Quaternionic Killing Spinors

In [17] we proved a lower bound for the spectrum of the Dirac operator on quaternionic Kähler manifolds. In the present article we study the limiting case, i.e. manifolds where the lower bound is attained as an eigenvalue. We give an equivalent formulation in terms of a quaternionic Killing equation and show that the only symmetric quaternionic Kähler manifolds with smallest possible eigenvalue are the quaternionic projective spaces.     

Single jet photoproduction at HERA in next-to-leading order QCD

We present results for next-to-leading order calculations of single jet inclusive cross sections by resolved photons inep-collisions at HERA. The dependence on the jet recombination cut and on the choice of the renormalization and factorization scales is studied in detail.     

On the stability of the polaron in one dimensional disordered systems

A one-dimensional disordered system of electrons described by a tight binding model interacting with vibrational degrees of freedom (in harmonic approximation) is considered. A stable configuration is determined by a numerical minimization of the total energy which is based on the adiabatic approximation. The behaviour of the electron density (charge density wave) and the density of states is analysed. The localization properties are investigated as well. In contrast to the corresponding disordered system with vanishing electron-phonon coupling the present model has an energy gap. The formation of the gap and the polaron band is shown to be quite different for both onsite and intersite types of coupling terms. For large disorder, the lattice distortion and the gap disappear if only the vibrational contribution to the intersite coupling is important. They increase, however, if only the vibrational contribution to the site energies is taken into account. In both cases the localization length decreases upon increasing the electron-phonon coupling energy. The results are discussed with respect to low dimensional organic materials and amorphous semiconductors.     

Reductive Insertion of Elemental Chalcogens into Boron–Boron Multiple Bonds

The syntheses of sulfur‐ and selenium‐bridged cyclic compounds containing boron stabilized by N‐heterocyclic carbenes (NHCs) have been achieved by the reductive insertion of elemental chalcogens into boron–boron multiple bonds. The three pairs of bonding electrons between the boron atoms in the triply bonded diboryne enabled six‐electron reduction reactions, resulting in the formation of [2.2.1]‐bicyclic systems wherein bridgehead boron atoms are spanned by three chalcogen bridges. A similar reaction using a diborene (boron–boron double bond) resulted in the reductive transfer of both pairs of bonding electrons to three sulfur atoms, yielding a NHC‐stabilized trisulfidodiborolane. The demonstration of these six‐ and four‐electron reductions lends support to the presence of three and two pairs of bonding electrons between the boron atoms of the diboryne and diborene, respectively, a fact that may be useful in future discussions on bond order.     

The Synthesis of B2(SIDip)2 and its Reactivity Between the Diboracumulenic and Diborynic Extremes

A new compound with the formula L‐B₂‐L wherein the stabilizing ligand (L) is 1,3‐bis[diisopropylphenyl]‐4,5‐dihydroimidazol‐2‐ylidene (SIDip) has been synthesized, isolated, and characterized. The π‐acidity of the SIDip ligand, intermediate between the relatively non‐acidic IDip (1,3‐bis[diisopropylphenyl]imidazol‐2‐ylidene) ligand and the much more highly acidic CAAC (1‐[2,6‐diisopropylphenyl]‐3,3,5,5‐tetramethylpyrrolidin‐2‐ylidene) ligand, gives rise to a compound with spectroscopic, electrochemical, and structural properties between those of L‐B₂‐L compounds stabilized by CAAC and IDip. Reactions of all three L‐B₂‐L compounds with CO demonstrate the differences caused by their respective ligands, as the π‐acidities of the CAAC and SIDip carbenes enabled the isolation of bis(boraketene) compounds (L(OC)B‐B(CO)L), which could not be isolated from reactions with B₂(IDip)₂. However, only B₂(IDip)₂ and B₂(SIDip)₂ could be converted into bicyclic bis(boralactone) compounds.     

Ansa‐Bridged Bis(benzene) Titanium Complexes

Taking advantage of an improved synthesis of [Ti(η⁶‐C₆H₆)₂], we report here the first examples of ansa‐bridged bis(benzene) titanium complexes. Deprotonation of [Ti(η⁶‐C₆H₆)₂] with nBuLi in the presence of N,N,N′,N′′,N′′‐pentamethyldiethylenetriamine (pmdta) leads to the corresponding 1,1′‐dilithio salt [Ti(η⁶‐C₆H₅Li)₂] ? pmdta that enables the preparation of the first one‐ and two‐atom‐bridged complexes by simple salt metathesis. The ansa complexes were fully characterized (NMR spectroscopy, UV/Vis spectroscopy, elemental analysis, and X‐ray crystallography) and further studied electrochemically and computationally. Moreover, [Ti(η⁶‐C₆H₆)₂] is found to react with the Lewis base 1,3‐dimethylimidazole‐2‐ylidene (IMe) to give the bent sandwich complex [Ti(η⁶‐C₆H₆)₂(IMe)].     

Ansa‐Complexes of [Mn(η5‐C5H5)(η6‐C6H6)]: Preparation,Characterization, and Reactivity of [n]Manganoarenophanes (n=1, 2, 3)

We report the synthesis of [n]manganoarenophanes (n=1, 2) featuring boron, silicon, germanium, and tin as ansa‐bridging elements. Their preparation was achieved by salt‐elimination reactions of the dilithiated precursor [Mn(η⁵‐C₅H₄Li)(η⁶‐C₆H₅Li)]?pmdta (pmdta=N,N,N′,N′,N′′‐pentamethyldiethylenetriamine) with corresponding element dichlorides. Besides characterization by multinuclear NMR spectroscopy and elemental analysis, the identity of two single‐atom‐bridged derivatives, [Mn(η⁵‐C₅H₄)(η⁶‐C₆H₅)SntBu₂] and [Mn(η⁵‐C₅H₄)(η⁶‐C₆H₅)SiPh₂], could also be determined by X‐ray structural analysis. We investigated for the first time the reactivity of these ansa‐cyclopentadienyl–benzene manganese compounds. The reaction of the distannyl‐bridged complex [Mn(η⁵‐C₅H₄)(η⁶‐C₆H₅)Sn₂tBu₄] with elemental sulfur was shown to proceed through the expected oxidative addition of the Sn?Sn bond to give a triatomic ansa‐bridge. The investigation of the ring‐opening polymerization (ROP) capability of [Mn(η⁵‐C₅H₄)(η⁶‐C₆H₅)SntBu₂] with [Pt(PEt₃)₃] showed that an unexpected, unselective insertion into the C_ipso?Sn bonds of [Mn(η⁵‐C₅H₄)(η⁶‐C₆H₅)SntBu₂] had occurred.     

N‐Alkoxyheterocycles As Irreversible Photooxidants

Irreversible photooxidation based on N–O bond fragmentation is demonstrated for N‐methoxyheterocycles in both the singlet and triplet excited state manifolds. The energetic requirements for bond fragmentation are studied in detail. Bond fragmentation in the excited singlet manifold is possible for ππ* singlet states with energies significantly larger than the N–O bond dissociation energy of ca 55 kcal mol^?1. For the nπ* triplet states, N–O bond fragmentation does not occur in the excited state for orbital overlap and energetic reasons. Irreversible photooxidation occurs in the singlet states by bond fragmentation followed by electron transfer. Irreversible photooxidation occurs in the triplet states via bimolecular electron transfer to the donor followed by bond fragmentation. Using these two sensitization schemes, donors can be irreversibly oxidized with oxidation potentials ranging from ca 1.6–2.2 V vs SCE. The corresponding N‐ethylheterocycles are characterized as conventional reversible photooxidants in their triplet states. The utility of these sensitizers is demonstrated by irreversibly generating the guanosine radical cation in buffered aqueous solution.     

Rapid determination of 226Ra in drinking water samples using dispersive liquid-liquid microextraction coupled with liquid scintillation counting

A new radioanalytical method was developed for rapid determination of ²²⁶Ra in drinking water samples. The method is based on extraction and preconcentration of ²²⁶Ra from a water sample to an organic solvent using a dispersive liquid-liquid microextraction (DLLME) technique followed by radiometric measurement using liquid scintillation counting. In DLLME for ²²⁶Ra, a mixture of an organic extractant (toluene doped with dibenzo-21-crown-7 and 2-theonyltrifluoroacetone) and a disperser solvent (acetonitrile) is rapidly injected into the water sample resulting in the formation of an emulsion. Within the emulsion, ²²⁶Ra reacts with dibenzo-21-crown-7 and 2-theonyltrifluoroacetone and partitions into the fine droplets of toluene. The water/toluene phases were separated by addition of acetonitrile as a de-emulsifier solvent. The toluene phase containing ²²⁶Ra was then measured by liquid scintillation counting. Several parameters were studied to optimize the extraction efficiency of ²²⁶Ra, including water immiscible organic solvent, disperser and de-emulsifier solvent type and their volume, chelating ligands for ²²⁶Ra and their concentrations, inorganic salt additive and its concentration, and equilibrium pH. With the optimized DLLME conditions, the accuracy (expressed as relative bias, B _r ) and method repeatability (expressed as relative precision, S _B ) were determined by spiking ²²⁶Ra at the maximum acceptable concentration level (0.5 Bq L⁻¹) according to the Guidelines for Canadian Drinking Water Quality. Accuracy and repeatability were found to be less than −5% (B _r ) and less than 6% (S _B ), respectively, for both tap water and bottled natural spring water samples. The minimum detectable activity and sample turnaround time for determination of ²²⁶Ra was 33 mBq L⁻¹ and less than 3 h, respectively. The DLLME technique is selective for extraction of ²²⁶Ra from its decay progenies.