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The DFT/vdW-WF2 method, recently developed to include the van der Waals (vdW) interactions in density functional theory (DFT) using the maximally localized Wannier functions, is improved by taking into account screening effects and applied to the study of adsorption of rare gases and small molecules, H, CH, and HO on the Cu(111) metal surface, and of H on Al(111), and Xe on Pb(111), which are all cases where screening effects are expected to be important. Screening is included in DFT/vdW-WF2 by following different recipes, also considering the single-layer approximation adopted to mimic a screened metal substrate. Comparison of the computed equilibrium binding energies and distances, and the coefficients characterizing the adparticle-surface van der Waals interactions, with available experimental and theoretical reference data show that the improvement with respect to the original …