Product Integration Rules at Clenshaw-Curtis and Related Points: A Robust Implementation

Product integration rules generalizing the Fej?r, Clenshaw-Curtis,and Filippi quadrature rules respectively are derived for integralswith trigonometric and hyperbolic weight factors. The Chebyshevmoments of the weight functions are found to be given by well-conditionedexpressions, in terms of hypergeometric functions ₀F₁. An a priori error estimator is discussed which is shown bothto avoid wasteful invocation of the integration rule and toincrease significantly the robustness of the automatic quadratureprocedure. Then, specializing to extended Clenshaw-Curtis (ECC) rules,three types of a posteriori error estimates are considered andthe existence of a great risk of their failure is demonstratedby large scale validation tests. An empirical error estimator,superseding them for slowly varying integrands, is found toresult in a spectacular increase in the output reliability. Finally, enhancements in the control of the interval subdivisionstrategy aiming at increasing code robustness is discussed.Comparison with the code DQAWO of QUADPACK, with about a hundredthousand solved integrals, is illustrative of the increasedrobustness and error estimate reliability of our computer codeimplementation of the ECC rules.     

Catenated polysulfur ligands: the pentasulfides of di-η5-cyclopentadienyl-zirconium(IV) and -hafnium(IV)

The thiols Cp₂M(SH)₂, where M = Ti and Zr, react to form the complexes Cp₂MS₅ when treated with mono- and di-sulfur transfer reagents. Treatment of Cp₂MCl₂ with Li₂S₂ and sulfur gave Cp₂MS₅, M = Ti, Zr and Hf, in better yield. The new Zr and Hf complexes have a six-membered MS₅ ring in a chair conformation similar to the previously observed for M = Ti. Variable temperature NMR studies show that the barriers to MS₅ ring inversion decrease in the order Ti > Hf > Zr.     

Polymer Intermediates and Polymers Derived from 5-t-Butyl-m-Xylene

Abstract

A series of condensation polymer intermediates, which included several new compositions, was prepared from 5-t-butyl-m-xylene (I) so that the effect of the bulky t-butyl group on polymer properties could be determined. Compound (I) was oxidized with nitric acid to obtain 5-t-butyl-isophthalic acid (II), which was converted successively to the diacid chloride, the diamide, the dinitrile, and finally to 5-t-butyl-m-xylene-α,α′-diamine (VI); the overall yield was 80%. The dimethyl ester of (II) was prepared and converted to 5-t-butyl-m-xylene-α,α′-diol (VIII), a new composition, in 79.5% overall yield; the diphenyl ester was also prepared. The sodium salt of (II) was catalytically reduced to obtain 5-t-butyl-1,3-cyclohexanedicarboxylic acid (IIa) in 95% yield. (IIa) was converted successively to the diacid chloride, the diamide, the dinitrile, and finally to 5-t-butyl-1,3-cyclohexanebis(methylamine) (VIa), a new composition; the overall yield was 37%. (IIa) was also converted to the dimethyl ester and finally to 5-t-butyl-1,3-cyclohexanedimethanol (VIIIa), a new composition; the overall yield was 64%. Condensation polymers were prepared from the intermediates (II), (IIa), (VI), (VIa), (VIII), and (VIIIa). These polymers had higher glass transition temperatures (T_g) than corresponding polymers containing no t-butyl groups. This general effect of the t-butyl group to increase the T_g value of the polymer was noted in all polymers prepared, regardless of whether the intermediate carrying the t-butyl group was a diacid, a diol, or a diamine, or whether the polymer was a polyamide, a polyester, or a polyurethane.     

Expanding the 0D Rb7M3X16 (M=Sb,Bi; X=Br,I) Family: Dual-Band Luminescence in Rb7Sb3Br16

Inorganic, lead-free metal halides are widely sought after following the rise of the halide perovskites as outstanding optoelectronic materials, due to their enhanced stability and reduced toxicity. Herein, we report on the solvothermal synthesis of Rb₇Sb₃Br₁₆, which exhibits a 0D structure comprised of [SbBr₆]³⁻ octahedra and edge-sharing bioctahedra [Sb₂Br₁₀]⁴⁻ dimers that order into layers along the c-axis. This all-inorganic material is air-stable and exhibits weak orange photoluminescence (PL) at room temperature. Low-temperature PL and PL excitation (PLE) measurements reveal the presence of two distinct emission bands that originate from these structural units, with the high-energy emission quenching as temperature rises beyond 150 K. We are also able to obtain Rb₇Bi₃Br₁₆ and Rb₇Bi₃I₁₆ which both crystallize in orthorhombic symmetry, with Rb₇Bi₃Br₁₆ presenting weak low-temperature luminescence while Rb₇Bi₃I₁₆ is non-luminescent. This work expands the library of emissive inorganic metal halides and provides further evidence for the efficacy of low-dimensional Sb−X luminescent centers based on octahedral and edge-sharing [Sb₂X₁₀]⁴⁻ dimers.     

White CsPbBr3: Characterizing the One-Dimensional Cesium Lead Bromide Polymorph

Inorganic lead halide perovskites have gained immense scientific interest for optoelectronic applications. In this work, we present a one-dimensional polymorph of cesium lead bromide (δ-CsPbBr₃) synthesized through a simple anion-exchange reaction, wherein distorted edge-sharing PbBr₆ octahedra form 1D chains isolated by Cs ions. δ-CsPbBr₃ was characterized by Raman spectroscopy, X-ray diffraction, ²⁰⁷Pb and ¹³³Cs solid-state NMR, and by optical emission and absorption spectroscopies. This non-perovskite material irreversibly transforms into the well-known three-dimensional perovskite phase (γ-CsPbBr₃) upon heating to above 151 °C. The indirect bandgap was determined by absorption measurements and calculation to be 2.9 eV. δ-CsPbBr₃ exhibits broadband yellow photoluminescence with a quantum yield of 3.2 %±0.2 % at room temperature and 95 %±5 % at 77 K, and this emission is attributed to the recombination of self-trapped excitons. This study emphasizes that the metastable δ-CsPbBr₃ may be a persistent, concomitant phase in Cs−Pb-Br-containing materials systems, such as those used in solar cells and LEDs, and it showcases the characterization tools used for its detection.     

Thermodynamic Complexation of Dopamine with Zinc(II) in Media with Different Dielectric Constants

The complexation of zinc(II) with dopamine has been investigated by spectrophotometric measurements in mixed solvent system at an ionic strength of 0.2 mol•dm－3 sodium chloride, employed at at (15±0.1), (25±0.1), (35±0.1) ℃ at inin a pH range of ca. 6 to ca. 7 with a high ratio of ligand to metal. The effect of solvent systems on protonation and complexation are was was discussed. Linear relationships are werewere observed by plotting lg K versus 1/D, where K and D show stability and dielectric constants, respectively.     

High-resolution spectroscopy of the ν8 band of methylene bromide using a quantum cascade laser

A continuous wave cavity ringdown spectrometer with a Fabry-Perot quantum cascade laser has been used to collect a rotationally-resolved infrared spectrum of the ν₈ vibrational band of methylene bromide in a slit nozzle expansion. In our laboratory, previous observations of the vibrational band were limited by spectral coverage to only the P and Q-branches and by the 24 MHz step-size of the laser [1]. The issue of limited spectral coverage has been resolved using a Fresnel rhomb and a wire grid polarizer to protect the laser from the destabilizing effects of back-reflection from the ringdown cavity. The frequency step-size of the spectrometer has been reduced from 24 MHz to 2 MHz. With both of these instrument enhancements, we have been able to record the R-branch of the vibrational band, and can resolve many lines that were previously blended in spectra acquired using a pinhole expansion nozzle. Significant hyperfine splitting was observed for the low-J transitions in the P and R-branches. It was possible to neglect the effects of hyperfine splitting for transitions involving J″ > 2 in the spectral assignment, and simulations using the constants obtained by fitting to Watson’s S-reduced Hamiltonian for CH₂⁷⁹Br⁸¹Br, and the A-reduced form for CH₂⁷⁹Br₂ and CH₂⁸¹Br₂, provide a good match to experimental spectra. A total of 297 transitions have been assigned for all three isotopologues, with a standard deviation of 0.00024 cm⁻¹(∼7 MHz).     

Shedding new light on ZnCl2-mediated addition reactions of Grignard reagents to ketones: structural authentication of key intermediates and diffusion-ordered NMR studies

Building on recent advances in synthesis showing that the addition of inorganic salts to Grignard reagents can greatly enhance their performance in alkylation reactions to ketones, this study explores the reactions of EtMgCl with benzophenone in the presence of stoichiometric or catalytic amounts of ZnCl(2) with the aim of furthering the understanding of the role and constitution of the organometallic species involved in these transformations. Investigations into the metathesis reactions of three molar equivalents of EtMgCl with ZnCl(2) led to the isolation and characterisation (X-ray crystallography and (1)H and (13)C NMR spectroscopy) of novel magnesium "zinc-rich" zincate [{(THF)(6)Mg(2)Cl(3)}(+){Zn(2)Et(5)}(-)] (1), whose complicated constitution in THF solutions was assessed by variable-temperature (1)H DOSY NMR studies. Compound 1 reacted with one equivalent of benzophenone to yield magnesium magnesiate [{(THF)(6)Mg(2)Cl(3)}(+){Mg(2)(OC(Et)Ph(2))(2)Cl(3)(THF)}(-)] (3), whose structure was determined by X-ray crystallography. (1)H NMR monitoring of this reaction showed two equivalents of ZnEt(2) formed as a co-product, which together with the "magnesium only constitution" of 3 provides experimental insights into how zinc can be efficiently recycled in these reactions, and therefore used catalytically. The chemoselectivity of this reaction can be rationalised in terms of the synergic effect of magnesium and zinc and contrasts with the results obtained when benzophenone was allowed to react with EtMgCl in the absence of ZnCl(2), where the reduction of the ketone takes place preferentially. The reduction product [{(THF)(5)Mg(3)Cl(4){OC(H)Ph(CF(3))}(2)] (4) obtained from the reaction of EtMgCl with 2,2,2-trifluoroacetophenone was established by X-ray crystallography and multinuclear ((1)H, (13)C and (19)F) NMR spectroscopy. Compounds 3 and 4 exhibit new structural motifs in magnesium chemistry having MgCl(2) integrated within their constitution, which highlights the new role of this inorganic salt in providing structural support for the newly generated alkoxide ligand.