  Exploring the role of van der Waals (vdW) forces on the adsorption of
molecules on extended metal surfaces has become possible in recent years thanks
to exciting developments in density functional theory (DFT). Among these newly
developed vdW-inclusive methods, interatomic vdW approaches that account for
the nonlocal screening within the bulk [V. G. Ruiz, W. Liu, E. Zojer, M.
Scheffler, and A. Tkatchenko, Phys. Rev. Lett. 108, 146103 (2012)] and improved
nonlocal functionals [J. Klimes, D. R. Bowler, and A. Michaelides, J. Phys.:
Condens. Matter 22, 022201(2010)] have emerged as promising candidates to
account efficiently and accurately for the lack of long-range vdW forces in
most popular DFT exchange-correlation functionals. Here we have used these two
approaches to compute benzene adsorption on a range of close-packed (111)
surfaces upon which it either physisorbs (Cu, Ag, and Au) or chemisorbs (Rh,
Pd, Ir, and Pt). We have thoroughly compared the performance between the two
classes of vdW-inclusive methods and when available compared the results
obtained with experimental data. By examining the computed adsorption energies,
equilibrium distances, and binding curves we conclude that both methods allow
for an accurate treatment of adsorption at equilibrium adsorbate-substrate
distances. To this end, explicit inclusion of electrodynamic screening in the
interatomic vdW scheme and optimized exchange functionals in the case of
nonlocal vdW density functionals is mandatory. Nevertheless, some discrepancies
are found between these two classes of methods at large adsorbate-substrate
separations.
