Classical limit of relativistic quantal system with attractive Coulomb interaction

Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r ²〉 − 〈r〉²]^1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.     

Mimicking transition metals in borrowing hydrogen from alcohols

Borrowing hydrogen from alcohols, storing it on a catalyst and subsequent transfer of the hydrogen from the catalyst to an in situ generated imine is the hallmark of a transition metal mediated catalytic N-alkylation of amines. However, such a borrowing hydrogen mechanism with a transition metal free catalytic system which stores hydrogen molecules in the catalyst backbone is yet to be established. Herein, we demonstrate that a phenalenyl ligand can imitate the role of transition metals in storing and transferring hydrogen molecules leading to borrowing hydrogen mediated alkylation of anilines by alcohols including a wide range of substrate scope. A close inspection of the mechanistic pathway by characterizing several intermediates through various spectroscopic techniques, deuterium labelling experiments, and DFT study concluded that the phenalenyl radical based backbone sequentially adds H⁺, H˙ and an electron through a dearomatization process which are subsequently used as reducing equivalents to the C–N double bond in a catalytic fashion.

An efficient method is developed for harvesting hydrogen, its storage and catalytic transfer by an odd alternant hydrocarbon. The strategy is reminiscent of transition metals in borrowing hydrogen mediated processes.     

Oxofluorovanadates(V). IV. Dioxotetrafluorovanadates

Preparation and properties of the salts of the series MVO₂F₄, where M = NH, Na⁺, K⁺, 1/2 Ni²⁺, and 1/3 [Co(NH₃)₆]³⁺ are described. Molecular conductivity of Na₃VO₂F₄ at different dilutions indicates that Na₃VO₂F₄ dissociates into 3 Na⁺ and VOaF ions. Ion exchange study of (NH₄)₃VO₂F₄ solution through cation exchange resin (H⁺ form) suggests that the corresponding acid decomposes partly to vanadium pentoxide. Reaction between (NH₄)₃VO₂F₄ with BaCl₂ and AgNO₃ solutions shows the formation of BaVO₂F₃ and AgVO₃ respectively. Thermogravimetric study of (NH₄)₃VO₂F₄ shows the formation of impure vanadium pentoxide as the ultimate product on heating up to 450°C. X-ray powder diffraction data are given for (NH₄)₃VO₂F₄ and Na₃VO₂F₄.     

The microwave spectrum and structure of trifluoro-ethylene

The microwave spectrum of trifluoroethylene F₂C=CHF is reported, and a number of ground state and vibrationally excited state lines are assigned. The ground state rotational constants are: 10665.31, 3872.36, 2837.97 MHz. The dipole components are μ_a = 0.075 D, μ_b = 1.30 D, and μ_total = 1.30 D. Calculations of the inertia defect of the ground and excited states indicate that the equilibrium configuration is planar.     

Mesoporous Core–Shell Fenton Nanocatalyst: A Mild,Operationally Simple Approach to the Synthesis of Adipic Acid

Mesoporous nanoparticles composed of γ‐Al₂O₃ cores and α‐Fe₂O₃ shells were synthesized in aqueous medium. The surface charge of γ‐Al₂O₃ helps to form the core–shell nanocrystals. The core–shell structure and formation mechanism have been investigated by wide‐angle XRD, energy‐dispersive X‐ray spectroscopy, and elemental mapping by ultrahigh‐resolution (UHR) TEM and X‐ray photoelectron spectroscopy. The N₂ adsorption–desorption isotherm of this core–shell materials, which is of type IV, is characteristic of a mesoporous material having a BET surface area of 385 m² g^?1 and an average pore size of about 3.2 nm. The SEM images revealed that the mesoporosity in this core–shell material is due to self‐aggregation of tiny spherical nanocrystals with sizes of about 15–20 nm. Diffuse‐reflectance UV/Vis spectra, elemental mapping by UHRTEM, and wide‐angle XRD patterns indicate that the materials are composed of aluminum oxide cores and iron oxide shells. These Al₂O₃@Fe₂O₃ core–shell nanoparticles act as a heterogeneous Fenton nanocatalyst in the presence of hydrogen peroxide, and show high catalytic efficiency for the one‐pot conversion of cyclohexanone to adipic acid in water. The heterogeneous nature of the catalyst was confirmed by a hot filtration test and analysis of the reaction mixture by atomic absorption spectroscopy. The kinetics of the reaction was monitored by gas chromatography and ¹H NMR spectroscopy. The new core–shell catalyst remained in a separate solid phase, which could easily be removed from the reaction mixture by simple filtration and the catalyst reused efficiently.     

Organic–Inorganic Hybrid Supermicroporous Iron(III) Phosphonate Nanoparticles as an Efficient Catalyst for the Synthesis of Biofuels

Here we report a novel family of crystalline, supermicroporous iron(III) phosphonate nanomaterials (HFeP‐1‐3, HFeP‐1‐2, and HFeP‐1‐4) with different Fe^III‐to‐organophosphonate ligand mole ratios. The materials were synthesized by using a hydrothermal reaction between benzene‐1,3,5‐triphosphonic acid and iron(III) chloride under acidic conditions (pH≈4.0). Powder X‐ray diffraction, N₂ sorption, transmission and scanning electron microscopy (TEM and SEM) image analysis, thermogravimetric and differential thermal analysis (TGA‐DTA), and FTIR spectroscopic tools were used to characterize the materials. The triclinic crystal phase [P$\bar 1$ (2) space group] of the hybrid iron phosphonate was established by a Rietveld refinement of the PXRD analysis of HFeP‐1‐3 by using the MAUD program. The unit cell parameters are a=8.749(1), b=8.578(1), c=17.725(3) Å; α=104.47(3), β=97.64(1), γ=113.56(3)°; and V=1013.41 ų. With these crystal parameters, we proposed an 24‐membered‐ring open framework structure for HFeP‐1. Compound HFeP‐1‐3, with an starting Fe/ligand molar ratio of 3.0, shows the highest Brunauer–Emmett–Telller (BET) surface area of 556 m²g^?1 and uniform supermicropores of approximately 1.1 nm. The acidic surface of the porous iron(III) phosphonate nanoparticles was used in a highly efficient and recyclable catalytic transesterification reaction for the synthesis of biofuels under mild reaction conditions.     

Structurally Stabilized Organosilane‐Templated Thermostable Mesoporous Titania

Structurally thermostable mesoporous anatase TiO₂ (m‐TiO₂) nanoparticles, uniquely decorated with atomically dispersed SiO₂, is reported for the first time. The inorganic Si portion of the novel organosilane template, used as a mesopores‐directing agent, is found to be incorporated in the pore walls of the titania aggregates, mainly as isolated sites. This is evident by transmission electron microscopy and high‐angle annular dark field scanning transmission electron microscopy, combined with electron dispersive X‐ray spectroscopy. This type of unique structure provides exceptional stability to this new material against thermal collapse of the mesoporous structure, which is reflected in its high surface area (the highest known for anatase titania), even after high‐temperature (550 °C) calcination. Control of crystallite size, pore diameter, and surface area is achieved by varying the molar ratios of the titanium precursor and the template during synthesis. These mesoporous materials retain their porosity and high surface area after template removal and further NaOH/HCl treatment to remove silica. We investigate their performance for dye‐sensitized solar cells (DSSCs) with bilayer TiO₂ electrodes, which are prepared by applying a coating of m‐TiO₂ onto a commercial titania (P25) film. The high surface area of the upper mesoporous layer in the P25–m‐TiO₂ DSSC significantly increases the dye loading ability of the photoanode. The photocurrent and fill factor for the DSSC with the bilayer TiO₂ electrode are greatly improved. The large increase in photocurrent current (ca. 56 %) in the P25–m‐TiO₂ DSSC is believed to play a significant role in achieving a remarkable increase in the photovoltaic efficiency (60 %) of the device, compared to DSSCs with a monolayer of P25 as the electrode.     

Recent advances of lead-free metal halide perovskite single crystals and nanocrystals: synthesis,crystal structure,optical properties,and their diverse applications

Lead halide hybrid perovskites have received massive research attention because of their unique inherent photophysical properties that driven them for potential application in the fields of photovoltaics, light-emitting devices, lasing, X-ray detector, and so on. Perovskite single crystals and nanocrystals are generally synthesized via various low-cost solution-processed techniques. The emergence of simple growth approaches of perovskite structures enable to fabricate low-cost and highly efficient devices. However, toxicity of Pb atoms and instability of perovskite structures obstruct further commercialization of these technologies. Recent efforts have been shifted to discover novel, eco-friendly, and stable lead-free metal halide perovskite (LFHP) materials and exploring their different growth processes for various device applications. This review aims to provide an up-to-date analysis of recent progress report on LFHPs and will mainly focus on their growth processes in the single crystalline and nanocrystalline forms. This review also tries to understand how the perovskite crystal structure impacts on their fundamental properties. In addition, we discuss the current progress in various field of applications and their future aspects.