On the solution of Maxwell's equations in polygonal domains

This paper is concerned with the structure of the singular and regular parts of the solution of time‐harmonic Maxwell's equations in polygonal plane domains and their effective numerical treatment. The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation and it is proved that the solution of the boundary value problem does not belong locally to H² when the boundary of the domain has non‐acute angles. A splitting of the solution into a regular part belonging to the space H², and an explicitly described singular part is presented. For the numerical treatment of the boundary value problem, we propose a finite element discretization which combines local mesh grading and the singular field methods and derive a priori error estimates that show optimal convergence as known for the classical finite element method for problems with regular solutions. Copyright © 2006 John Wiley & Sons, Ltd.     

Reductive claisen rearrangements of anthraquinone allyl ethers

Gentle heating of allyloxyanthraquinones with sodium dithionite in dimethylformanide - water effects a rapid and controlled rearrangement to give high yields of 2-allyanthraquinones.     

Eu8(NCN)5-deltaI6+2delta (delta= 0.05): a novel rare-earth carbodiimide iodide containing oligomeric tritetrahedral Eu8 clusters

Eu8(NCN)4.95I6.10 is the first compound with discrete tritetrahedral Eu8 clusters which are interconnected by coordinating NCN2- carbodiimide anions on their triangular faces to form separated layers, the latter being bridged by iodide and carbodiimide anions.     

Non-Template-Centered, Closed Tetravanadium Phosphate and Phosphonate Clusters

Tetranuclear V(III) complexes, [HB(pz)(3)](4)V(4)(&mgr;-C(6)H(5)OPO(3))(4) (I), its acetonitrile solvate (I.4CH(3)CN), and [HB(pz)(3)](4)V(4)(&mgr;-O(2)NC(6)H(4)OPO(3))(4).4C(7)H(8).H(2)O (II), and tetranuclear vanadyl complexes, (t-Bupz)(4)V(4)O(4)(&mgr;-C(6)H(5)PO(3))(4).2H(2)O (III) and (t-Bupz)(5)V(4)O(4)(&mgr;-C(6)H(5)PO(3))(4).4CH(3)CN.0.6 H(2)O (IV), have been prepared and characterized by spectroscopic, magnetic, and electrochemical methods (pz = pyrazole, t-Bupz = tert-butylpyrazole). The use of organic solvents and bulky organic groups as ancillary ligands leads to formation of neutral species instead of the anionic clusters commonly found in the hydrothermal synthesis of vanadium organophosphate/phosphonate systems. Complexes I.4CH(3)CN and IV have also been characterized by single-crystal X-ray diffraction. Crystal data: I.4CH(3)CN, triclinic, P&onemacr;, a = 15.495(3) ?, b = 17.000(3) ?, c = 17.949(4) ?, alpha = 89.17(3) degrees, beta = 86.00(3) degrees, gamma = 78.60(3) degrees, Z = 2; IV, triclinic, P&onemacr;, a = 15.541(3) ?, b = 16.340(2) ?, c = 19.069(5) ?, alpha = 83.58(2) degrees, beta = 79.67(2) degrees, gamma = 63.68(1) degrees, Z = 2. Both are closed clusters, the core structure of the first consisting of a cubane-like arrangement of metal octahedra and phosphate tetrahedra and the core structure of the second consisting of a distorted, collapsed variant of the first. Unlike other vanadium phosphate clusters, these compounds form in the absence of a central, templating agent. As such they represent the simplest form of a closed cluster in which steric forces and cluster connectivity requirements play the primary role in organizing the cluster framework.     

Unexpected Correlation Between Boron Chain Condensation and Hydrogen Evolution Reaction (HER) Activity in Highly Active Vanadium Borides: Enabling Predictions

Transition‐metal borides (TMBs) have recently attracted attention as excellent hydrogen evolution (HER) electrocatalysts in bulk crystalline materials. Herein, we show for the first time that VB and V₃B₄ have high electrocatalytic HER activity. Furthermore, we show that the HER activity (in 0.5 m H₂SO₄) increases with increasing boron chain condensation in vanadium borides: Using a ?23 mV overpotential decrement derived from ?0.296 mV (for VB at ?10 mA cm^?2 current density) and ?0.273 mV (for V₃B₄) we accurately predict the overpotential of VB₂ (?0.204 mV) as well as that of unstudied V₂B₃ (?0.250 mV) and hypothetical “V₅B₈” (?0.227 mV). We then derived an exponential equation that predicts the overpotentials of known and hypothetical V_xB_y phases containing at least a boron chain. These results provide a direct correlation between crystal structure and HER activity, thus paving the way for the design of even better electrocatalytic materials through structure–activity relationships.     

[CrBr2(NH3)4][CrBr4(NH3)2], a new chromium(III) complex

Green single crystals of trans‐tetraamminedibromidochromium(III) trans‐diamminetetrabromidochromate(III), [CrBr₂(NH₃)₄][CrBr₄(NH₃)₂], are found to contain two symmetry‐independent sixfold coordinated Cr^III cations on centres of inversion. The structure is composed of octahedral trans‐[CrBr₂(NH₃)₄]⁺ cations and octahedral trans‐[CrBr₄(NH₃)₂]⁻ anions, and adopts a distorted CsCl‐type lattice. The cations and anions are linked by N—H...Br interactions. This is the first example in which both ions are mixed ammine–bromide Cr^III complexes.     

Synthesis,Characterization, and Magnetic Properties of the New Boride Solid Solutions M0.5Ru6.5B3 (M = Cr,Mn, Co,Ni)

Powder samples and single crystals of the borides M_0.5Ru_6.5B₃ (M = Cr, Mn, Co, Ni) were synthesized by arc‐melting the elements in a water‐cooled copper crucible under argon. The new phases were structurally characterized by single‐crystal and powder X‐ray diffraction as well as EDX‐Analyses. They crystallize in the hexagonal Th₇Fe₃ structure type (space group P6₃mc, no. 186, Z = 2) and a pronounced site preferential M/Ru substitution is observed. Magnetic properties of the compounds were investigated and Pauli paramagnetism was observed in all cases. However, a strong temperature dependency is subsequently observed in Mn_0.5Ru_6.5B₃ below 250 K, but no hint of magnetic ordering was found.