Adaptive local grid refinement algorithms for finite-element collocation

An adaptive grid refinement procedure allows accurate solutions to advection-dominated, time-dependent flows using finite-element collocation. The technique relies on a data structure that is readily amenable to parallel computing. The paper discusses computational aspects of the method.     

Methodology for the preparation of C1-monoalkylated 1,2-dihydro[C70)] derivatives: formation of the "other" regioisomer

Deprotonation of 1,2-C(70)H(2) with TBAOH, followed by alkylation with methyl bromoacetate, results in formation of a C1-monoalkylated 1,2-dihydro-C(70) derivative. The position of the alkyl group (C1) was established by NMR spectroscopy and comparison with literature spectra of C2-monoalkylated analogs. Presumably, C1-alkylation is the major process due to selective deprotonation of 1,2-C(70)H(2) at C1. Substitution of benzyl bromide for methyl bromoacetate results in rapid dialkylation, unless the amount of base is carefully controlled, in which case C1-monobenzylation is the major process. This methodology for alkylation at C1 is complimentary to methods for the C2-monoalkylation of C(70) with Zn and methyl bromoacetate.     

Improved limits on the mass of the tau neutrino

Several methods to determine (or set an upper bound on) the mass of the tau neutrino are described. The decay spectrum of \(\tau \to e\bar \nu _e \nu _\tau \) near the high center-of-mass electron-energy end is particularly sensitive to the tau-neutrino mass. It is shown that an upper bound of 20 MeV or lower may be feasible. In addition, improved limits on the mass and mixing angle of a heavy component of the tau-neutrino may be readily obtained. We also discuss the purely leptonic decays of theD andF mesons, and show how measurements of the ratiosB(D→τν_τ/B(D→μν_μ,B(F→τν_τ/B(D→μν_μ can be sensitive to tau-neutrino masses of 30 MeV or greater.     

Design,synthesis, and evaluation of 6-carboxyalkyl and 6-phosphonoxyalkyl derivatives of 7-oxo-8-ribitylaminolumazines as inhibitors of riboflavin synthase and lumazine synthase

A series of 6-carboxyalkyl and 6-phosphonoxyalkyl derivatives of 7-oxo-8-D-ribityllumazine were synthesized as inhibitors of both Escherichia coli riboflavin synthase and Bacillus subtilis lumazine synthase. The compounds were designed to bind to both the ribitylpurine binding site and the phosphate binding site of lumazine synthase. In the carboxyalkyl series, maximum activity against both enzymes was observed with the 3'-carboxypropyl compound 22. Lengthening or shortening the chain linking the carboxyl group to the lumazine by one carbon resulted in decreased activity. In the phosphonoxyalkyl series, the 3'-phosphonoxypropyl compound 33 was more potent than the 4'-phosphonoxybutyl derivative 39 against lumazine synthase, but it was less potent against riboflavin synthase. Molecular modeling suggested that the terminal carboxyl group of 6-(3'-carboxypropyl)-7-oxo-8-D-ribityllumazine (22) may bind to the side chains of Arg127 and Lys135 of the enzyme. A hypothetical molecular model was also constructed for the binding of 6-(2'-carboxyethyl)-7-oxolumazine (15) in the active site of E. coli riboflavin synthase, which demonstrated that the active site could readily accommodate two molecules of the inhibitor.     

Synthesis of spiro-fused (C5)-isoxazolino-(C4)-pyrazolones (1-oxa-2,7,8-triazaspiro[4,4]-2,8-dien-6-ones) via 1,3-dipolar cycloaddition and cycloelimination

An efficient and selective method for the synthesis of spiro-fused (C5)-isoxazolino-(C4)-pyrazolones (C) is reported. The process consists of utilizing the Baylis-Hillman reaction-or a quicker, stepwise MAC procedure-to give I followed by 1,3-dipolar cycloaddition and Swern oxidation to give beta-ketoesters H, which were condensed with hydrazine derivatives to provide hydrazones that underwent cycloelimination. These novel spiro-fused (C5)-isoxazolino-(C4)-pyrazolones were confirmed by spectroscopic analysis as well as single-crystal X-ray of 5. We also concluded that all condensations/cycloeliminations, except with hydrazine itself, were more effective with catalysts or higher reaction temperatures. For example, TiCl(4) was an efficient catalyst for hydrazone formation and cycloelimination with methylhydrazine, while phenyl-, benzyl-, and (4-methoxyphenyl)hydrazine reacted effectively without catalyst in refluxing xylene.     

Energetics of the Preyssler anion's molecular orbitals: quantifying the effect of the encapsulated-cation's charge

The ground state electronic properties of metal-exchanged Preyssler heteropolyoxoanions [M(n+)P(5)W(30)O(110)](n-15), in which the encapsulated M(n+) ions are the spherical, diamagnetic ions Na(+), Ca(2+), Sr(2+), Y(3+), La(3+) and Th(4+), are studied using a combination of electrochemical, optical, and NMR experiments. We have designed experiments that focus on the influence of the charge (n) of the encapsulated cations, which themselves have no redox response, and its effect upon the W-O framework MOs. As n increases, the cluster anions accept electrons into their LUMOs with increasing ease, and their lowest-energy LMCT bands reveal a corresponding blue shift, which is indicative of an increase of the LUMO-HOMO energy splitting with increasing n. (183)W NMR spectra are used to identify the atomic origin of the LUMO states, which are shown to be composed primarily of orbitals from the ring of 5 W atoms near M(n+). The cation charge correlates directly and linearly with the half-wave potentials of the first redox couples, the LMCT band energies, and the W chemical shifts. We have combined this suite of experimental results to construct an energy level diagram of the frontier MOs for the Preyssler cluster anions. In so doing, we provide a fundamental perspective that is not otherwise available on the cation's role with specific regard to the electronic behavior of the W-O orbitals. These results are expected to provide benchmarking information as theorists begin to study these large POM systems.     

Synthesis of the ladybug alkaloids (±)-propyleine and (±)-isopropyleine. Modification of the published structure of propyleine

The total syntheses of the ladybug alkaloids (±)-propyleine and (±)-isopropyleine are described. Evidence that the alkaloid propyleine is actually a rapidly interconverting mixture of propyleine and a previously unknown isomer isopropyleine is presented.     

Some symmetry-induced isotope effects in the kinetics of recombination reactions

Symmetry-induced isotope effects in recombination and collision-induced dissociation reactions are discussed. Progress on understanding the anomalous isotope effects in ozone is reviewed. Then, calculations are performed for the simpler reaction xNe+yNe+H<-->xNeyNe+H, where x and y label either identical or different isotopes. The atomic masses in the model are chosen so that symmetry is the only difference between the systems. Starting from a single potential energy surface, the properties of the bound, quasibound, and continuum states of the neon dimer are calculated. Then, the vibration rotation infinite order sudden approximation is used to calculate cross sections for all possible inelastic and dissociative processes. A rate constant matrix that exactly satisfies detailed balance is constructed. It allows recombination to occur both via direct three-body collisions and via tunneling into the quasibound states of the energy transfer mechanism. The eigenvalue rate coefficients are determined. Significant isotope effects are clearly found, and their behavior depends on the pressure, temperature, and mechanism of the reaction. Both spin statistics and symmetry breaking produce isotope effects. Under most conditions the breaking of symmetry enhances the rates, but a wide spectrum of effects is observed; they range from isotope effects with a normal mass dependence to huge, mass-independent isotope effects to cancellation and even to reversal of the isotope effects. This is the first calculation of symmetry-induced isotope effects in recombination rates from first principles. The relevance of the present effects to ozone recombination is discussed.