Theoretical design of stable small aluminium–magnesium binary clusters

Abstract

We explore in detail the potential energy surfaces of the Al_xMg_y (x, y = 1–4) systems as case studies to test the utility and limitations of simple rules based on electron counts and the phenomenological shell model (PSM) for bimetallic clusters. We find that it is feasible to design stable structures that are members of this set of small Al–Mg binary clusters, using simple electron count rules, including the classical 4n + 2 Hückel model, and the most recently proposed PSM. The thermodynamic stability of the title compounds has been evaluated using several different descriptors, including the fragmentation energies and the electronic structure of the systems. Three stable systems emerge from the analysis: the Al₄Mg, Al₂Mg₂ and Al₄Mg₄ clusters. The relative stability of Al₄Mg is explained by the stability of the Al₄²⁻ subunit to which the Mg atom donates its electrons. Here the Mg²⁺ sits above the aromatic 10 π-electron Al₄²⁻ planar ring. The Al₂Mg₂ and Al₄Mg₄ clusters present more complicated 3D structures, and their stabilities are rationalized as a consequence of their closed shell nature in the PSM, with 10 and 20 itinerant electrons, respectively.