Calix[4]arene-linked bisporphyrin hosts for fullerenes: binding strength, solvation effects, and porphyrin-fullerene charge transfer bands

A calix[4]arene scaffolding has been used to construct bisporphyrin ("jaws" porphyrin) hosts for supramolecular binding of fullerene guests. Fullerene affinities were optimized by varying the nature of the covalent linkage of the porphyrins to the calixarenes. Binding constants for C60 and C70 in toluene were explored as a function of substituents at the periphery of the porphyrin, and 3,5-di-tert-butylphenyl groups gave rise to the highest fullerene affinities (26,000 M(-1) for C60). The origin of this high fullerene affinity has been traced to differential solvation effects rather than to electronic effects. Studies of binding constants as a function of solvent (toluene < benzonitrile < dichloromethane < cyclohexane) correlate inversely with fullerene solubility, indicating that desolvation of the fullerene is a major factor determining the magnitude of binding constants. The energetics of fullerene binding have been determined in terms of DelatH and DeltaS and are consistent with an enthalpy-driven, solvation-dependent process. A direct relationship between supramolecular binding of a fullerene guest to a bisporphyrin host and the appearance of a broad NIR absorption band have been established. The energy of this band moves in a predictable manner as a function of the electronic structure of the porphyrin, thereby establishing its origin in porphyrin-to-fullerene charge transfer.     

Size-dependent extinction coefficients of PbS quantum dots

We report here on a detailed study on PbS colloidal quantum dots. A characterization via X-ray diffraction (XRD) and high-resolution transmission electron microscopy (HRTEM) allowed us to reliably determine the diameter and the shape of the nanocrystals. These data, together with second-derivative analysis of the absorption spectra, allowed us to determine the size dependence of seven transitions in the absorption spectrum; some of these transitions were identified on the basis of their normalized confinement energy. The size dependence of the first excitonic transition was best modeled by a four-band envelope approach which considers the anisotropy of the band edges (Andreev, A. D.; Lipovskii, A. A. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 15402-15404). The extinction coefficients were calculated using concentrations obtained from inductively coupled plasma atomic emission spectrometry (ICP-AES), and their size dependence was found to follow a power law with exponent equal to approximately 2.5. In contrast with what was expected from the effective mass approximation, the per particle absorption cross section of the lowest transition was found to be strongly dependent on the particle size.     

Gell-Mann and Low Formula for Degenerate Unperturbed States

The Gell-Mann and Low switching allows to transform eigenstates of an unperturbed Hamiltonian H ₀ into eigenstates of the modified Hamiltonian H ₀ + V. This switching can be performed when the initial eigenstate is not degenerate, under some gap conditions with the remainder of the spectrum. We show here how to extend this approach to the case when the ground state of the unperturbed Hamiltonian is degenerate. More precisely, we prove that the switching procedure can still be performed when the initial states are eigenstates of the finite rank self-adjoint operator P₀VP₀{\mathcal{P}_{0}V\mathcal{P}_{0}} , where P₀{\mathcal{P}_0} is the projection onto a degenerate eigenspace of H ₀.     

Butadienic building blocks from 2-nitrothiophene as precursors of nitrogen heterocycles: intriguing dichotomic behavior

With the goal of their exploitation for the synthesis of heterocycles, sulfides 10 and sulfones 11, derived from the initial ring-opening of 2-nitrothiophene (5) with pyrrolidine/AgNO3 in EtOH, were reacted with diazomethane. Interesting dichotomic behavior was found to yield pyrazolines 17 from 10 and isoxazolines 18 (as the main products) from 11. Intriguingly enough, in the latter case, an unexpected apparent C-C methylene insertion was also observed, leading to the homologous cyclopropanes 19 as secondary products.     

Symmetry and Localization for Magnetic Schrödinger Operators: Landau Levels,Gabor Frames and All That

We investigate the relation between broken time-reversal symmetry and localization of the electronic states, in the explicitly tractable case of the Landau model. We first review, for the reader’s convenience, the symmetries of the Landau Hamiltonian and the relation of the latter with the Segal-Bargmann representation of Quantum Mechanics. We then study the localization properties of the Landau eigenstates by applying an abstract version of the Balian-Low Theorem to the operators corresponding to the coordinates of the centre of the cyclotron orbit in the classical theory. Our proof of the Balian-Low Theorem, although based on Battle’s main argument, has the advantage of being representation-independent.

     

DNS of buoyancy-dominated turbulent flows on a bluff body using the immersed boundary method

A novel immersed boundary (IB) method has been developed for simulating multi-material heat transfer problem – a cylinder in a channel heated from below with mixed convection. The method is based on a second-order velocity/scalar reconstruction near the IB. A novel algorithm has been developed for the IB method to handle conjugate heat transfer. The fluid–solid interface is constructed as a collection of disjoint faces of control volumes associated to different material zones. Coupling conditions for the material zones have been developed such that continuity and conservation of the scalar flux are satisfied by a second-order interpolation. Predictions of the local Nusselt number on the cylinder surface show good agreement with the experimental data. The effect of the Boussinesq approximation on this problem was also investigated. Comparison with the variable density formulation suggests that, in spite of a small thermal expansion coefficient of water, the variable density formulation in a transitional flow with mixed convection is preferable.     

Synthesis of 1H-pyrazino[1,2-a]pyrido[2,3-e]pyrazine and 2H-Pyrano[2,3-b]pyrido[2,3-e]pyrazine Derivatives

With a continuing interest on heteropolycyclic structures which may show biological activities, we synthesized new tricyclic derivatives in which the pyridopyrazine skeleton is fused with pyrazine 7 and 8, B , n = 1. However, the initial design of obtaining also the cyclohomologous structure B (n = 2) produced instead a pyranopyridopyrazine derivative 11 . Thus during the attempt to prepare a pyridodiazepine intermediate, beside a very small amount of the desired product 10 , the pyridopyrazine 9 was obtained. The latter compound reacted with chloroacetyl chloride/chloroketene to give 4-carbethoxy-10-(chloroacetyl)-5,10-dihydro-5-methyl-2H-pyrano[2,3-b]pyrido[2,3-e]pyrazin-2-one ( 11 ). In studying the behavior of this derivative, compounds 12–14 were obtained. Compounds 4b,c, 5a,b, 7, 8, 9 and 14 have been submitted to preliminary pharmacological screening as CNS depressant agents.