Monte Carlo Study of the Diffusion of CO Molecules inside Anthraquinone Hexagons on Cu(111)*

Using Monte Carlo calculations of the two-di\-men\-sion\-al (2D) lattice gas model, we study the diffusion of CO molecules inside anthraquinone (AQ) hexagons on a Cu(111) plane. We use experimentally-derived CO-CO interactions\footnote{K.L. Wong, $\dots$, L. Bartels, J.\ Chem.Phys.{\bf 123}, 201102 (2005)} and the analytic expression for the long-range surface-state- mediated interactions\footnote{K. Berland, TLE, and P. Hyldgaard, Phys.Rev.\ B {\bf 80}, 155431 (2009)} to describe the CO-AQ interactions. We assume that the CO-CO interactions are not affected by the presence of AQ's and that the CO-AQ interactions can be controlled by varying the intra-surface-state (ISS) reflectance $r$ and the ISS phase shift $\delta$ of the indirect-electronic adsorbate-pair interactions. Comparing our results with experimental observations, we find that not only pair but also surface-state-mediated trio interactions\footnote{P. Hyldgaard and T.L. Einstein, EPL {\bf 59}, 265 (2002)} are needed to understand the data.