Strichartz Estimates for Non-Elliptic Schrödinger Equations on Compact Manifolds

In this note we consider the Schrödinger equation on compact manifolds equipped with possibly degenerate metrics. We prove Strichartz estimates with a loss of derivatives. The rate of loss of derivatives depends on the degeneracy of metrics. For the non-degenerate case we obtain, as an application of the main result, the same Strichartz estimates as that in the elliptic case. This extends Strichartz estimates for Riemannian metrics proved by Burq-Gérard-Tzvetkov to the non-elliptic case and improves the result by Salort for the degenerate case. We also investigate the optimality of the result for the case on 𝕊³ × 𝕊³.     

Interaction in the molten system Rb2O‐P2O5‐TiO2‐NiO. Crystal structure of the langbeinite‐related Rb2Ni0.5Ti1.5(PO4)3

The interaction in the molten system Rb₂O‐P₂O₅‐TiO₂‐NiO was investigated at different molar ratios Rb/P = 0.5‐1.3, fixed Ti/P = 0.15, Ti/Ni = 1.0 at temperature range 1073–953 K. The conditions of formation of complex phosphates RbTi₂(PO₄)₃, Rb₂Ni_0.5Ti_1.5(PO₄)₃ and RbNiPO₄ have been determined. The new phosphate Rb₂Ni_0.5Ti_1.5(PO₄)₃ (space group P2₁3, a = 9.9386(2) Å) has been obtained and investigated by the single crystal X‐ray diffraction and FTIR‐spectroscopy. It has langbeinite‐like structure, that is built up from mixed (Ni/Ti)O₆‐octahedra and РО₄‐tetrahedra. Rubidium atoms are located in closed cavities of 3D‐framework.     

Pyranoside‐into‐Furanoside Rearrangement: New Reaction in Carbohydrate Chemistry and Its Application in Oligosaccharide Synthesis

Great interest in natural furanoside‐containing compounds has challenged the development of preparative methods for their synthesis. Herein a novel reaction in carbohydrate chemistry, namely a pyranoside‐into‐furanoside (PIF) rearrangement permitting the transformation of selectively O‐substituted pyranosides into the corresponding furanosides is reported. The discovered process includes acid‐promoted sulfation accompanied by rearrangement of the pyranoside ring into a furanoside ring followed by solvolytic O‐desulfation. This process, which has no analogy in organic chemistry, was shown to be a very useful tool for the synthesis of furanoside‐containing complex oligosaccharides, which was demonstrated by synthesizing disaccharide derivatives α‐D ‐Galp‐(1→3)‐β‐D ‐ Galf ‐OPr, 3‐O‐s ‐lactyl‐β‐D ‐ Galf ‐(1→3)‐β‐D ‐Glcp‐OPr, and α‐L ‐ Fucf ‐(1→4)‐β‐D ‐GlcpA‐OPr related to polysaccharides from the bacteria Klebsiella pneumoniae and Enterococcus faecalis and the brown seaweed Chordaria flagelliformis.     

Controlled Generation of 9-Boratriptycene by Lewis Adduct Dissociation: Accessing a Non-Planar Triarylborane

A highly bent triarylborane, 9-boratriptycene, was generated in solution by selective protodeboronation of the corresponding tetra-aryl boron ate complex with the strong Brønsted acid HNTf₂. The iptycene core confers enhanced Lewis acidity to 9-boratriptycene, making it unique in terms of structure and reactivity. We studied the stereoelectronic properties of 9-boratriptycene by quantifying its association with small N- and O-centered Lewis bases, as well as with sterically hindered phosphines. The resultant Lewis adducts exhibited unique structural, spectroscopic, and photophysical properties. Beyond the high pyramidalization of the 9-boratriptycene scaffold and its low reorganization energy upon Lewis base coordination, quantum chemical calculations revealed that the absence of π donation from the triptycene aryl rings to the boron vacant p_z orbital is one of the main reasons for its high Lewis acidity.     

σ-Aromaticity-Induced Stabilization of Heterometallic Supertetrahedral Clusters [Zn6Ge16]4− and [Cd6Ge16]4−

In this work, the largest heterometallic supertetrahedral clusters, [Zn₆Ge₁₆]⁴⁻ and [Cd₆Ge₁₆]⁴⁻, were directly self-assembled through highly-charged [Ge₄]⁴⁻ units and transition metal cations, in which 3-center–2-electron σ bonding in Ge₂Zn or Ge₂Cd triangles plays a vital role in the stabilization of the whole structure. The cluster structures have an open framework with a large central cavity of diameter 4.6 Å for Zn and 5.0 Å for Cd, respectively. Time-dependent HRESI-MS spectra show that the larger clusters grow from smaller components with a single [Ge₄]⁴⁻ and ZnMes₂ units. Calculations performed at the DFT level indicate a very large HOMO–LUMO energy gap in [M₆Ge₁₆]⁴⁻ (2.22 eV), suggesting high kinetic stability that may offer opportunities in materials science. These observations offer a new strategy for the assembly of heterometallic clusters with high symmetry.     

Stability,electronic, and optical properties of two-dimensional phosphoborane

The structure and properties of two-dimensional phosphoborane sheets were computationally investigated using Density Functional Theory calculations. The calculated phonon spectrum and band structure point to dynamic stability and allowed characterization of the predicted two-dimensional material as a direct-gap semiconductor with a band gap of ~1.5 eV. The calculation of the optical properties showed that the two-dimensional material has a relatively small absorptivity coefficient. The parameters of the mechanical properties characterize the two-dimensional phosphoborane as a relatively soft material, similar to the monolayer of MoS₂. Assessment of thermal stability by the method of molecular dynamics indicates sufficient stability of the predicted material, which makes it possible to observe it experimentally.     

Neutron Reflectometry in Russia: Current State and Prospects

Crystallography Reports - The review is devoted to the current state of affairs and prospects for development in the field of neutron reflectometry on the existing and future neutron sources in the...     

Electrochemically driven C–N bond formation from CO2 and ammonia at the triple-phase boundary

Electrosynthetic techniques are gaining prominence across the fields of chemistry, engineering and energy science. However, most works within the direction of synthetic heterogeneous electrocatalysis focus on water electrolysis and CO₂ reduction. In this work, we moved to expand the scope of small molecule electrosynthesis by developing a synthetic scheme which couples CO₂ and NH₃ at a gas–liquid–solid boundary to produce species with C–N bonds. Specifically, by bringing in CO₂ from the gas phase and NH₃ from the liquid phase together over solid copper catalysts, we have succeeded in forming formamide and acetamide products for the first time from these reactants. In a subsequent complementary step, we have combined electrochemical analysis and a newly developed operando spectroelectrochemical method, capable of probing the aforementioned gas–liquid–solid boundary, to extract an initial level of mechanistic analysis regarding the reaction pathways of these reactions and the current system''s limitations. We believe that the development and understanding of this set of reaction pathways will play significant role in expanding the community''s understanding of on-surface electrosynthetic reactions as well as push this set of inherently sustainable technologies towards widespread applicability.

Electrocatalytic formation of C–N bonds was achieved through the electrolysis of CO₂ and NH₃ over Cu catalysts. A combined analytical and spectroscopic approach gave insights into the reaction mechanism leading to formamide and acetamide products.     

A series of three-dimensional coordination polymers with general formula [{Ln(H2O)n}{Re6Te8(CN)6}] · xH2O (Ln = Eu,Gd, Tb,Dy, Ho,Er, Tm,Yb; n = 3, 4, x = 0, 2.5)

A series of new compounds containing rare earth cations (Eu to Yb) and paramagnetic cluster anion [Re₆Te₈(CN)₆]³⁻ was prepared and investigated. The X-ray structural analyses have revealed that the compounds [{Ln(H₂O)₄}{Re₆Te₈(CN)₆}] · 2.5H₂O; Ln = Eu (1), Tb (3), Dy (4), Ho (5), Er (6), Tm (7), [{Gd(H₂O)₃}{Re₆Te₈(CN)₆}] · 2.5H₂O (2) and [{Yb(H₂O)₄}{Re₆Te₈(CN)₆}] (8) are three-dimensional polymers based on Re–CN–Ln interactions. Measurements of magnetic susceptibility for 2 and 5 showed that effective magnetic moment (at 300 K) was 8.13 μ_B for compound 2 and 10.79 μ_B for compound 5 with weak antiferromagnetic ordering appeared at low temperatures.