The Linear KdV Equation with an Interface

The interface problem for the linear Korteweg–de Vries (KdV) equation in one-dimensional piecewise homogeneous domains is examined by constructing an explicit solution in each domain. The location of the interface is known and a number of compatibility conditions at the boundary are imposed. We provide an explicit characterization of sufficient interface conditions for the construction of a solution using Fokas’s Unified Transform Method. The problem and the method considered here extend that of earlier papers to problems with more than two spatial derivatives.     

Oxidation of some cage hydrocarbons by dioxiranes. Nature of the transition structure for the reaction of C-H bonds with dimethyldioxirane: a comparison of B3PW91 density functional theory with experiment

Dimethyl- (DMD) and methyl(trifluoromethyl)-dioxiranes were used for oxyfunctionalization of spiro{1',7-cyclopropan-(E)-2-methylbicyclo[2.2.1]heptane} (), tricyclo[3.2.2.0(2,4)]nonane (), exo-endo-endo- () and exo-exo-exo- () heptacyclo[9.3.1.0(2,10).0(3,8).0(4,6).0(5,9).0(12,14)]pentadecane, yielding tertiary alcohols as the main products. The rate constants for oxidation of by DMD were measured and the Arrhenius parameters determined. The DFT theory (B3LYP and B3PW91) using restricted and unrestricted methods was employed to study the oxidation reaction of the C-H bond of cage hydrocarbons , adamantane, and acetone with DMD. The kinetic isotopic effect calculated using unrestricted methods agreed with experiment. The reaction mechanism in terms of the concerted oxygen insertion vs. the radical part is discussed.     

Bis[bis-(4-alkoxyphenyl)amino] derivatives of dithienylethene, bithiophene, dithienothiophene and dithienopyrrole: palladium-catalysed synthesis and highly delocalised radical cations

Five diamines with thiophene-based bridges--(E)-1,2-bis{5-[bis(4-butoxyphenyl)amino]-2-thienyl}ethylene (1), 5,5'-bis[bis(4-methoxyphenyl)amino]-2,2'-bithiophene (2), 2,6-bis[bis(4-butoxyphenyl)amino]dithieno[3,2-b:2',3'-d]thiophene (3), N-(4-tert-butylphenyl)-2,6-bis[bis(4-methoxyphenyl)amino]dithieno[3,2-b:2',3'-d]pyrrole (4 a) and N-tert-butyl-2,6-bis[bis(4-methoxyphenyl)amino]dithieno[3,2-b:2',3'-d]pyrrole (4 b)--have been synthesised. The syntheses make use of the palladium(0)-catalysed coupling of brominated thiophene species with diarylamines, in some cases accelerated by microwave irradiation. The molecules all undergo facile oxidation, 4 b being the most readily oxidised at about -0.4 V versus ferrocenium/ferrocene, and solutions of the corresponding radical cations were generated by addition of tris(4-bromophenyl)aminium hexachloroantimonate to the neutral species. The near-IR spectra of the radical cations show absorptions characteristic of symmetrical delocalised species (that is, class III mixed-valence species); analysis of these absorptions in the framework of Hush theory indicates strong coupling between the two amine redox centres, stronger than that observed in species with phenylene-based bridging groups of comparable length. The strong coupling can be attributed to high-lying orbitals of the thiophene-based bridging units. ESR spectroscopy indicates that the coupling constant to the amino nitrogen atoms is somewhat reduced relative to that in a stilbene-bridged analogue. The neutral species and the corresponding radical cations have been studied with the aid of density functional theory and time-dependent density functional theory. The DFT-calculated ESR parameters are in good agreement with experiment, while calculated spin densities suggest increased bridge character to the oxidation in these species relative to that in comparable species with phenylene-based bridges.     

Diphenyl(dipyrazolyl)methane complexes of Ni: synthesis, structural characterization, and chromotropism of NiBr2 derivatives

The reaction of NiBr2 with the bidentate ligand diphenyl(dipyrazolyl)methane (dpdpm) gives the pentacoordinated complexes [(dpdpm)Ni(mu-Br)Br]2 (1), [(dpdpm)NiBr2(H2O)] (2a), and [(dpdpm)NiBr(H2O)2]Br (2b), or the octahedral complexes [(dpdpm)NiBr(H2O)2(CH3CN)]Br (3), [(dpdpm)2NiBr2] (4), and [(dpdpm)2NiBr(H2O)]Br (5). All of these complexes are paramagnetic, both in the solid state and in solution, and have been characterized by spectroscopic (IR, NMR, and UV-vis-NIR) and X-ray diffraction studies. The unoccupied coordination site in the pentacoordinated compounds allows long-range interactions, in the solid state, between the Ni center and a Ph substituent of the dpdpm ligand. These weak interactions are replaced by Ni-solvent interactions, both in the solid state and in solution, facilitating the interconversion of these compounds under various reaction conditions and leading to interesting solvato-, vapo-, and thermochromic properties. UV-vis-NIR spectroscopy has been used to study these phenomena. Absorption spectra for the room-temperature methanol or acetonitrile solutions of the pentacoordinate or octahedral compounds show three main bands in the region of 350-1000 nm that represent spin-allowed (d-d) transitions from the ground state 3A2g to the excited states 3T2g, 3T1g(3F), and 3T1g(3P). A weak shoulder was also detected on the middle peak in most spectra (700-800 nm), representing the spin-forbidden 3A2g-->1Eg transition. On the other hand, the spectra of high-temperature CH2Cl2 or acetone solutions of all complexes show four main bands at ca. 490, 650-660, 860, and 1000 nm, in addition to a shoulder on the first or second band.     

The effectiveness of three multi-component binding models in describing the binary competitive equilibrium adsorption of two cytochrome b(5) mutants

Competitive adsorption isotherms for two conservative surface charge-neutralizing mutants of cytochrome b(5), E11Q and E44Q, previously measured with competitor concentration held constant over the range of the isotherm, were used to test three widely-used multi-component isotherm models. The extended Langmuir-Freundlich, Langmuir and Jovanovic-Freundlich models each adequately described the weaker infinite dilution adsorption of the E44Q protein in the presence of the strong binding E11Q. The extended Langmuir-Freundlich model generally gave the lowest errors at higher concentrations, and the Jovanovic-Freundlich model gave the best fits when using empirically optimized maximal loading values based on multi-component as well as pure-component isotherm data.     

Highly active/selective and adjustable zirconium polymerization catalysts stabilized by aminopyridinato ligands

This paper describes a substantial enhancement of the aminopyridinato ligand stabilized early transition metal chemistry by introducing the sterically very demanding 2,6-dialkylphenyl substituted aminopyridinato ligands derived from (2,6-diisopropylphenyl)-[6-(2,6-dimethylphenyl)-pyridin-2-yl]-amine (1a-H, ApH) and (2,6-diisopropylphenyl)-[6-(2,4,6-triisopropylphenyl)-pyridin-2-yl]- amine (1b-H, Ap^∗H). The corresponding bis aminopyridinato zirconium dichloro complexes, [Ap₂ZrCl₂] (3a) and [Ap₂^∗ZrCl₂] (3b) and the dimethyl analogues, [Ap₂ZrMe₂] (4a) and [Ap₂^∗ZrMe₂] (4b) (Me = methyl) were synthesized, using standard salt metathesis routes. Single-crystal X-ray diffraction was carried out for the dichloro derivatives. Both zirconium metal centers have a distorted octahedral environment with a cis-orientation of the chloride ligands in 3a and a closer to trans-arrangement in 3b. The dimethyl derivatives are proven to be highly active ethylene polymerization catalysts after activation with [R₂N(Me)H][B(C₆F₅)₄] (R = C₁₆H₃₃-C₁₈H₃₇). During attempted co-polymerizations of α-olefins (propylene) and ethylene high activity and selectivity for ethylene and nearly no co-monomer incorporation was observed. Increasing the steric bulk of the ligand going from (2,6-dimethylphenyl) to (2,4,6-triisopropylphenyl) substituted pyridines, switches the catalyst system from producing long chain α-olefins to polymerization of ethylene in a living fashion. In contrast to the dimethyl complexes only [Ap₂^∗ZrCl₂] in the presence of MAO at elevated temperature gave decent polymerization activity. NMR investigations of the reaction of dichloro complexes with 25 equiv. of MAO or AlMe₃ at room temperature revealed, that [Ap₂ZrCl₂] decomposes under ligand transfer to aluminum and formation of [ApAlMe₂], while [Ap₂^∗ZrCl₂] remains almost unreacted under the same conditions. The aminopyridinato dimethyl aluminum complexes, [ApAlMe₂] (5a) and [Ap^∗AlMe₂] (5b) were synthesized independently and structurally characterized. The aluminum complexes 5a and b show no catalytic activity towards ethylene, when “activated” with[R₂N(Me)H][B(C₆F₅)₄].     

Mechanistic aspects of the formation of aldehydes and nitriles in photosensitized reactions of aldoxime ethers

The photooxidation of a series of aldoxime ethers was studied by laser flash photolysis and steady-state (product studies) methods. Nanosecond laser flash photolysis studies have shown that chloranil (CA)-sensitized reactions of the O-methyl (1), O-ethyl (2), O-benzyl (3), and O-tert-butyl (4) benzaldehyde oximes result in the formation of the corresponding radical cations. In polar non-nucleophilic solvents such as acetonitrile, there are several follow-up pathways available depending on the structure of the aldoxime ether and the energetics of the reaction pathway. When the free energy of electron transfer (DeltaGET) becomes endothermic, syn-anti isomerization is the dominant pathway. This isomerization pathway is a result of triplet energy transfer from CA to the aldoxime ether. For substrates with alpha-protons (aldoxime ethers 1-3), the follow-up reactions involve deprotonation at the alpha-position followed by beta-scission to form the benziminyl radical (and an aldehyde). The benziminyl radical reacts to give benzaldehyde, the major product under these conditions. A small amount of benzonitrile is also observed. In the absence of alpha-hydrogens (aldoxime ether 4), the major product is benzonitrile, which is thought to occur via reaction of the excited (triplet) sensitizer with the aldoxime ether. Abstraction of the iminyl hydrogen yields an imidoyl radical, which undergoes a beta-scission to yield benzonitrile. An alternative pathway involving electron transfer followed by removal of the iminyl proton was not deemed viable based on charge densities obtained from DFT (B3LYP/6-31G*) calculations. Similarly, a rearrangement pathway involving an intramolecular hydrogen atom transfer process was ruled out through experiments with a deuterium-labeled benzaldehyde oxime ether. Studies involving nucleophilic solvents have shown that all aldoxime ethers reacted with MeOH by clean second-order kinetics with rate constants of 0.7 to 1.2 x 10(7) M(-1) s(-1), which suggests that there is only a small steric effect in these reactions. The steady-state experiments demonstrated that under these conditions no nitrile is formed. This is explained by a mechanistic scheme involving nucleophilic attack on the nitrogen of the aldoxime ether radical cation, followed by solvent-assisted [1,3]-proton transfer and elimination of an alcohol, similar to the results obtained for a series of acetophenone oxime ethers.     

Laser spectroscopy of the Lamb shift in muonic hydrogen

The muonic hydrogen atom in the 2s state provides the possibility of achieving high precision laser spectroscopy experiments from which a high precision value of the proton radius can be deduced. This will ultimately allow an increased precision in the test of QED in bound systems. Important progress has been made in recent years in the ability to stop muons in a low pressure gas target and in the understanding of the 2s-metastability in muonic hydrogen. As a consequence the 2s–2p laser spectroscopy experiment is now feasible and we present here the basic experimental concept considered by our collaboration. This revised version was published online in August 2006 with corrections to the Cover Date.