Theoretical Predictions of Novel Superconducting Phases of BaGe₃ Stable at Atmospheric and High Pressures

A series of new superconducting binary silicides and germanides have recently been synthesized under high-pressure high-temperature conditions. A representative member of this group, BaGe₃, was theoretically investigated using evolutionary structure searches coupled with structural analogies in the pressure range from 1 atm to 250 GPa, where three new phases were discovered. At 1 atm, in addition to the synthesized <i>P</i>6₃/<i>mmc</i> phase, we predicted two new phases, <i>I</i>4/<i>mmm</i> and <i>Amm</i>2, to be dynamically stable. The <i>Amm</i>2 structure comprises Ge clusters and triangular prisms intercalated with Ba and Ge atoms, a unique structural motif unknown to this group. The <i>I</i>4/<i>mmm</i> structure has been previously synthesized in binary silicides and is calculated to be thermodynamically stable in BaGe₃ between 15.6 and 35.4 GPa. Above 35.4 GPa, two new phases of <i>P</i>6̅<i>m</i>2 and <i>R</i>3̅<i>m</i> symmetry become the global minima and remain so up to the highest pressure considered. These two phases have very similar enthalpies, and both feature layers of double Kagome nets of Ge intercalated with Ba–Ge layers. The predicted phases are suggested to be metallic with itinerant electrons and to be potentially superconducting from the considerable electron–phonon coupling strength. Density functional perturbation calculations combined with the Allen–Dynes-modified McMillan formula were used to estimate the superconducting critical temperatures (<i>T</i>_c) for these new phases, which, with slight pressure variations, are comparable to the experimental <i>T</i>_c measured for the <i>P</i>6₃/<i>mmc</i> phase

DFT‑D Investigation of Active and Dormant Methylaluminoxane (MAO) Species Grafted onto a Magnesium Dichloride Cluster: A Model Study of Supported MAO

Density functional theory calculations were carried out to study the interaction of various models for methylaluminoxane and the active and dormant species in polymerization with the (110) MgCl₂ surface. MAO species may bind to the surface via Al–Cl, Mg–O, and Al−μ-CH₃–Mg bonds. Our results suggest that the activity of supported MAO may be higher than of homogeneous MAO because the support stabilizes (AlOMe)_<i>n</i>·(AlMe₃)_<i>m</i>, precursors to the active species in polymerization. Moreover, the support lowers the free energy of formation of species that are active in polymerization relative to those that are dormant. Finally, it may be that the support decreases the energy associated with the cation–anion separation in [Cp₂ZrMe]⁺[Me­(AlOMe)_<i>n</i>]⁻, a species that is likely dormant in homogeneous processes, hinting that the support has the possibility of increasing the number of potentially active sites

High Pressure Potassium Polyhydrides: A Chemical Perspective

Doping hydrogen by an impurity has emerged as a possible route toward the metallization of hydrogen at experimentally achievable pressures. Evolutionary structure searches coupled with density functional theory calculations have been employed to determine the most stable stoichiometries and structures of potassium polyhydrides, KH_<i>n</i> <i>n</i> > 1, under pressure. Stabilization occurs at pressures as low as 3 GPa, but KH₅, the most stable stoichiometry throughout most of the pressure regime considered, does not become metallic until <i>P</i> > 300 GPa. There are, however, suggestions of metallicity in metastable phases at 100 GPa. Detailed structural, electronic, and chemical analyses of the emergent hydrogenic motifs are provided and related to the rest of the alkali series. The softness of the alkali metal cation is shown to be related to the formation of symmetrical H₃^– molecules in compressed alkali metal polyhydrides

Compressed Cesium Polyhydrides: Cs⁺ Sublattices and H₃^– Three-Connected Nets

The cesium polyhydrides (CsH_<i>n</i>, <i>n</i> > 1) are predicted to become stable, with respect to decomposition into CsH and H₂, at pressures as low as 2 GPa. The CsH₃ stoichiometry is found to have the lowest enthalpy of formation from CsH and H₂ between 30 and 200 GPa. Evolutionary algorithms predict five distinct, mechanically stable, nearly isoenthalpic CsH₃ phases consisting of H₃^– molecules and Cs⁺ atoms. The H₃^– sublattices in two of these adopt a hexagonal three-connected net; in the other three the net is twisted, like the silicon sublattice in the α-ThSi₂ structure. The former emerge as being metallic below 100 GPa in our screened hybrid density functional theory calculations, whereas the latter remain insulating up to pressures greater than 250 GPa. The Cs⁺ cations in the most-stable <i>I</i>4₁/<i>amd</i> CsH₃ phase adopt the positions of the Cs atoms in Cs-IV, and the H₃^– molecules are found in the (interstitial) regions which display a maximum in the electron density

The Dynamic Equilibrium Between (AlOMe)_<i>n</i> Cages and (AlOMe)_<i>n</i>·(AlMe₃)_<i>m</i> Nanotubes in Methylaluminoxane (MAO): A First-Principles Investigation

Species likely to be present in methylaluminoxane (MAO) are studied via dispersion-corrected DFT, which we show is able to accurately predict thermochemical parameters for the dimerization of trimethylaluminum (TMA). Both cage-like, (AlOMe)_{<i>n</i>,<i>c</i>}, and TMA-bound nanotubes, (AlOMe)_{<i>n</i>,<i>t</i>}·(AlMe₃)_<i>m</i>, are found to be important components of MAO. The most stable structures have aluminum/oxygen atoms in environments whose average hybridization approaches sp³/sp². The (AlOMe)_{<i>n</i>,<i>t</i>}·(AlMe₃)_<i>m</i> isomers with the lowest free energies possess Al−μ-Me–Al bonds. At 298 K a novel <i>T</i>_<i>d</i>-(AlOMe)_16,c oligomer is one of the most stable structures among the six stoichiometries with the lowest free energies: (AlOMe)_20,<i>c</i>·(AlMe₃)₂, <i>T</i>_<i>d</i>-(AlOMe)_16,<i>c</i>, (AlOMe)_18,<i>c</i>, (AlOMe)_20,<i>c</i>·(AlMe₃), (AlOMe)_10,<i>t</i>·(AlMe₃)₄, and (AlOMe)_20,<i>c</i>. As the temperature rises, the abundance of (AlOMe)_{<i>n</i>,<i>t</i>}·(AlMe₃)_<i>m</i> decreases, and that of (AlOMe)_{<i>n</i>,<i>c</i>} increases. Because the former are expected to be precursors for the active species in polymerization, this may in part be the reason why the cocatalytic activity of MAO decreases at higher temperatures

Composition and Constitution of Compressed Strontium Polyhydrides

The structures of the strontium polyhydrides, SrH_<i>n</i> with <i>n</i> > 2, under pressure are studied using evolutionary algorithms coupled with density functional theory calculations. A number of phases with even <i>n</i> are found to be thermodynamically stable below 150 GPa. Particularly interesting is the SrH₄ stoichiometry, which comprises the convex hull at 50, 100, and 150 GPa. Its hydrogenic sublattice contains H₂ and H^– units, and throughout the pressure range considered, it adopts one of two configurations which were previously predicted for CaH₄ under pressure. At 150 GPa, the SrH₆ stoichiometry has the lowest enthalpy of formation. The most stable configuration assumes <i>P</i>3̅ symmetry, and its lattice consists of one-dimensional H₂···H^– hydrogenic chains. Symmetrization of these chains results in the formation of _∞¹[H^δ−] helices, which are reminiscent of the trigonal phase of sulfur. The <i>R</i>3̅<i>m</i>-SrH₆ phase, which is comprised of these helices, becomes dynamically stable by 250 GPa and has a high density of states at the Fermi level. We explore the geometric relationships between <i>R</i>3̅<i>m</i>-SrH₆ and the Im3̅<i>m</i>-CaH₆ and <i>Imm</i>2-BaH₆ structures found in prior investigations

Polyhydrides of the Alkaline Earth Metals: A Look at the Extremes under Pressure

Evolutionary structure searches are coupled with density functional theory calculations to predict the most stable stoichiometries and structures of beryllium and barium polyhydrides, MH_<i>n</i> with <i>n</i> > 2 and M = Be/Ba, under pressure. Even though the BeH_<i>n</i> stoichiometries we explored do not become thermodynamically stable with respect to decomposition into the classic hydride BeH₂ and H₂ up to 200 GPa, we find a new phase of BeH₂ with <i>R</i>3̅<i>m</i> symmetry above 150 GPa. The barium polyhydrides become thermodynamically preferred by 20 GPa. They sport complex hydrogenic sublattices composed of H^–, H₃^–, and H₂ units. BaH₆ is the first stoichiometry to emerge as stable and metallic (∼60 GPa using the Perdew–Burke–Ernzerhof functional), and the <i>P</i>4/<i>mmm</i> symmetry structure is estimated to become superconducting below 30–38 K at 100 GPa. Phases with an even greater hydrogen content lie on the convex hull at higher pressures, and an intriguing BaH₁₀ stoichiometery becomes the global thermodynamic minimum around 150 GPa. BaH₁₀ remains metallic over its predicted domain of existence, and its Ba–Ba distances resemble those found in the complex Ba–IVc structure at 19 GPa

Crystal Structures and Electronic Properties of Xe–Cl Compounds at High Pressure

Crystal structure prediction techniques coupled with enthalpies obtained at 0 K from density functional theory calculations suggest that pressure can be used to stabilize the chlorides of xenon. In particular, XeCl and XeCl₂ were calculated to become metastable by 10 GPa and thermodynamically stable with respect to the elemental phases by 60 GPa. Whereas at low pressures Cl₂ dimers were found in the stable phases, zigzag Cl chains were present in <i>Cmcm</i> XeCl at 60 GPa and atomistic chlorine comprised <i>P</i>6₃/<i>mmc</i> XeCl and <i>Fd</i>3̅<i>m</i> XeCl₂ at 100 GPa. A XeCl₄ phase that was metastable at 100 GPa contained monomers, dimers, and trimers of chlorine. XeCl, XeCl₂, and XeCl₄ were metallic at 100 GPa, and at this pressure they were predicted to be superconducting below 9.0, 4.3, and 0.3 K, respectively. Spectroscopic properties of the predicted phases are presented to aid in their eventual characterization, should they ever be synthesized

On the Nature of Ge–Pb Bonding in the Solid State. Synthesis, Structural Characterization, and Electronic Structures of Two Unprecedented Germanide-Plumbides

Reported are the syntheses and the crystallographic characterization of two structurally related solid-state compounds: (Eu_1–<i>x</i>Ca_<i>x</i>)₂Ge₂Pb (space group <i>Pbam</i>) and (Sr_<i>x</i>Eu_1–<i>x</i>)₂Ge₂Pb (space group <i>Cmmm</i>). Both structures boast anionic sublattices with fully ordered Ge and Pb at the atomic level, which is unusual for elements of the same group. Despite the nearly identical formulas and the similar chemical makeup, the nature of the chemical bonding in the two compounds is subtly different; in the (Eu_1–<i>x</i>Ca_<i>x</i>)₂Ge₂Pb structure, Ge and Pb are positioned at a relatively shorter distance from one another (<3.0 Å). The close proximity of the atoms leads to interactions, which are seen for the first time in an extended structure and can be suggested to have a covalent character. This conjecture is supported by extensive electronic band-structure calculations using first principles. Magnetic susceptibility measurements reveal Eu²⁺ ground state ([Xe]­4f⁷ configuration) and the presence of an antiferromagnetic ordering at cryogenic temperatures

On the Nature of Ge–Pb Bonding in the Solid State. Synthesis, Structural Characterization, and Electronic Structures of Two Unprecedented Germanide-Plumbides

Reported are the syntheses and the crystallographic characterization of two structurally related solid-state compounds: (Eu_1–<i>x</i>Ca_<i>x</i>)₂Ge₂Pb (space group <i>Pbam</i>) and (Sr_<i>x</i>Eu_1–<i>x</i>)₂Ge₂Pb (space group <i>Cmmm</i>). Both structures boast anionic sublattices with fully ordered Ge and Pb at the atomic level, which is unusual for elements of the same group. Despite the nearly identical formulas and the similar chemical makeup, the nature of the chemical bonding in the two compounds is subtly different; in the (Eu_1–<i>x</i>Ca_<i>x</i>)₂Ge₂Pb structure, Ge and Pb are positioned at a relatively shorter distance from one another (<3.0 Å). The close proximity of the atoms leads to interactions, which are seen for the first time in an extended structure and can be suggested to have a covalent character. This conjecture is supported by extensive electronic band-structure calculations using first principles. Magnetic susceptibility measurements reveal Eu²⁺ ground state ([Xe]­4f⁷ configuration) and the presence of an antiferromagnetic ordering at cryogenic temperatures