Role of high-order Fourier terms for stability of monolayer-surface structures: Numerical simulations

The role of high-order atom-surface Fourier terms is analyzed for the monolayer with coverage $\ensuremath{\theta}=\frac{3}{7}$ on (111) surface in cells with variable number of adsorbate atoms, allowed to relax to obtain the global minimum in each of the unit cells. A Fourier expansion with one or two shells of reciprocal cell vectors is used and three different models for the lateral interactions in the monolayer are tested, from purely repulsive to a real HFD-B2 potential. It is found that the simple commensurate $(\sqrt{7}\ifmmode\times\else\texttimes\fi{}\sqrt{7})R19.1\ifmmode^\circ\else\textdegree\fi{}$ three-atom structure is the most stable only when the contribution of the second Fourier term is included. In contrast to the conventional view, higher corrugation of the single-term Fourier model favors incommensurability. Evidence is collected that the high-order Fourier terms are mandatory for the stabilization of commensurate structures of an infinite monolayer.