In this work, we present a thorough assessment of the performance of some representative double-hybrid density functionals (revPBE0-DH-NL and B2PLYP-NL) as well as their parent hybrid and GGA counterparts, in combination with the most modern version of the nonlocal (NL) van der Waals correction to describe very large weakly interacting molecular systems dominated by noncovalent interactions. Prior to the assessment, an accurate and homogeneous set of reference interaction energies was computed for the supramolecular complexes constituting the L7 and S12L data sets by using the novel, precise, and efficient DLPNO-CCSD(T) method at the complete basis set limit (CBS). The correction of the basis set superposition error and the inclusion of the deformation energies (for the S12L set) have been crucial for obtaining precise DLPNO-CCSD(T)/CBS interaction energies. Among the density functionals evaluated, the double-hybrid revPBE0-DH-NL and B2PLYP-NL with the three-body dispersion correction provide remarkably accurate association energies very close to the chemical accuracy. Overall, the NL van der Waals approach combined with proper density functionals can be seen as an accurate and affordable computational tool for the modeling of large weakly bonded supramolecular systems.Financial support by the “Ministerio de Economía y Competitividad” (MINECO) of Spain and European FEDER funds through projects CTQ2011-27253 and CTQ2012-31914 is acknowledged. The support of the Generalitat Valenciana (Prometeo/2012/053) is also acknowledged. J.A. thanks the EU for the FP7-PEOPLE-2012-IEF-329513 grant. J.C. acknowledges the “Ministerio de Educación, Cultura y Deporte” (MECD) of Spain for a predoctoral FPU grant
