Orbital origins of helices and magic electron counts in the Nowotny chimney ladders: the 18 - n rule and a path to incommensurability.

Valence electron count is one of the key factors influencing the stability and structure of metals and alloys. However, unlike in molecular compounds, the origins of the preferred electron counts of many metallic phases remain largely mysterious. Perhaps the clearest-cut of such electron counting rules is exhibited by the Nowotny chimney ladder (NCL) phases, compounds remarkable for their helical structural motifs in which transition metal (T) helices serve as channels for a second set of helices formed from main group (E) elements. These phases exhibit density of states pseudogaps or band gaps, and thus special stability and useful physical properties, when their valence electron count corresponds to 14 electrons per T atom. In this Article, we illustrate, using DFT-calibrated Hückel calculations and the reversed approximation Molecular Orbital analysis, that the 14-electron rule of the NCLs is, in fact, a specific instance of an 18 - n rule emerging for T-E intermetallics, where n is the number of E-supported T-T bonds per T atom. The structural flexibility of the NCL series arises from the role of the E atoms as supports for these T-T bonds, which simply requires the E atoms to be as uniformly distributed within the T sublattice as possible. This picture offers a strategy for identifying other intermetallic structures that may be amenable to incommensurability between T and E sublattices.