Even factors with a bounded number of components in iterated line graphs

We consider even factors with a bounded number of components in the n-times iterated line graphs L ⁿ (G). We present a characterization of a simple graph G such that L ⁿ (G) has an even factor with at most k components, based on the existence of a certain type of subgraphs in G. Moreover, we use this result to give some upper bounds for the minimum number of components of even factors in L ⁿ (G) and also show that the minimum number of components of even factors in L ⁿ (G) is stable under the closure operation on a claw-free graph G, which extends some known results. Our results show that it seems to be NP-hard to determine the minimum number of components of even factors of iterated line graphs. We also propose some problems for further research.     

Enhanced Four-Electron Oxygen Reduction Selectivity of Clamp-Shaped Cobalt(II) Porphyrin(2.1.2.1) Complexes

The molecular structure, electrochemistry, spectroelectrochemistry and electrocatalytic oxygen reduction reaction (ORR) features of two Co^II porphyrin(2.1.2.1) complexes bearing Ph or F₅Ph groups at the two meso-positions of the macrocycle are examined. Single crystal X-ray analysis reveal a highly bent, nonplanar macrocyclic conformation of the complex resulting in clamp-shaped molecular structures. Cyclic voltammetry paired with UV/Vis spectroelectrochemistry in PhCN/0.1 M TBAP suggest that the first electron addition corresponds to a macrocyclic-centered reduction while spectral changes observed during the first oxidation are consistent with a metal-centered Co^II/Co^III process. The activity of the clamp-shaped complexes towards heterogeneous ORR in 0.1 M KOH show selectivity towards the 4e⁻ ORR pathway giving H₂O. DFT first-principle calculations on the porphyrin catalyst indicates a lower overpotential for 4e⁻ ORR as compared to the 2e⁻ pathway, consistent with experimental data.     

Radical-Bridged Heterometallic Single-Molecule Magnets Incorporating Four Lanthanoceniums

The syntheses and magnetic properties of organometallic heterometallic compounds [K(THF)₆]{Co^I[(μ₃-HAN)RE₂Cp*₄]₂} ( 1-RE ) and [K(Crypt)]₂{Co^I[(μ₃-HAN)RE₂Cp*₄]₂} ( 2-RE ) containing hexaazatrinaphthylene radicals (HAN⋅³⁻) and four rare earth (RE) ions are reported. 1-RE shows isolable species with ligand-based mixed valency as revealed by cyclic voltammetry (CV) thus leading to the isolation of 2-RE via one-electron chemical reduction. Strong electronic communication in mixed-valency supports stronger overall ferromagnetic behaviors in 2-RE than 1-RE containing Gd and Dy ions. Ac magnetic susceptibility data reveal 1-Dy and 2-Dy both exhibit slow magnetic relaxation. Importantly, larger coercive field was observed in the hysteresis of 2-Dy at 2.0 K, indicating the enhanced SMM behavior compared with 1-Dy . Ligand-based mixed-valency strategy has been used for the first time to improve the magnetic coupling in lanthanide (Ln) SMMs, thus opening up new ways to construct strongly coupled Ln-SMMs.     

Chemo-, Stereo- and Regioselective Fluoroallylation/Annulation of Hydrazones with gem-Difluorocyclopropanes via Tunable Palladium/NHC Catalysis

Defluorinative manipulation of polyfluorinated molecules has shown great promise due to its granting of synthetic versatility to inert C−F bonds. The development of chemo-, stereo- and regioselective strategies to realize highly efficient formation of either the linear/branched or E/Z products from gem-difluorocyclopropanes (gem-F₂CPs) is a challenging task. Herein, we have realized palladium/NHC-catalyzed fluoroallylation/annulation of hydrazones with gem-F₂CPs that incorporate the hydrazone N₂ moiety into the products. The thermodynamically unstable fluorinated E-allylation products with aryl ketone hydrazones were obtained for the first time, while the di-alkyl ketone hydrazones yielded the monofluorinated products with branched selectivity under similar reaction conditions. With aldehyde hydrazones, two kinds of pyrazoles were obtained via a defluorinative allylation/annulation cascade, in which different carbon atoms of gem-F₂CPs could be incorporated into the pyrazole rings regiospecifically. DFT calculations revealed that the divergent selectivity was kinetically controlled and the final C−C bond formation proceeded through a 7-membered TS.     

Coordinating the Edge Defects of Bismuth with Sulfur for Enhanced CO2 Electroreduction to Formate

Bismuth-based materials have been recognized as promising catalysts for the electrocatalytic CO₂ reduction reaction (ECO₂RR). However, they show poor selectivity due to competing hydrogen evolution reaction (HER). In this study, we have developed an edge defect modulation strategy for Bi by coordinating the edge defects of bismuth (Bi) with sulfur, to promote ECO₂RR selectivity and inhibit the competing HER. The prepared catalysts demonstrate excellent product selectivity, with a high HCOO⁻ Faraday efficiency of ≈95 % and an HCOO⁻ partial current of ≈250 mA cm⁻² under alkaline electrolytes. Density function theory calculations reveal that sulfur tends to bind to the Bi edge defects, reducing the coordination-unsaturated Bi sites (*H adsorption sites), and regulating the charge states of neighboring Bi sites to improve *OCHO adsorption. This work deepens our understanding of ECO₂RR mechanism on bismuth-based catalysts, guiding for the design of advanced ECO₂RR catalysts.     

NH4+ Charge Carrier Coordinated H-Bonded Organic Small Molecule for Fast and Superstable Rechargeable Zinc Batteries

Organic small molecules as high-capacity cathodes for Zn-organic batteries have inspired numerous interests, but are trapped by their easy-dissolution in electrolytes. Here we knit ultrastable lock-and-key hydrogen-bonding networks between 2, 7-dinitropyrene-4, 5, 9, 10-tetraone (DNPT) and NH₄⁺ charge carrier. DNPT with octuple-active carbonyl/nitro centers (H-bond acceptor) are redox-exclusively accessible for flexible tetrahedral NH₄⁺ ions (H-bond donator) but exclude larger and rigid Zn²⁺, due to a lower activation energy (0.14 vs. 0.31 eV). NH₄⁺ coordinated H-bonding chemistry conquers the stability barrier of DNPT in electrolyte, and gives fast diffusion kinetics of non-metallic charge carrier. A stable two-step 4e⁻ NH₄⁺ coordination with DNPT cathode harvests a high capacity (320 mAh g⁻¹), a high-rate capability (50 A g⁻¹) and an ultralong life (60,000 cycles). This finding points to a new paradigm for H-bond stabilized organic small molecules to design advanced zinc batteries.     

Sodium Carbazolide and Derivatives as Solid-State Electrolytes for Sodium-Ion Batteries

Replacing widely used organic liquid electrolytes with solid-state electrolytes (SSEs) could effectively solve the safety issues in sodium-ion batteries. Efforts on seeking novel solid-state electrolytes have been continued for decades. However, issues about SSEs still exist, such as low ionic conductivity at ambient temperature, difficulty in manufacturing, low electrochemical stability, poor compatibility with electrodes, etc. Here, sodium carbazolide (Na-CZ) and its THF-coordinated derivatives are rationally fabricated as Na⁺ conductors, and two of their crystal structures are successfully solved. Among these materials, THF-coordinated complexes exhibit fast Na⁺ conductivities, i.e., 1.20×10⁻⁴ S cm⁻¹ and 1.95×10⁻³ S cm⁻¹ at 90 °C for Na-CZ-1THF and Na-CZ-2THF, respectively, which are among the top Na⁺ conductors under the same condition. Furthermore, stable Na plating/stripping is observed even over 400 h cycling, showing outstanding interfacial stability and compatibility against Na electrode. More advantages such as ease of synthesis, low-cost, and cold pressing for molding can be obtained. In situ NMR results revealed that the evaporation of THF may play an essential role in the Na⁺ migration, where the movement of THF creates defects/vacancies and facilitates the migration of Na⁺.     

Photocatalytic Free Radical-Controlled Synthesis of High-Performance Single-Atom Catalysts

Single-atom catalysts (SACs) have emerged as crucial players in catalysis research, prompting extensive investigation and application. The precise control of metal atom nucleation and growth has garnered significant attention. In this study, we present a straightforward approach for preparing SACs utilizing a photocatalytic radical control strategy. Notably, we demonstrate for the first time that radicals generated during the photochemical process effectively hinder the aggregation of individual atoms. By leveraging the cooperative anchoring of nitrogen atoms and crystal lattice oxygen on the support, we successfully stabilize the single atom. Our Pd₁/TiO₂ catalysts exhibit remarkable catalytic activity and stability in the Suzuki–Miyaura cross-coupling reaction, which was 43 times higher than Pd/C. Furthermore, we successfully depose Pd atoms onto various substrates, including TiO₂, CeO₂, and WO₃. The photocatalytic radical control strategy can be extended to other single-atom catalysts, such as Ir, Pt, Rh, and Ru, underscoring its broad applicability.     

A Janus Separator based on Cation Exchange Resin and Fe Nanoparticles-decorated Single-wall Carbon Nanotubes with Triply Synergistic Effects for High-areal Capacity Zn−I2 Batteries

Zn−I₂ batteries stand out in the family of aqueous Zn-metal batteries (AZMBs) due to their low-cost and immanent safety. However, Zn dendrite growth, polyiodide shuttle effect and sluggish I₂ redox kinetics result in dramatically capacity decay of Zn−I₂ batteries. Herein, a Janus separator composed of functional layers on anode/cathode sides is designed to resolve these issues simultaneously. The cathode layer of Fe nanoparticles-decorated single-wall carbon nanotubes can effectively anchor polyiodide and catalyze the redox kinetics of iodine species, while the anode layer of cation exchange resin rich in −SO₃⁻ groups is beneficial to attract Zn²⁺ ions and repel detrimental SO₄²⁻/polyiodide, improving the stability of cathode/anode interfaces synergistically. Consequently, the Janus separator endows outstanding cycling stability of symmetrical cells and high-areal-capacity Zn−I₂ batteries with a lifespan over 2500 h and a high-areal capacity of 3.6 mAh cm⁻².     

Photo-Driven Quasi-Topological Transformation Exposing Highly Active Nitrogen Cation Sites for Enhanced Photocatalytic H2O2 Production

Herein, the exposure of highly-active nitrogen cation sites has been accomplished by photo-driven quasi-topological transformation of a 1,10-phenanthroline-5,6-dione-based covalent organic framework (COF), which contributes to hydrogen peroxide (H₂O₂) synthesis during the 2-electron O₂ photoreduction. The exposed nitrogen cation sites with photo-enhanced Lewis acidity not only act as the electron-transfer motor to adjust the inherent charge distribution, powering continuous and stable charge separation, and broadening visible-light adsorption, but also providing a large number of active sites for O₂ adsorption. The optimal catalyst shows a high H₂O₂ production rate of 11965 μmol g⁻¹ h⁻¹ under visible light irradiation and a remarkable apparent quantum yield of 12.9 % at 400 nm, better than most of the previously reported COF photocatalysts. This work provides new insights for designing photo-switchable nitrogen cation sites as catalytic centers toward efficient solar to chemical energy conversion.