Synthesis of Fluorescent Pyrrolo[1,2-a]pyrimidines from Fischer Carbene Complexes as Building Blocks.

A novel synthetic methodology is reported for the synthesis of fluorescent pyrrolo[1,2-a]pyrimidines. Fischer carbene complexes served as the synthetic platform for (3+3) cyclization to form the heterocyclic moiety. The reaction process furnished two products, their ratio being modulated by the metal, base, and solvent. The selectivity exhibited was studied by analyzing the potential energy surface with density functional theory tools. The photophysical properties of absorption and emission were also evaluated. The dyes absorbed at wavelengths of 240-440 nm, depending on the substituents. The maximum emission wavelength was in the range of 470-513 nm, with quantum yields of 0.36-1.0 and a high Stokes shift range of 75-226 nm.

Singular boundary behaviour and large solutions for fractional elliptic equations.

We perform a unified analysis for the boundary behaviour of solutions to nonlocal fractional equations posed in bounded domains. Based on previous findings for some models of the fractional Laplacian operator, we show how it strongly differs from the boundary behaviour of solutions to elliptic problems modelled upon the Laplace-Poisson equation with zero boundary data. In the classical case it is known that, at least in a suitable weak sense, solutions of the homogeneous Dirichlet problem with a forcing term tend to zero at the boundary. Limits of these solutions then produce solutions of some non-homogeneous Dirichlet problem as the interior data concentrate suitably to the boundary. Here, we show that, for equations driven by a wide class of nonlocal fractional operators, different blow-up phenomena may occur at the boundary of the domain. We describe such explosive behaviours and obtain precise quantitative estimates depending on simple parameters of the nonlocal operators. Our unifying technique is based on a careful study of the inverse operator in terms of the corresponding Green function.

Synthesis of Polysubstituted Symmetrical BODIPYs via Fischer Carbene Complexes: Theoretical, Photophysical and Electrochemical Evaluation.

A series of new symmetrical highly substituted BODIPYs 6 a-l was synthesized through a prefunctionalization approach in 35 %-89 % yields from the pyrrole core. This strategy allowed modulation of the substituents at the different positions based on the choice of Fischer's alkynyl carbenes, oxazolones and aldehydes used as precursors. The substituent variation at positions 2, 6, 3 and 5 had the greatest effect on the modulation of their photophysical properties such as absorption (λabs ) and emission (λem ) wavelengths, extinction coefficient (ϵ), quantum yields (ϕ), Stokes shifts (Δν), fluorescence decay, radiative (krad ) and non-radiative (knr ) constants and the CIE 1931 coordinates. Theoretical calculations allowed to corroborate the effect of the substituents of meso-position on the modification of the dihedral angles. Cyclic voltammetry studies revealed that the BODIPY series presents similar redox potential behavior, being electrochemically active even in successive cycles, which suggests that transport by diffusion is the dominant process.

Effect of the substituents of new coumarin-imidazo[1,2-a]heterocyclic-3-acrylate derivatives on nonlinear optical properties: a combined experimental-theoretical approach.

A series of new coumarin-imidazo[1,2-a]heterocyclic-3-acrylate derivatives 7a-h were synthesized by the Heck reaction between the corresponding 3-(imidazo[1,2-a]pyrimidines)-(2-yl)-2H-chromen-2-ones 4a-e and methyl acrylate in 45-87% yields. The effect of the distinct substituents on third-order nonlinear optical properties was examined, experimentally measuring their nonlinear refractive indexes by the Z-scan technique. Density functional theory and time-dependent density functional theory were utilized with the B3LYP, CAM-B3LYP, PBE (PBEPBE), and M062X functionals on Gaussian09 software to calculate the vertical excitation, relaxation of the brightest excited states, conformation, HOMO-LUMO gaps, oscillator strength, polarizability, and hyperpolarizabilities of all derivatives. Although all acrylates showed a nonlinear response at a certain level of power, the compounds bearing a diethylamino electron-donating group exhibited higher nonlinear refractive index values (∼10-9 cm2 W-1), which is in agreement with the trend in the computational calculations of the first and second hyperpolarization. According to the structural analysis, the electron-withdrawing group (acrylate) is mainly responsible for the loss of coplanarity because of increasing the dihedral angle between the coumarin and imidazo[1,2-a]heterocyclic moieties (to 39.1°). On the other hand, the unsubstituted compound 4a presented the greatest nonlinearity due to its almost coplanar structure (n2 ∼ 10-8 cm2 W-1), highlighting the importance of this feature.

Some free boundary problems involving non-local diffusion and aggregation.

We report on recent progress in the study of evolution processes involving degenerate parabolic equations which may exhibit free boundaries. The equations we have selected follow two recent trends in diffusion theory: considering anomalous diffusion with long-range effects, which leads to fractional operators or other operators involving kernels with large tails; and the combination of diffusion and aggregation effects, leading to delicate long-term equilibria whose description is still incipient.