Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind: where the solution (t) is assumedto have the form f(t) = x(t)+r^?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme.     

Tentoxin as a scaffold for drug discovery. Total solid-phase synthesis of tentoxin and a library of analogues

[reaction: see text] A solid-phase method for the synthesis of tentoxin has been developed. Two key steps-dehydration and N-alkylation-are carried out while the peptide is anchored to the resin. The method, which has been validated by the preparation of a library of tentoxin analogues, should be applicable to the generation of further libraries that have the tentoxin scaffold structure, as well as other structures containing N-alkylated didehydroamino acids.     

Palladium-catalyzed cascade reaction of alpha,beta-unsaturated sulfones with aryl iodides

Unlike traditionally used acyclic 1,2-disubstituted alkenes, the reaction of alpha,beta-unsaturated phenyl sulfones with aryl iodides under Heck reaction conditions (Pd(OAc)(2) as catalyst, Ag(2)CO(3) as base in DMF at 120 (0)C) takes place mainly by a cascade process, involving one unit of the alkene and three units of the aryl iodide, to afford a substituted 9-phenylsulfonyl-9,10-dihydrophenanthrene. The dominant formation of this 3:1 coupling product, instead of the Heck trisubstituted olefin, shows that aromatic C-H bond activation processes can compete with the usually fast syn beta-hydrogen elimination step in the Heck arylation of an acyclic olefin. The structural scope of this palladium-catalyzed cascade arylation of alpha,beta-unsaturated sulfones has proved to be wide with regard to substitution at the beta-position (alkyl, aryl, or alkenyl substitution), substitution at the sulfone unit (alkyl or phenyl sulfones), and configuration at the CdoublebondC bond (trans or cis). Moreover, although less favored than in the case of the arylation of alpha,beta-unsaturated sulfones, similarly substituted 9,10-dihydrophenanthrenes have also been obtained in the case of alpha,beta-unsaturated phosphine oxides and alpha,beta-unsaturated phosphonate esters. A Pd(0)-Pd(II)-Pd(IV) mechanistic pathway involving the successive formation of highly electrophilic sigma-alkylpalladium intermediates and palladacycles is proposed for this multicomponent arylation.     

2',7'-Difluorofluorescein excited-state proton reactions: correlation between time-resolved emission and steady-state fluorescence intensity

The presence of excited-state buffer-mediated proton exchange reactions influences the steady-state fluorescence signals from dyes in solution. Since biomolecules in general have some chemical groups that can act as proton acceptors/donors and are usually dissolved in buffer solutions which can also behave as appropriate proton acceptors/donors, the excited-state proton exchange reactions may result in distorted steady-state fluorescence signals. In a previous paper (J. Phys. Chem. A 2005, 109, 734-747), we evaluated kinetic and other pertinent parameters for the excited-state proton reactions of the prototropic forms of 2',7'-difluorofluorescein (Oregon Green 488, OG488), recording a fluorescence decay surface at different pH values and acetate buffer concentrations, analyzed by means of global compartmental analysis. In this article we use the rate constants and the corrected pre-exponential factors from the previously recorded fluorescence decay traces to simulate the decay times and associated pre-exponentials at different acetate buffer concentrations and constant pH and compare these theoretically calculated values with new experimental data. We also calculate the steady-state fluorescence intensity vs pH and vs acetate buffer concentration (at constant pH) and compare these calculated emission values with the experimental data previously published. The agreement between the experimental and simulated data is excellent.     

Excited-state dynamics of fac-[ReI(L)(CO)3(phen)]+ and fac-[ReI(L)(CO)3(5-NO2-phen)]+ (L = imidazole, 4-ethylpyridine; phen = 1,10-phenanthroline) complexes

The nature and dynamics of the lowest excited states of fac-[Re(I)(L)(CO)(3)(phen)](+) and fac-[Re(I)(L)(CO)(3)(5-NO(2)-phen)](+) [L = Cl(-), 4-ethyl-pyridine (4-Etpy), imidazole (imH); phen = 1,10-phenanthroline] have been investigated by picosecond visible and IR transient absorption spectroscopy in aqueous (L = imH), acetonitrile (L = 4-Etpy, imH), and MeOH (L = imH) solutions. The phen complexes have long-lived Re(I) --> phen (3)MLCT excited states, characterized by CO stretching frequencies that are upshifted relative to their ground-state values and by widely split IR bands due to the out-of-phase A'(2) and A"nu(CO) vibrations. The lowest excited states of the 5-NO(2)-phen complexes also have (3)MLCT character; the larger upward nu(CO) shifts accord with much more extensive charge transfer from the Re(I)(CO)(3) unit to 5-NO(2)-phen in these states. Transient visible absorption spectra indicate that the excited electron is delocalized over the 5-NO(2)-phen ligand, which acquires radical anionic character. Similarly, involvement of the -NO(2) group in the Franck-Condon MLCT transition is manifested by the presence of an enhanced nu(NO(2)) band in the preresonance Raman spectrum of [Re(I)(4-Etpy)(CO)(3)(5-NO(2)-phen)](+). The Re(I) --> 5-NO(2)-phen (3)MLCT excited states are very short-lived: 7.6, 170, and 43 ps for L = Cl(-), 4-Etpy, and imH, respectively, in CH(3)CN solutions. The (3)MLCT excited state of [Re(I)(imH)(CO)(3)(5-NO(2)-phen)](+) is even shorter-lived in MeOH (15 ps) and H(2)O (1.3 ps). In addition to (3)MLCT, excitation of [Re(I)(imH)(CO)(3)(5-NO(2)-phen)](+) populates a (3)LLCT (imH --> 5-NO(2)-phen) excited state. Most of the (3)LLCT population decays to the ground state (time constants of 19 (H(2)O), 50 (MeOH), and 72 ps (CH(3)CN)); in a small fraction, however, deprotonation of the imH.+ ligand occurs, producing a long-lived species, [Re(I)(im.)(CO)(3)(5-NO(2)-phen).-]+.     

Modular bis(oxazoline) ligands for palladium catalyzed allylic alkylation: unprecedented conformational behaviour of a bis(oxazoline) palladium eta3-1,3-diphenylallyl complex

New families of enantiopure bis(oxazolines) with 4,5-trans (5 a-g) or 4,5-cis (6 c) stereochemistry at the individual rings have been prepared in high yield. Their eta(3)-allyl palladium complexes (8 a-g, 9 c and 10) have been used as catalytic precursors in allylic alkylation reactions with excellent enantioselectivities (up to 96 %) for the trans oxazoline derivatives, while Pd/6 c system was inactive. NMR studies on palladium eta(3)-1,3-diphenylallyl intermediates (11 a, c and e) showed the presence of syn/syn- and syn/anti-allyl isomers in solution; this resembles the first example of eta(3)-eta(1)-eta(3) isomerism in Pd allylic complexes containing bis(oxazolines) derived from malonic acid.     

Tailored pump-probe transient spectroscopy with time-dependent density-functional theory: controlling absorption spectra

Recent advances in laser technology allow us to follow electronic motion at its natural time-scale with ultra-fast time resolution, leading the way towards attosecond physics experiments of extreme precision. In this work, we assess the use of tailored pumps in order to enhance (or reduce) some given features of the probe absorption (for example, absorption in the visible range of otherwise transparent samples). This type of manipulation of the system response could be helpful for its full characterization, since it would allow us to visualize transitions that are dark when using unshaped pulses. In order to investigate these possibilities, we perform first a theoretical analysis of the non-equilibrium response function in this context, aided by one simple numerical model of the hydrogen atom. Then, we proceed to investigate the feasibility of using time-dependent density-functional theory as a means to implement, theoretically, this absorption-optimization idea, for more complex atoms or molecules. We conclude that the proposed idea could in principle be brought to the laboratory: tailored pump pulses can excite systems into light-absorbing states. However, we also highlight the severe numerical and theoretical difficulties posed by the problem: large-scale non-equilibrium quantum dynamics are cumbersome, even with TDDFT, and the shortcomings of state-of-the-art TDDFT functionals may still be serious for these out-of-equilibrium situations.     

Low‐Symmetry Ω‐Shaped Zinc Phthalocyanine Sensitizers with Panchromatic Light‐Harvesting Properties for Dye‐Sensitized Solar Cells

Two low‐symmetry phthalocyanines (Pcs) substituted with thiophene units at the non‐peripheral (α) and peripheral (β) positions were synthesized and their optical, electronic‐structure, and electrochemical properties were investigated. The substitution of thiophene units at the α positions of the phthalocyanine skeleton resulted in a red shift of the Q band and significantly modified the molecular‐orbital electronic distributions just below the HOMO and just above the LUMO, with distortion of the typical Gouterman four‐orbital arrangement of MOs. Two amphiphilic Ω‐shaped ZnPcs ( αPcS1 and αPcS2 ) bearing a π‐conjugated side chain with an adsorption site at an α position of the Pc macrocycle were synthesized as sensitizers for dye‐sensitized solar cells (DSSCs). The absorption spectra of αPcS1 and αPcS2 showed red shifted Q bands and a broad band from 350 to 550 nm assignable to the intramolecular charge‐transfer transition from the ZnPc core to the side chains. Time‐dependent DFT calculations provided a clear interpretation of the effect of the thiophene conjugation on the typical phthalocyanine core π MOs. Compound αPcS1 was used as a light‐harvesting dye on a TiO₂ electrode for a DSSC, which showed a panchromatic response in the range 400–800 nm with a power conversion efficiency of 5.5 % under one‐sun conditions.     

A New Total Synthesis of Withasomnine

The pyrazole alkaloid withasomnine 1, has been synthesized by construction of the 1,2-diazabicyclo [3.3.0] octa-2,4-diene system in a single step.     

Abelian varieties with finite abelian group action

An automorphism of an abelian variety induces a decomposition of the variety up to isogeny. There are two such results, namely the isotypical decomposition and Roan’s decomposition theorem. We show that they are essentially the same. Moreover, we generalize in a sense this result to abelian varieties with action of an arbitrary finite abelian group. An early version of this article was inadvertently published before all the revisions had been completed and then retracted [https://doi.org/10.1007/s00013-018-1244-3]. This article is the final peer reviewed version.