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).
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