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Though YB6 and LaB6 share the same crystal structure, atomic valence electron configuration, and phonon modes, they exhibit drastically different phonon-mediated superconductivity. YB6 superconducts below 8.4 K, giving it the second-highest critical temperature of known borides, second only to MgB2. LaB6 does not superconduct until near-absolute zero temperatures (below 0.45 K), however. Though previous studies have quantified the canonical superconductivity descriptors of YB6's greater Fermi-level (Ef) density of states and higher electron-phonon coupling (EPC), the root of this difference has not been assessed with full detail of the electronic structure. Through chemical bonding, we determine low-lying, unoccupied 4f atomic orbitals in lanthanum to be the key difference between these superconductors. These orbitals, which are not accessible in YB6, hybridize with π B-B bonds and bring this π-system lower in energy than the σ B-B bonds otherwise at Ef. This inversion of bands is crucial: the optical phonon modes we show responsible for superconductivity cause the σ-orbitals of YB6 to change drastically in overlap, but couple weakly to the π-orbitals of LaB6. These phonons in YB6 even access a crossing of electronic states, indicating strong EPC. No such crossing in LaB6 is observed. Finally, a supercell (the M k-point) is shown to undergo Peierls-like effects in YB6, introducing additional EPC from both softened acoustic phonons and the same electron-coupled optical modes as in the unit cell. Overall, we find that LaB6 and YB6 have fundamentally different mechanisms of superconductivity, despite their otherwise near-identity.

Catalytic systems are complex and dynamic, exploring vast chemical spaces on multiple timescales. In this perspective, we discuss the dynamic behavior of fluxional, heterogeneous thermal and electrocatalysts and the ensembles of many isomers which govern their behavior. We develop a new paradigm in catalysis theory in which highly fluxional systems, namely sub-nano clusters, isomerize on a much shorter timescale than that of the catalyzed reaction, so macroscopic properties arise from the thermal ensemble of isomers, not just the ground state. Accurate chemical predictions can only be reached through a many-structure picture of the catalyst, and we explain the breakdown of conventional methods such as linear scaling relations and size-selected prevention of sintering. We capitalize on the forward-looking discussion of the means of controlling the size of these dynamic ensembles. This control, such that the most effective or selective isomers can dominate the system, is essential for the fluxional catalyst to be practicable, and their targeted synthesis to be possible. It will also provide a fundamental lever of catalyst design. Finally, we discuss computational tools and experimental methods for probing ensembles and the role of specific isomers. We hope that catalyst optimization using chemically informed descriptors of ensemble nature and size will become a new norm in the field of catalysis and have broad impacts in sustainable energy, efficient chemical production, and more.