MADof 14.5 kcal/mol for the G2-1 set. Non-covalent binding properties of moleculesare assessed using the S22 benchmark set of non-covalently bonded dimers andthe X40 set of dimers of small halogenated molecules, using wavefunction-basedquantum chemistry results for references. For the S22 set, hybrid-vdW-DF-cxperforms better than standard vdW-DF-cx for the mostly hydrogen-bonded systems.Hybrid-vdW-DF2 offers a slight improvement over standard vdW-DF2. Similartrends are found for the X40 set, with hybrid-vdW-DF-cx performing particularlywell for binding involving the strongly polar hydrogen halides, but poorly forsystems with tiny binding energies. Our study of the X40 set reveals both thepotential of mixing Fock exchange with vdW-DF, but also highlights shortcomingsof the hybrids constructed here. The solid performance of hybrid-vdW-DF-cx forcovalent-bonded systems, as well as the strengths and issues uncovered fornon-covalently bonded systems, makes this study a good starting point fordeveloping even more precise hybrid vdW-DFs.

Assessment of two hybrid van der Waals density functionals for covalent and non-covalent binding of molecules