Lanthanide hexaborides (LnB₆ ) have disparate and often anomalous properties, from structurally homogeneous mixed valency, to superconductivity, spectral anomalies, and unexplained phase transitions. It is unclear how such a diversity of properties may arise in the solids of identical crystal structures and seemingly very similar electronic structures. Building on our previous model for SmB₆ (mixed valent, with a peak in specific heat, and pressure induced magnetic phase transitions), we present a unifying dynamic bonding model for LnB₆ that explains simultaneously EuB₆ (possessing an anomalous peak in specific heat at low T, magnetic phase transitions, and no mixed valency), YbB₆ (mixed valent topological insulator), and rather ordinary LaB₆ . We show that Ln can engage in covalent bonding with boron, and, in some members of the LnB₆ family, also easily access alternative bonding states through the electron-phonon coupling. The accessibility, relative energetics, and bonding nature of the states involved dictate the properties.

The oxygen reduction reaction (ORR) plays a key role in renewable energy transformation processes. Unfortunately, it is inherently sluggish, which greatly limits its industrial application. Sub-nano-cluster-decorated electrode interfaces are promising candidate ORR electrocatalysts. However, understanding the nature of the active sites on these catalysts under electrocatalytic conditions presents a formidable challenge for both experiment and theory, due to their dynamic fluxional character. Here, we combine global optimization with the electronic Grand Canonical DFT to elucidate the structure and dynamics of subnano Ptnclusters deposited on electrified graphite. We show that, under electrochemical conditions, these clusters exist as statistical ensembles of multiple states, whose fluxionality is greatly affected by the applied potential, electrolyte, and adsorbate coverage. The results reveal the presence of potential-dependent active sites and, hence, reaction energetics.

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 (E_f) 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 E_f. 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.

The Sabatier activity volcano provides intuitive guide for catalyst design, but also imposes fundamental limitations on the composition and maximal activity of catalysts. We show that the ORR activity volcano is shifted and reshaped by the potential-dependent fluxionality of subnano cluster catalysts. Fluxionality causes the typically under-binding Ag/Au to gain optimal activity in the cluster form, and surpass Pt/Pd. Furthermore, isomerization of clusters as a function of the potential breaks linear scaling relationships, enabling surpassing the volcano “apex” relative to the bulk. The effect is likely general for fluxional cluster catalysts.

Samarium hexaboride is an anomaly, having many exotic and seemingly mutually incompatible properties. It was proposed to be a mixed-valent semiconductor, and later a topological Kondo insulator, and yet has a Fermi surface despite being an insulator. We propose a new and unified understanding of SmB6 centered on the hitherto unrecognized dynamical bonding effect: the coexistence of two Sm-B bonding modes within SmB6 , corresponding to different oxidation states of the Sm. The mixed valency arises in SmB6 from thermal population of these distinct minima enabled by motion of B. Our model simultaneously explains the thermal valence fluctuations, appearance of magnetic Fermi surface, excess entropy at low temperatures, pressure-induced phase transitions, and related features in Raman spectra and their unexpected dependence on temperature and boron isotope.