Enantiomerically Pure Phosphaalkene–Oxazolines (PhAk‐Ox): Synthesis,Scope and Copolymerization with Styrene

The design of a synthetic route to a class of enantiomerically pure phosphaalkene–oxazolines (PhAk‐Ox) is presented. The condensation of a lithium silylphosphide and a ketone (the phospha‐Peterson reaction) was used as the P?C bond‐forming step. Attempted condensation of PhC(?O)Ox (Ox=CNOCH(iPr)C H₂) and MesP(SiMe₃)Li gave the unusual heterocycle (MesP)₂C(Ph)?CN‐(S)‐CH(iPr)CH₂O ( 3 ). However, PhAk‐Ox (S,E)‐MesP?C(Ph)CMe₂Ox ( 1 a ) was successfully prepared by treating MesP(SiMe₃)Li with PhC(?O)CMe₂Ox (52 %). To demonstrate the modularity and tunability of the phospha‐Peterson synthesis several other phosphaalkene–oxazolines were prepared in an analogous manner to 1 a : TripP?C(Ph)CMe₂Ox ( 1 b ; Trip=2,4,6‐triisopropylphenyl), 2‐iPrC₆H₄P?C(Ph)CMe₂Ox ( 1 c ), 2‐tBuC₆H₄P?C(Ph)CMe₂Ox ( 1 d ), MesP?C(4‐MeOC₆H₄)CMe₂Ox ( 1 e ), MesP?C(Ph)C(CH₂)₄Ox ( 1 f ), and MesP?C(3,5‐(CF₃)₂C₆H₃)C(CH₂)₄Ox ( 1 g ). To evaluate the PhAk‐Ox compounds as prospective precursors to chiral phosphine polymers, monomer 1 a and styrene were subjected to radical‐initiated copolymerization conditions to afford [{MesPC(Ph)(CMe₂Ox)}_x{CH₂CHPh}_y]_n ( 9 a : x=0.13n, y=0.87n; GPC: M_w=7400 g mol^?1, PDI=1.15).     

Preparation of enol ester epoxides and their ring-opening to α-silyloxyaldehydes

The Z-selective ruthenium-catalyzed addition of aromatic carboxylic acids to alkynes was followed by dioxirane epoxidation to furnish enol ester epoxides with cis configuration. Upon treatment of enol ester epoxides with tert-butyldimethylsilyl triflate in the presence of 2,6-lutidine, synthetically useful α-silyloxyaldehydes were obtained. This novel transformation was facilitated by microwave irradiation.     

Models for incomplete nucleophilic attack on a protonated carbonyl group and electron-deficient alkenes: salts and zwitterions from 1-dimethylamino-naphthalene-8-carbaldehyde

The X-ray crystal structures of salts and zwitterionic Knoevenagel products from 1-dimethylamino-naphthalene-8-carbaldehyde show long N-C bonds between peri-groups which provide models for incomplete nucleophilic attack on a protonated carbonyl group and electron-deficient alkenes respectively. For the salts the N-C bonds lie in the range 1.625-1.638 ? with C-OH bonds intermediate in length between single and double bonds, while for the zwitterions the N-C bonds lie in the range 1.612-1.660 ?. The structural assignment of the former is supported by solid state (13)C and (15)N NMR studies on doubly isotopically-labelled material. Several zwitterions were converted to naphtha[1,8-bc]azepines by a mechanism involving the tertiary amino effect.     

Skew-adjacency matrices of graphs

The spectra of the skew-adjacency matrices of a graph are considered as a possible way to distinguish adjacency cospectral graphs. This leads to the following topics: graphs whose skew-adjacency matrices are all cospectral; relations between the matchings polynomial of a graph and the characteristic polynomials of its adjacency and skew-adjacency matrices; skew-spectral radii and an analogue of the Perron–Frobenius theorem; and, the number of skew-adjacency matrices of a graph with distinct spectra.     

On multiscale homogenization problems in boundary layer theory

This paper is concerned with the homogenization of the equations describing a magnetohydrodynamic boundary layer flow past a flat plate, the flow being subjected to velocities caused by injection and suction. The fluid is assumed incompressible, viscous and electrically conducting with a magnetic field applied transversally to the direction of the flow. The velocities of injection and suction and the applied magnetic field are represented by rapidly oscillating functions according to several scales. We derive the homogenized equations, prove convergence results and establish error estimates in a weighted Sobolev norm and in C ⁰-norm. We also examine the asymptotic behavior of the solutions of the equations governing a boundary layer flow past a rough plate with a locally periodic oscillating structure.     

10 GHz ultra-stable short optical pulse generation via phase-modulation enhanced dual-loop optoelectronic oscillator

We report on a high rate, ultra-low timing jitter, short optical pulse generator based on cascaded amplitude and phase modulation in an optoelectronic oscillator. The radio-frequency supermodes are shown to be greatly suppressed with the dual-loop architecture, and a highly coherent and flat optical frequency comb is generated. Optical pulses of 12.8 ps duration are obtained with 27.5 fs integrated timing jitter from 100 Hz to 10 MHz.     

Structure and hydrolysis of the U(IV), U(V), and U(VI) aqua ions from ab initio molecular simulations

Ab initio molecular dynamics simulations at 300 K, based on density functional theory, are performed to study the hydration shell geometries, solvent dipole, and first hydrolysis reaction of the uranium(IV) (U(4+)) and uranyl(V) (UO(2)(+)) ions in aqueous solution. The solvent dipole and first hydrolysis reaction of aqueous uranyl(VI) (UO(2)(2+)) are also probed. The first shell of U(4+) is coordinated by 8-9 water ligands, with an average U-O distance of 2.42 ?. The average first shell coordination number and distance are in agreement with experimental estimates of 8-11 and 2.40-2.44 ?, respectively. The simulated EXAFS of U(4+) matches well with recent experimental data. The first shell of UO(2)(+) is coordinated by five water ligands in the equatorial plane, with the average U═O(ax) and U-O distances being 1.85 ? and 2.54 ?, respectively. Overall, the hydration shell structure of UO(2)(+) closely matches that of UO(2)(2+), except for small expansions in the average U═O(ax) and U-O distances. Each ion strongly polarizes their respective first-shell water ligands. The computed acidity constants (pK(a)) of U(4+) and UO(2)(2+) are 0.93 and 4.95, in good agreement with the experimental values of 0.54 and 5.24, respectively. The predicted pK(a) value of UO(2)(+) is 8.5.     

Synthesis and structural diversity of barium (N,N-dimethylamino)diboranates

The reaction of a slurry of BaBr(2) in a minimal amount of tetrahydrofuran (THF) with 2 equiv of Na(H(3)BNMe(2)BH(3)) in diethyl ether followed by crystallization from diethyl ether at -20 °C yields crystals of Ba(H(3)BNMe(2)BH(3))(2)(Et(2)O)(2) (1). Drying 1 at room temperature under vacuum gives the partially desolvated analogue Ba(H(3)BNMe(2)BH(3))(2)(Et(2)O)(x) (1') as a free-flowing white solid, where the value of x varies from <0.1 to about 0.4 depending on whether desolvation is carried out with or without heating. The reaction of 1 or 1' with Lewis bases that bind more strongly to barium than diethyl ether results in the formation of new complexes Ba(H(3)BNMe(2)BH(3))(2)(L), where L = 1,2-dimethoxyethane (2), N,N,N',N'-tetramethylethylenediamine (3), 12-crown-4 (4), 18-crown-6 (5), N,N,N',N'-tetraethylethylenediamine (6), and N,N,N',N",N"-pentamethylethylenetriamine (7). Recrystallization of 4 and 5 from THF affords the related compounds Ba(H(3)BNMe(2)BH(3))(2)(12-crown-4)(THF)·THF (4') and Ba(H(3)BNMe(2)BH(3))(2)(18-crown-6)·2THF (5'). In addition, the reaction of BaBr(2) with 2 equiv of Na(H(3)BNMe(2)BH(3)) in the presence of diglyme yields Ba(H(3)BNMe(2)BH(3))(2)(diglyme)(2) (8), and the reaction of 1 with 15-crown-5 affords the diadduct [Ba(15-crown-5)(2)][H(3)BNMe(2)BH(3)](2) (9). Finally, the reaction of BaBr(2) with Na(H(3)BNMe(2)BH(3)) in THF, followed by the addition of 12-crown-4, affords the unusual salt [Na(12-crown-4)(2)][Ba(H(3)BNMe(2)BH(3))(3)(THF)(2)] (10). All of these complexes have been characterized by IR and (1)H and (11)B NMR spectroscopy, and the structures of compounds 1-3, 4', 5', and 6-10 have been determined by single-crystal X-ray diffraction. As the steric demand of the Lewis bases increases, the structure changes from polymers to dimers to monomers and then to charge-separated species. Despite the fact that several of the barium complexes are monomeric in the solid state, none is appreciably volatile up to 200 °C at 10(-2) Torr.     

Reactions of Nb2 and Nb3 with CO, D2, N2, and O2: reconciling experimental kinetics with density functional theory-calculated reaction profiles

Calculated energy profiles for the reactions of neutral Nb(2) and Nb(3) metal clusters with CO, D(2), N(2), and O(2) are presented. In each reaction path, both a physisorption energy minimum, where the reactant remains intact, and a chemisorption energy minimum, where the reactant has dissociated, are calculated and linked by saddle points. We calculate branching ratios for the forward (dissociative) and reverse reactions which we compare with the experimental kinetic data. It is found that a combination of average thermal energies and barrier heights leads to wide variation in branching ratios which compares favourably to previously determined experimental reaction rates.