Does Huygens' principle hold for small perturbations of the wave equation?

The perturbed wave equation □u + q(x)u = 0 in $\text{R}$³ × $\text{R}$ with C∞ ($\text{R}$³) compactly supported initial data at t = 0 is considered. It is proven that the Huygens' principle does not hold for this equation if the potential is (essentially) non-negative, well-behaved at infinity and small in a suitable sense. The treatment is elementary and based on energy estimates and the positivity of the Riemann function for the wave equation in three space dimensions. The result still holds if the solution u is “small” over some space-time propagation cone. In the ease in which q has compact support, stronger results of this type for the above equation are obtained.     

A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow

The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.     

Unexpected reactivity of the burgess reagent with thiols: synthesis of symmetrical disulfides

Reaction of the Burgess reagent with a series of aliphatic and aromatic thiols led to the corresponding symmetrical disulfides in high yields. No olefins were detected in the reactions of aliphatic thiols.     

An improved understanding of the reaction of bis(bromomethyl)quinoxaline 1-N-oxides with amines using substituent effects

The reaction of bis(bromomethyl)quinoxaline N-oxides with amines is interesting from a reaction mechanism perspective and due to the reported biological activity of compounds in this general class. The complex mechanism of this reaction (particularly in the case of primary amines) is complicated further when C6 or C7 substituted mono-N-oxides are considered. In this study, the synthesis and subsequent characterization of a series of 2,3-bis(bromomethyl)quinoxaline 1-N-oxides is reported. Experimental and computational evidence is used to show that the observed product ratios from the reaction with diethylamine reflect the influence of both the C6/C7 substituent and the N-oxide functional group on the initial nucleophilic substitution reaction.     

Synthetic study toward 17-thiasteroids: synthesis of the 1-thiahydrinden-5-one subunit using a new annulation procedure and investigation of its reduction

The enantioselective syntheses of ketones 6 and 7 featuring the CD subunit of 17-thiasteroid are described. The key bicyclic 1-thiahydrindenone (S)-5 was assembled in three steps from Michael adduct (S)-12 via β-keto ester 15 using a one-pot sequential process involving cleavage of both the ketal group and the tert-butyl ester group, decarboxylation, and finally intramolecular aldol condensation. Hydridoalkyl cuprate-induced conjugate reduction of 1-thiahydrindenone (S)-5 and its corresponding sulfone (S)-23 gave 1-thiahydrindanones 6 and 7, respectively, which display unexpectedly the unnatural cis-ring junctions.     

Photoelectron spectroscopy and thermochemistry of tert-butylisocyanide-substituted cobalt tricarbonyl nitrosyl

A new organometallic complex, Co(CO)2NOtBuNC, was synthesized and investigated by photoelectron spectroscopy (PES) and threshold photoelectron photoion coincidence (TPEPICO) spectrometry in order to determine its ionization energy as well as the bond energies in the ionic forms. The assignment of the nine peaks in the PES was based on Kohn-Sham molecular orbital energies, and an adiabatic ionization energy of 7.30 +/- 0.05 eV was determined. In the TPEPICO experiment, the following 0 K onsets were determined for the various fragment ions: CoCONOtBuNC+ (8.17 +/- 0.05 eV); CoNOtBuNC+ (9.01 +/- 0.05 eV); and CotBuNC+ (10.42 +/- 0.05 eV). Because the photon source did not extend above 14 eV, we could not observe the bare Co+ ion in the experiment. The heat of formation of the CotBuNC+ ion was estimated by ab initio and DFT calculations of the CoL+ + tBuNC --> CotBuNC+ + L (L = CO, NO, NH3, H2O, PMe3) substitution enthalpies.     

Dissociation dynamics of sequential ionic reactions: heats of formation of tri-, di-, and monoethylphosphine

The sequential ethene (C2H4) loss channels of energy-selected ethylphosphine ions have been studied using threshold photoelectron photoion coincidence (TPEPICO) spectroscopy in which ion time-of-flight (TOF) distributions are recorded as a function of the photon energy. The ion TOF distributions and breakdown diagrams have been modeled in terms of the statistical RRKM theory for unimolecular reactions, providing 0 K dissociation onsets, E0, for the ethene loss channels. Three RRKM curves were used to model the five measurements, since two of the reactions differ only by the internal energy of the parent ion. This series of dissociations provides a detailed check of the calculation of the product energy distribution for sequential reactions. From the determined E0's, the heats of formation of several ethylphosphine neutrals and ions have been determined: Delta(f)H degrees 298K[P(C(2)H(5))3] = -152.7 +/- 2.8 kJ/mol, Delta(f)H degrees 298K[P(C(2)H(5))3+] = 571.6 +/- 4.0 kJ/mol, Delta(f)H degrees 298K[HP(C(2)H(5))2] = -89.6 +/- 2.1 kJ/mol, Delta(f)H degrees 298K[HP(C(2)H(5))2+] = 669.9 +/- 2.5 kJ/mol, Delta(f)H degrees 298K[H(2)PC(2)H(5)] = -36.5 +/- 1.5 kJ/mol, Delta(f)H degrees 298K[H(2)PC(2)H(5)+] = 784.0 +/- 1.9 kJ/mol. These values have been supported by G2 and G3 calculations using isodesmic reactions. Coupled cluster calculations have been used to show that the C2H4 loss channel, which involves a hydrogen transfer step, proceeds without a reverse energy barrier.     

Molecular structure, vinyl rotation barrier, and vibrational dynamics of 2,6-dichlorostyrene. A theoretical and experimental research

The molecular structure of 2,6-dichlorostyrene has been analyzed at MP2 and DFT levels using different basis sets concluding in a nonplanar geometry. The influence of either the level of theory or the nature of the substituent has been assessed. The vinyl-phenyl torsion barrier has also been investigated as a function of level of theory. The ultimate factors responsible for the torsion barrier have been studied using two different partitioning schemes, i.e., the total electronic potential energy and the natural bond orbital, NBO. A topological analysis of the electron density within the atom-in-molecule, AIM, theory predicts soft intramolecular chlorine (ring)-hydrogen (vinyl) contacts when the system becomes planar. A first complete vibrational study has been performed using theoretical data and experimental vibrational frequencies from IR, Raman and, for the first time, inelastic neutron scattering, INS, spectra. The new assignment proposed is based on a scaled quantum mechanical, SQM, force field and the wavenumber linear scaling, WLS, approach.     

Mechanism of the catalyzed by cysteine electroreduction of the insoluble in water cobalt(II) salt as a component of carbon paste electrode

The mechanism of the Co(II) catalytic electroreduction of water insoluble CoR₂ salt in the presence of cysteine was developed. CoR₂ = cobalt(II) cyclohexylbutyrate is the component of a carbon paste electrode. Electrode surface consecutive reactions are: (a) fast (equilibrium) reaction of the complex formation, (b) rate-determining reversible reaction of the promoting process of CoR(Ac⁺) complex formation, (c) rate-determining irreversible reaction of the electroactive complex formation with ligand-induced adsorption, and (d) fast irreversible reaction of the electroreduction. Reactions (a,b) connected with CoR₂ dissolution and reactions (c,d) connected with CoR₂ electroreduction are catalyzed by . Regeneration of (reactions “b,d”) and accumulation of atomic Co(0) (reaction “d”) take place. Experimental data [Sugawara et al., Bioelectrochem Bioenergetics 26:469, 1991]: i _a vs E (i _a is anodic peak, E is cathodic accumulation potential), i _a vs , and i _a vs pH have been quantitatively explained.     

Microenvironment-switchable singlet oxygen generation by axially-coordinated hydrophilic ruthenium phthalocyanine dendrimers

A series of new metallodendrimers built around a ruthenium phthalocyanine core has been prepared. Employing a convergent synthetic strategy, pyridine-containing ligands were prepared and then assembled onto the ruthenium phthalocyanine through axial ligand coordination. The growing shell of oligoethylene glycol chains surrounding the lipophilic core allows solubilisation in water. Photophysical studies show that all the metallodendrimers are strongly phosphorescent and the deactivation pathway of their triplet state depends on the medium in which the compounds are dissolved. On one hand, quenching of the triplet state by the dendritic shell is observed and found to be substantially enhanced in aqueous media. On the other, the dendrimer shields the phthalocyanine from oxygen. This notwithstanding, the phthalocyanines are able to generate singlet oxygen in less polar environments such as in CHCl(3) or THF solution, while in water the generation of singlet oxygen is almost completely switched off.