Structure–Reactivity Relationships in the Hydrogenation of Carbon Dioxide with Ruthenium Complexes Bearing Pyridinylazolato Ligands

Pyridinylazolato (N–N′) ruthenium(II) complexes of the type [(N–N′)RuCl(PMe₃)₃] have been obtained in high yields by treating the corresponding functionalised azolylpyridines with [RuCl₂(PMe₃)₄] in the presence of a base. ¹⁵N NMR spectroscopy was used to elucidate the electronic influence of the substituents attached to the azolyl ring. The findings are in agreement with slight differences in the bond lengths of the ruthenium complexes. Furthermore, the electronic nature of the azolate moiety modulates the catalytic activity of the ruthenium complexes in the hydrogenation of carbon dioxide under supercritical conditions and in the transfer hydrogenation of acetophenone. DFT calculations were performed to shed light on the mechanism of the hydrogenation of carbon dioxide and to clarify the impact of the electronic nature of the pyridinylazolate ligands.     

A Rechargeable Hydrogen Battery Based on Ru Catalysis

Apart from energy generation, the storage and liberation of energy are among the major problems in establishing a sustainable energy supply chain. Herein we report the development of a rechargeable H₂ battery which is based on the principle of the Ru‐catalyzed hydrogenation of CO₂ to formic acid (charging process) and the Ru‐catalyzed decomposition of formic acid to CO₂ and H₂ (discharging process). Both processes are driven by the same catalyst at elevated temperature either under pressure (charging process) or pressure‐free conditions (discharging process). Up to five charging–discharging cycles were performed without decrease of storage capacity. The resulting CO₂/H₂ mixture is free of CO and can be employed directly in fuel‐cell technology.     

Ultraviolet oscillator strengths for carbon,nitrogen and oxygen ions

Oscillator strengths were calculated for u.v. transitions in carbon, nitrogen and oxygen ions. Single and multiconfiguration numerical Hartree-Fock wavefunctions were used to represent initial and final states of the various transitions, and both dipole length and dipole velocity transition matrix elements were calculated. A careful choice of a few important configurations leads in most cases to multiconfiguration results which are in good agreement with experiment, and with other theoretical calculations.     

Computing transitive closure of bipolar weighted digraphs

We define a bipolar weighted digraph as a weighted digraph together with the sign function on the arcs such that the weight of each arc lies between 0 and 1, and no two parallel arcs have the same sign. Bipolar weighted digraphs are utilized to model so-called fuzzy cognitive maps, which are used in science, engineering, and the social sciences to represent the causal structure of a body of knowledge. It has been noted in the literature that a transitive closure of a bipolar weighted digraph contains useful new information for the fuzzy cognitive map it models.In this paper we ask two questions: what is a sensible and useful definition of transitive closure of a bipolar weighted digraph, and how do we compute it? We give two answers to each of these questions, that is, we present two distinct models. First, we give a review of the fuzzy digraph model, which has been, in a different form and less rigorously, studied previously in the fuzzy systems literature. Second, we carefully develop a probabilistic model, which is related to the notion of network reliability.This paper is intended for a mathematical audience.     

Unrestricted Dirac-Fock theory: Relativistic determination of core polarization hyperfine interactions

The unrestricted Dirac-Fock (UDF) method is developed for determining relativistic contributions to the hyperfine interaction, notably that due to core polarization. Radial core-polarization of the one-electron (jj-coupled) spin orbitals is obtained by relaxing the restraint in restricted Dirac-Fock (RDF) theory that the radial part be independent of the magnetic quantum number, the projection m_j of j. Relativistic effects on the core polarization are obtained by comparison with results obtained from the non-relativistic spin polarized Hartree-Fock (m_s unrestricted) and spin plus orbital polarized Hartree- Fock (m_s plus m_j unrestricted) calculations. For the 5d transition series ions, the relativistic core polarization enhancement factor, S_s(z), is determined to be about a factor of two and so is much smaller than the isomer shift charge density enhancement factor (≈6) found earlier for these same ions. Comparison is made with limited experimental data available to date; for the case of atomic Re, excellent agreement is obtained with experiment.     

Diaryldichalcogenide radical cations

One-electron oxidation of two series of diaryldichalcogenides (C₆F₅E)₂ (13a–c) and (2,6-Mes₂C₆H₃E)₂ (16a–c) was studied (E = S, Se, Te). The reaction of 13a and 13b with AsF₅ and SbF₅ gave rise to the formation of thermally unstable radical cations [(C₆F₅S)₂]˙⁺ (14a) and [(C₆F₅Se)₂]˙⁺ (14b) that were isolated as [Sb₂F₁₁]^– and [As₂F₁₁]^– salts, respectively. The reaction of 13c with AsF₅ afforded only the product of a Te–C bond cleavage, namely the previously known dication [Te₄]²⁺ that was isolated as [AsF₆]^– salt. The reaction of (2,6-Mes₂C₆H₃E)₂ (16a–c) with [NO][SbF₆] provided the corresponding radical cations [(2,6-Mes₂C₆H₃E)₂]˙⁺ (17a–c; E = S, Se, Te) in the form of thermally stable [SbF₆]^– salts in nearly quantitative yields. The electronic and structural properties of these radical cations were probed by X-ray diffraction analysis, EPR spectroscopy, and density functional theory calculations and other methods.     

Exactly solvable models in supersymmetric quantum mechanics and connection with spectrum-generating algebras

Analytic expressions for the eigenvalues and eigenfunctions of nonrelativistic shape-invariant Hamiltonians can be derived using the well-known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess spectrum-generating algebras and are hence solvable by an independent group theory method. We demonstrate the equivalence of the two solution methods by developing an algebraic framework for shape-invariant Hamiltonians with a general parameter change involving nonlinear extensions of Lie algebras. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118, No. 3, pp. 362–374, March, 1999.     

Generation of a complete set of additive shape-invariant potentials from an Euler equation

In supersymmetric quantum mechanics, shape invariance is a sufficient condition for solvability. We show that all conventional additive shape-invariant superpotentials that are independent of ? can be generated from two partial differential equations. One of these is equivalent to the one-dimensional Euler equation expressing momentum conservation for inviscid fluid flow, and it is closed by the other. We solve these equations, generate the set of all conventional shape-invariant superpotentials, and show that there are no others in this category. We then develop an algorithm for generating all additive shape-invariant superpotentials including those that depend on ? explicitly.     

Low-Frequency Ultrasound Coupled with High-Pressure Technologies: Impact of Hybridized Techniques on the Recovery of Phytochemical Compounds

The coupling of innovative technologies has emerged as a smart alternative for the process intensification of bioactive compound extraction from plant matrices. In this regard, the development of hybridized techniques based on the low-frequency and high-power ultrasound and high-pressure technologies, such as supercritical fluid extraction, pressurized liquids extraction, and gas-expanded liquids extraction, can enhance the recovery yields of phytochemicals due to their different action mechanisms. Therefore, this paper reviewed and discussed the current scenario in this field where ultrasound-related technologies are coupled with high-pressure techniques. The main findings, gaps, challenges, advances in knowledge, innovations, and future perspectives were highlighted.     

Breit interaction determination of muonic hyperfine anomalies: Large but not giant

Muon-nuclear-hyperfine anomalies are determined from Breit interaction calculations based on unrestricted Dirac-Fock solutions which explicitly include all electrons and the negative muon. We obtain anomalies of a few (3) percent, which are much larger than corresponding Bohr-Weisskopf electron-nuclear anomalies, but are much smaller than the giant, ≈(36 ± 5)%, anomaly reported by Yamazaki et al. for μ^-Pd⁺ vs. Rh. We suggest the possibility that interstitial μ^-Pd⁺ was observed and that the small anomaly for substitutional μ^-Pd⁺ may also be seen at higher temperatures.