Generality of the 18-n Rule: Intermetallic Structural Chemistry Explained through Isolobal Analogies to Transition Metal Complexes

Intermetallic phases exhibit a vast structural diversity in which electron count is known to be one controlling factor. However, chemical bonding theory has yet to establish how electron counts and structure are interrelated for the majority of these compounds. Recently, a simple bonding picture for transition metal (T)–main group (E) intermetallics has begun to take shape based on isolobal analogies to molecular T complexes. This bonding picture is summarized in the 18-n rule: each T atom in a T–E intemetallic phase will need 18-n electrons to achieve a closed-shell 18-electron configuration, where n is the number of electron pairs it shares with other T atoms in multicenter interactions isolobal to T–T bonds. In this Article, we illustrate the generality of this rule with a survey over a wide range of T–E phases. First, we illustrate how three structural progressions with changing electron counts can be accounted for, both geometrically and electronically, with the 18-n rule: (1) the transition between the fluorite and complex β-FeSi2 types for TSi2 phases; (2) the sequence from the marcasite type to the arsenopyrite type and back to the marcasite type for TSb2 compounds; and (3) the evolution from the AuCu3 type to the ZrAl3 and TiAl3 types for TAl3 phases. We then turn to a broader survey of the applicability of the 18-n rule through a study of the following 34 binary structure types: PtHg4, CaF2 (fluorite), Fe3C, CoGa3, Co2Al5, Ru2B3, β-FeSi2, NiAs, Ni2Al3, Rh4Si5, CrSi2, Ir3Ga5, Mo3Al8, MnP, TiSi2, Ru2Sn3, TiAl3, MoSi2, CoSn, ZrAl3, CsCl, FeSi, AuCu3, ZrSi2, Mn2Hg5, FeS2 (oP6, marcasite), CoAs3 (skutterudite), PdSn2, CoSb2, Ir3Ge7, CuAl2, Re3Ge7, CrP2, and Mg2Ni. Through these analyses, the 18-n rule is established as a framework for interpreting the stability of 341 intermetallic phases and anticipating their properties.