The μ₃ Model of Acids and Bases: Extending the Lewis Theory to Intermetallics

A central challenge in the design of new metallic materials is the elucidation of the chemical factors underlying the structures of intermetallic compounds. Analogies to molecular bonding phenomena, such as the Zintl concept, have proven very productive in approaching this goal. In this Article, we extend a foundational concept of molecular chemistry to intermetallics: the Lewis theory of acids and bases. The connection is developed through the method of moments, as applied to DFT-calibrated Hückel calculations. We begin by illustrating that the third and fourth moments (μ₃ and μ₄) of the electronic density of states (DOS) distribution tune the properties of a pseudogap. μ₃ controls the balance of states above and below the DOS minimum, with μ₄ then determining the minimum’s depth. In this way, μ₃ predicts an ideal occupancy for the DOS distribution. The μ₃-ideal electron count is used to forge a link between the reactivity of transition metals toward intermetallic phase formation, and that of Lewis acids and bases toward adduct formation. This is accomplished through a moments-based definition of acidity which classifies systems that are electron-poor relative to the μ₃-ideal as μ₃-acidic, and those that are electron-rich as μ₃-basic. The reaction of μ₃ acids and bases, whether in the formation of a Lewis acid/base adduct or an intermetallic phase, tends to neutralize the μ₃ acidity or basicity of the reactants. This μ₃-neutralization is traced to the influence of electronegativity differences at heteroatomic contacts on the projected DOS curves of the atoms involved. The role of μ₃-acid/base interactions in intermetallic phases is demonstrated through the examination of 23 binary phases forming between 3d metals, the stability range of the CsCl type, and structural trends within the Ti–Ni system