Connector model for describing many-body interactions at surfaces

First-principles calculations based on density-functional theory indicate that high-order many-body interactions are significant in Al clusters on Al(110) and Al(100). The large number of many-body interactions renders a full-lattice-gas approach ineffective for such systems. To simplify the description of adsorbate interactions, we utilize two different schemes. First, we find effective parameters for Al adatom interactions using the leave-one-out cross-validation method. Second, we propose the connector model, which is based on additive single-atom connector units. The central idea of the connector model is to combine groups of many-body interactions into important structural units (e.g., step edges) that have a single interaction energy. We find that the connector model is more accurate and efficient in representing high-order many-body interactions than the traditional lattice-gas approach and it may be suitable for describing a variety of surface phenomena such as thin-film and crystal growth, adsorption, phase transitions, and catalysis at surfaces.