  Using a van der Waals density functional (vdW-DF) [Phys. Rev. Lett. 92,
246401 (2004)], we perform ab initio calculations for the adsorption energy of
benzene (Bz) on Cu(111) as a function of lateral position and height. We find
that the vdW-DF inclusion of nonlocal correlations (responsible for dispersive
interactions) changes the relative stability of eight binding-position options
and increases the binding energy by over an order of magnitude, achieving good
agreement with experiment. The admolecules can move almost freely along a
honeycomb web of "corridors" passing between fcc and hcp hollow sites via
bridge sites. Our diffusion barriers (for dilute and two condensed adsorbate
phases) are consistent with experimental observations. Further vdW-DF
calculations suggest that the more compact (hexagonal) Bz-overlayer phase, with
lattice constant a = 6.74 \AA, is due to direct Bz-Bz vdW attraction, which
extends to ~8 \AA. We attribute the second, sparser hexagonal Bz phase, with a
= 10.24 \AA, to indirect electronic interactions mediated by the metallic
surface state on Cu(111). To support this claim, we use a formal
Harris-functional approach to evaluate nonperturbationally the asymptotic form
of this indirect interaction. Thus, we can account well for benzene
self-organization on Cu(111).
