The 2:1 cocrystal of benzamide and penta­fluoro­benzoic acid

The crystal structure of the title compound, benzamide–2,3,4,5,6‐penta­fluoro­benzoic acid (2/1), 2C₇H₇NO·C₇HF₅O₂, consists of centrosymmetric hexa­meric supermolecules composed of four amide and two carboxylic acid mol­ecules connected via O—H⋯O and N—H⋯O hydrogen bonds. No phen­yl–perfluoro­phenyl π–π stacking inter­actions are observed in this cocrystal.     

On the reactivity of platina‐β‐diketones: a straightforward synthesis of trans‐acetylchlorobis(phosphine)platinum(II) complexes and their reactivity

The platina‐β‐diketone [Pt₂{(COMe)₂H}₂(µ‐Cl)₂] ( 1 ) was found to react with monodentate phosphines to yield acetyl(chloro)platinum(II) complexes trans‐[Pt(COMe)Cl(PR₃)₂] (PR₃ = PPh₃, 2a ; P(4‐FC₆H₄)₃, 2b ; PMePh₂, 2c ; PMe₂Ph, 2d ; P(n‐Bu)₃, 2e ; P(o‐tol)₃, 2f ; P(m‐tol)₃, 2g ; P(p‐tol)₃, 2h ). In the reaction with P(o‐tol)₃ the methyl(carbonyl)platinum(II) complex [Pt(Me)Cl(CO){P(o‐tol)₃}] ( 3a ) was found to be an intermediate. On the other hand, treating 1 with P(C₆F₅)₃ led to the formation of [Pt(Me)Cl(CO){P(C₆F₅)₃}] ( 3b ), even in excess of the phosphine. Phosphine ligands with a lower donor capability in complexes 2 and the arsine ligand in trans‐[Pt(COMe)Cl(AsPh₃)₂] ( 2i ) proved to be subject to substitution by stronger donating phosphine ligands, thus forming complexes trans‐[Pt(COMe)Cl(L)L′] (L/L′ = AsPh₃/PPh₃, 4a ; PPh₃/P(n‐Bu)₃, 4b ) and cis‐[Pt(COMe)Cl(dppe)] ( 4c ). Furthermore, in boiling benzene, complexes 2a – 2c and 2i underwent decarbonylation yielding quantitatively methyl(chloro)platinum(II) complexes trans‐[Pt(Me)Cl(L)₂] (L = PPh₃, 5a ; P(4‐FC₆H₄)₃, 5b ; PMePh₂, 5c ; AsPh₃, 5d ). The identities of all complexes were confirmed by ¹H, ¹³C and ³¹P NMR spectroscopy. Single‐crystal X‐ray diffraction analyses of 2a ·2CHCl₃, 2f and 5b showed that the platinum atom is square‐planar coordinated by two phosphine ligands (PPh₃, 2a ; P(o‐tol)₃, 2f ; P(4F‐C₆H₄)₃, 5b ) in mutual trans position as well as by an acetyl ligand ( 2a, 2f ) and a methyl ligand ( 5b ), respectively, trans to a chloro ligand. Single‐crystal X‐ray diffraction analysis of 3b exhibited a square‐planar platinum complex with the two π‐acceptor ligands CO and P(C₆F₅)₃ in mutual cis position (configuration index: SP‐4‐3). Copyright © 2005 John Wiley & Sons, Ltd.     

Simulations of energy and switching in AFLCDs with different boundary conditions

Using standard expressions for the various terms in the Gibbs free energy, the switching in antiferroelectric liquid crystal (AFLC) displays is simulated and the time evolution of various energy terms and of the liquid crystal director distributions are calculated. It is shown that when returning from a strong positive voltage to zero, one can reach two types of antiferroelectric state: the normal alternating state with the two bulk polarizations perpendicular to the electrodes and opposite to each other, and the alternative splayed symmetric state with two bulk polarizations parallel to the electrodes and again opposite to each other. The former case gives rise to tri-state switching characteristics, the latter to V-shaped switching. In general strong polar interaction with the alignment layer favours V-shaped switching while weak or no polar interaction give rise to tri-state switching characteristics. Since the V-shaped characteristic has so far only been demonstrated experimentally in ferroelectric liquid crystals (or antiferroelectric liquid crystals being in the ferroelectric state), the difference in AFLCs is discussed and the conditions for continuous switching are modelled. The simulations show that the switching characteristics of the antiferroelectric display can be controlled by the surface parameters.     

Boundary Solutions of Differential Inclusions and Recovering the Initial Data

The solutions of differential inclusions staying at the boundary of attained sets are investigated using the contingent cones to attained sets. The possibility of recovering the starting point and the time which elapsed since the beginning is shown when some fragments of an attained set are known.     

Parallel implementation of the p‐version of the finite element method for elliptic equations on a shared‐memory architecture

An implementation of the p‐version of the finite element method for solving two‐dimensional linear elliptic problems on a shared‐memory parallel computer is analyzed. The idea is to partition the problem among the available processors and perform computations corresponding to different elements in parallel. The parallelization is based on a domain decomposition technique using the Lagrange multipliers. The numerical experiments carried out on the Sequent system indicate very high performance of the mixed finite element algorithm in terms of attained speedups. This revised version was published online in August 2006 with corrections to the Cover Date.     

Chloride interference with non-stoichiometric copper sulphide copper(II)-selective electrodes : Part 2. Exact determination of the chloride interference region

A general equation for calculating the limit of the ligand interference region with the non-stoichiometric copper sulphide single-crystal electrode is described. The critical ligand concentration can be computed for a preselected maximal error in copper(II) ion determinations. The effect of the composition of the electrode material is discussed. The experimental results for the chloride interference show good agreement with theoretical predictions.     

Dilithium tetrabromonickelate (II) as a source of soft nucleophilic bromide : Reaction with epoxides

Dilithium tetrabromonickelate (II) in THF serves as a source of “soft” nucleophilic bromide and reacts regioselectively with epoxides to give bromohydrins in high yield.     

Complete spaces and zero-one measures

It is the purpose of this paper to characterize the complete spaces in the sense of [6] by measure-theoretic properties. Let (X,) be a measurable space and let be a subpaving of satisfying certain closure properties, then X is-complete iff every 0,1-valued-regular measure on is a Dirac measure. In particular, we obtain Hewitt's well-known theorem that a completely regular space X is realcompact iff every 0,1-valued Baire measure on X is a Dirac measure. The main tool for our investigations is an extension theorem for measures due to Topsoe [10].     

The mass gap for Higgs models on a unit lattice

An isomorphism is established between eertain compact and noncompact formulations of Abelian gauge theory on a lattice. For weak coupling, the mass gap predicted by the Higgs mechanism is then established.