We present transition metal-embedded (T@Gan) endohedral Ga-clusters as a favorable structural motif for superconductivity and develop empirical, molecule-based, electron counting rules that govern the hierarchical architectures that the clusters assume in binary phases. Among the binary T@Gan endohedral cluster systems, Mo8Ga41, Mo6Ga31, Rh2Ga9, and Ir2Ga9 are all previously known superconductors. The well-known exotic superconductor PuCoGa5 and related phases are also members of this endohedral gallide cluster family. We show that electron-deficient compounds like Mo8Ga41 prefer architectures with vertex-sharing gallium clusters, whereas electron-rich compounds, like PdGa5, prefer edge-sharing cluster architectures. The superconducting transition temperatures are highest for the electron-poor, corner-sharing architectures. Based on this analysis, the previously unknown endohedral cluster compound ReGa5 is postulated to exist at an intermediate electron count and a mix of corner sharing and edge sharing cluster architectures. The empirical prediction is shown to be correct and leads to the discovery of superconductivity in ReGa5. The Fermi levels for endohedral gallide cluster compounds are located in deep pseudogaps in the electronic densities of states, an important factor in determining their chemical stability, while at the same time limiting their superconducting transition temperatures.
Doping evolution of superconducting gaps and electronic densities of states in Ba(Fe
1−x
Co
x
)
2
As
2
iron pnictides
