Comparison of thermodynamic and kinetic aspects of oxidative addition of PhE-EPh (E = S, Se, Te) to Mo(CO)3(PR3)2, W(CO)3(PR3)2, and Mo(N[tBu]Ar)3 complexes. The role of oxidation state and ancillary ligands in metal complex induced chalcogenyl radical generation

Enthalpies of oxidative addition of PhE-EPh (E = S, Se, Te) to the M(0) complexes M(PiPr3)2(CO)3 (M = Mo, W) to form stable complexes M(*EPh)(PiPr3)2(CO)3 are reported and compared to analogous data for addition to the Mo(III) complexes Mo(N[tBu]Ar)3 (Ar = 3,5-C6H3Me2) to form diamagnetic Mo(IV) phenyl chalcogenide complexes Mo(N[tBu]Ar)3(EPh). Reactions are increasingly exothermic based on metal complex, Mo(PiPr3)2(CO)3 < W(PiPr3)2(CO)3 < Mo(N[tBu]Ar)3, and in terms of chalcogenide, PhTe-TePh < PhSe-SePh < PhS-SPh. These data are used to calculate LnM-EPh bond strengths, which are used to estimate the energetics of production of a free *EPh radical when a dichalcogenide interacts with a specific metal complex. To test these data, reactions of Mo(N[tBu]Ar)3 and Mo(PiPr3)2(CO)3 with PhSe-SePh were studied by stopped-flow kinetics. First- and second-order dependence on metal ion concentration was determined for these two complexes, respectively, in keeping with predictions based on thermochemical data. ESR data are reported for the full set of bound chalcogenyl radical complexes (PhE*)M(PiPr3)2(CO)3; g values increase on going from S to Se, to Te, and from Mo to W. Calculations of electron densities of the SOMO show increasing electron density on the chalcogen atom on going from S to Se to Te. The crystal structure of W(*TePh)(PiPr3)2(CO)3 is reported.     

Benzonitrile extrusion from molybdenum(IV) ketimide complexes obtained via radical C-E (E = O, S, Se) bond formation: toward a new nitrogen atom transfer reaction

Beta-elimination is explored as a possible means of nitrogen-atom transfer into organic molecules. Molybdenum(IV) ketimide complexes of formula (Ar[t-Bu]N)3Mo(N=C(X)Ph), where Ar = 3,5-Me2C6H3 and X = SC6F5, SeC6F5, or O2CPh, are formally derived from addition of the carbene fragment [:C(X)Ph] to the terminal nitrido molybdenum(VI) complex (Ar[t-Bu]N)3Mo identical with N in which the nitrido nitrogen atom is installed by scission of molecular nitrogen. Herein the pivotal (Ar[t-Bu]N)3Mo(N=C(X)Ph) complexes are obtained through independent synthesis, and their propensity to undergo beta-X elimination, i.e., conversion to (Ar[t-Bu]N)3MoX + PhC identical with N, is investigated. Radical C-X bond formation reactions ensue when benzonitrile is complexed to the three-coordinate molybdenum(III) complex (Ar[t-Bu]N)3Mo and then treated with 0.5 equiv of X2, leading to facile assembly of the key (Ar[t-Bu]N)3Mo(N=C(X)Ph) molecules. Treated herein are synthetic, structural, thermochemical, and kinetic aspects of (i) the radical C-X bond formation and (ii) the ensuing beta-X elimination processes. Beta-X elimination is found to be especially facile for X = O2CPh, and the reaction represents an attractive component of an overall synthetic cycle for incorporation of dinitrogen-derived nitrogen atoms into organic nitrile (R-C identical with N) molecules.     

Fast head-related transfer function measurement via reciprocity

An efficient method for head-related transfer function (HRTF) measurement is presented. By applying the acoustical principle of reciprocity, one can swap the speaker and the microphone positions in the traditional (direct) HRTF measurement setup, that is, insert a microspeaker into the subject's ear and position several microphones around the subject, enabling simultaneous HRTF acquisition at all microphone positions. The setup used for reciprocal HRTF measurement is described, and the obtained HRTFs are compared with the analytical solution for a sound-hard sphere and with KEMAR manikin HRTF obtained by the direct method. The reciprocally measured sphere HRTF agrees well with the analytical solution. The reciprocally measured and the directly measured KEMAR HRTFs are not exactly identical but agree well in spectrum shape and feature positions. To evaluate if the observed differences are significant, an auditory localization model based on work by J. C. Middlebrooks [J. Acoust. Soc. Am. 92, 2607-2624 (1992)] was used to predict where a virtual sound source synthesized with the reciprocally measured HRTF would be localized if the directly measured HRTF were used for the localization. It was found that the predicted localization direction generally lies close to the measurement direction, indicating that the HRTFs obtained via the two methods are in good agreement.     

Highly selective oxidative cleavage of beta-cyclodextrin-epoxide/aziridine complexes with IBX in water

Water, an environmentally friendly reaction medium, has been utilized for the reaction of IBX with various epoxides 1 and aziridines 2 as their beta-cyclodextrin complexes to afford for the first time alpha-hydroxyketones 3 and alpha-aminoketones 4, respectively.     

Synthesis of α-diazo-β-hydroxy esters using nanocrystalline MgO

Nanocrystalline magnesium oxide (NAP-MgO) has been found to be an effective heterogeneous, solid base catalyst for the direct aldol type reaction of ethyl diazoacetate and various aldehydes to afford the corresponding α-diazo-β-hydroxy esters in excellent yields with high selectivity under mild conditions.     

Heterobimetallic reductive cross-coupling of benzonitrile with carbon dioxide, pyridine, and benzophenone

Described herein are heterobimetallic radical cross-coupling reactions between the benzonitrile adduct of the molybdenum(III) complex Mo(N[t-Bu]Ar)3 (Ar = 3,5-C6H3Me2) and titanium(III) complexes with carbon dioxide, pyridine, and benzophenone. The titanium(III) system employed was either Ti(N[t-Bu]Ar)3 (Ar = 3,5-C6H3Me2) or Ti(N[t-Bu]Ph)3. Crystal structure studies are described for the Mo/PhCN/CO2/Ti coupled system and for an analogue of the Mo/PhCN/Ph2CO/Ti coupled system in which PhCN is replaced with 2,6-Me2C6H3CN. In the case of the couplings involving pyridine and benzophenone, C-C bond formation takes place with dearomatization, with the new C-C bond being formed between the nitrile carbon of PhCN and the para carbon of pyridine or one of the benzophenone phenyl groups. Of the radical metal complex/substrate adducts invoked in this work, that between titanium(III) and CO2 is the only one not directly observable. In all cases, the selective cross-coupling reactions are interpreted as arising by heterodimerization of titanium(III) substrate complexes (substrate = CO2, py, or Ph2CO) with the persistent molybdenum-PhCN radical adduct. All of the heterobimetallic coupling products are diamagnetic, and the metal ions Ti and Mo in them both are assigned to the formal 4+ oxidation state.     

Orthogonal polynomial approach to discrete Lax pairs for initial boundary-value problems of the QD algorithm

Using orthogonal polynomial theory, we construct the Lax pair for the quotient-difference algorithm in the natural Rutishauser variables. We start by considering the family of orthogonal polynomials corresponding to a given linear form. Shifts on the linear form give rise to adjacent families. A compatible set of linear problems is made up from two relations connecting adjacent and original polynomials. Lax pairs for several initial boundary-value problems are derived and we recover the discrete-time Toda chain equations of Hirota and of Suris. This approach allows us to derive a Bäcklund transform that relates these two different discrete-time Toda systems. We also show that they yield the same bilinear equation up to a gauge transformation. The singularity confinement property is discussed as well.     

Schlesinger Transformations for Linearisable Equations

A simple axiomatic characterization of the noncommutative Itô algebra is given and a pseudo-Euclidean fundamental representation for such algebra is described. It is proved that every Itô algebra with a quotient identity has a faithful representation in a Minkowski space and is canonically decomposed into the orthogonal sum of quantum Brownian (Wiener) algebra and quantum Lévy (Poisson) algebra. In particular, every quantum thermal noise of a finite number of degrees of freedom is the orthogonal sum of a quantum Wiener noise and a quantum Poisson noise as it is stated by the Lévy–Khinchin Theorem in the classical case. Two basic examples of noncommutative Itô finite group algebras are considered.     

Structural relaxation in polyethylene in the presence of silver oxide investigated by positron-lifetime spectroscopy

Structural relaxation in high-density virgin polyethylene and silver oxide doped polyethylene has been investigated using positron annihilation lifetime technique at 30 °C and 100 °C ageing temperatures. The ortho-positronium (o-Ps) pick-off lifetime and its intensity show no changes with isothermal ageing time for the virgin sample at 30 °C. In the case of the doped sample at 30 °C, the o-Ps intensity shows exponential relaxation in the short-time range. At 100 °C, the o-Ps lifetime remains almost constant, whereas the o-Ps intensity exhibits an exponential character in the virgin and doped samples, which can be fitted with exponential decay curves. The relaxation times have been evaluated from the structural relaxation function constructed using o-Ps intensity values, and the stretching exponent has been estimated using the Kohlrausch–Williams–Watts (KWW) function. Positron results indicate that the stretching exponent seems to be temperature dependent. PACS 78.70.Bj