Orthogonal polynomials on the unit circle and their derivatives

We characterize the sequences of orthogonal polynomials on the unit circle whose derivatives are also orthogonal polynomials on the unit circle. Some relations for the sequences of derivatives of orthogonal polynomials are provided. Finally, we pose some problems about orthogonality-preserving maps and differential equations for orthogonal polynomials on the unit circle.     

Spin and Majorana polarization in topological superconducting wires

We study a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in the proximity of a superconductor. Using both analytical and numerical techniques we calculate the electronic spin texture of the Majorana end states. We find that the spin polarization of these states depends on the relative magnitude of the Rashba and Dresselhaus SOC components. Moreover, we define and calculate a local "Majorana polarization" and "Majorana density" and argue that they can be used as order parameters to characterize the topological transition between the trivial system and the system exhibiting Majorana bound modes. We find that the local Majorana polarization is correlated to the transverse spin polarization, and we propose to test the presence of Majorana fermions in a 1D system by a spin-polarized density of states measurement.     

Formation of negative oxidation states of platinum and gold in redox ionic liquid: Electrochemical evidence

The electrochemical reduction of noble metal electrodes in the presence of redox ionic liquid, 1-ferrocenylethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, [FcEMIM][TFSI], was investigated by cyclic voltammetry. Our experiments suggest the formation of metal with negative oxidation states, in the cases of platinum and gold electrodes [M_n⁻, FcEMIM⁺]. By analogy with the previous work, the formation of these phases is concomitant with the insertion of the supporting electrolyte; which correspond in our experimental condition to the redox cation of the ionic liquid. As an exciting result, the electrochemical investigations of the reduced electrode in electrolytic solution, containing solvent and supporting electrolyte, evidence the presence of the ferrocene groups at the electrode surface. Moreover, the reduced electrode exhibits the presence of the ferrocene even after, contact with air, after ultrasound, and after physical polishing, highlighting the large stability of this organo-metallic phases formed in this media. The AFM investigations demonstrate the morphological change of the platinum surface after the reduction process. Finally, our works bring a formal electrochemical proof of the presence of the ionic liquid cation inside the electrode material after the cathodic treatment in this media.     

Gadolinium chelate coated gold nanoparticles as contrast agents for both X-ray computed tomography and magnetic resonance imaging

Functionalized gold nanoparticles were applied as contrast agents for both in vivo X-ray and magnetic resonance imaging. These particles were obtained by encapsulating gold cores within a multilayered organic shell which is composed of gadolinium chelates bound to each other through disulfide bonds. The contrast enhancement in MRI stems from the presence of gadolinium ions which are entrapped in the organic shell, whereas the gold core provides a strong X-ray absorption. This study revealed that these particles suited for dual modality imaging freely circulate in the blood vessels without undesirable accumulation in the lungs, spleen, and liver.     

Far-infrared spectroscopy of small polycyclic aromatic hydrocarbons

Both experimental and theoretical spectroscopic studies on small gas phase polycyclic aromatic hydrocarbons in the far-infrared spectral region are reported. The experimental set-up based on thermal emission and Fourier transform far infrared analysis led to the detection of relatively broad vibrational bands, unresolved in rotation, representative of each molecule. Detailed theoretical investigations were performed, including both ab initio calculations and spectral simulations. For the majority of the samples, this study provides the first detection of the vibrational modes associated with the skeleton motions.     

Excited-state absorption properties of platinum(II) terpyridyl acetylides

A comprehensive photophysical study is presented which compares the ground- and excited-state properties of four platinum(II) terpyridyl acetylide compounds of the general formula [Pt(tBu3tpy)(CCR)]+, where tBu3tpy is 4,4',4' '-tri-tert-butyl-2,2':6',2' '-terpyridine and R is an alkyl or aryl group. [Ru(tBu3tpy)3]2+ and the pivotal synthetic precursor [Pt(tBu3tpy)Cl]+ were also investigated in the current work. The latter two complexes possess short excited-state lifetimes and were investigated using ultrafast spectrometry while the other four compounds were evaluated using conventional nanosecond transient-absorption spectroscopy. The original intention of this study was to comprehend the nature of the impressive excited-state absorptions that emanate from this class of transition-metal chromophores. Transient-absorbance-difference spectra across the series contain the same salient features, which are modulated only slightly in wavelength and markedly in intensity as a function of the appended acetylide ligand. More intense absorption transients are observed in the arylacetylide structures relative to those bearing an alkylacetylide, consistent with transitions coupled to the pi system of the ancillary ligand. Reductive spectroelectrochemical measurements successfully generated the electronic spectrum of the tBu3tpy radical anion in all six complexes at room temperature. These measurements confirm that electronic absorptions associated with the tBu3tpy radical anion simply do not account for the intense optical transitions observed in the excited state of the Pt(II) chromophores. Transient-trapping experiments using the spectroscopically silent reductive quencher DABCO clearly demonstrate the loss of most transient-absorption features in the acetylide complexes throughout the UV, visible, and near-IR regions following bimolecular excited-state electron transfer, suggesting that these features are strongly tied to the photogenerated hole which is delocalized across the Pt center and the ancillary acetylide ligand.     

Coexistence of Two Thermally Induced Intramolecular Electron Transfer Processes in a Series of Metal Complexes [M(Cat‐N‐BQ)(Cat‐N‐SQ)]/[M(Cat‐N‐BQ)2] (M=Co,Fe, and Ni) bearing Non‐Innocent Catechol‐Based Ligands: A Combined Experimental and Theoretical Study

The different thermally induced intermolecular electron transfer (IET) processes that can take place in the series of complexes [M(Cat‐N‐BQ)(Cat‐N‐SQ)]/[M(Cat‐N‐BQ)₂], for which M=Co ( 2 ), Fe ( 3 ) and Ni( 4 ), and Cat‐N‐BQ and Cat‐N‐SQ denote the mononegative (Cat‐N‐BQ^?) or dinegative (Cat‐N‐SQ^2?) radical forms of the tridentate Schiff‐base ligand 3,5‐di‐tert‐butyl‐1,2‐quinone‐1‐(2‐hydroxy‐3,5‐di‐tert‐butylphenyl)imine, have been studied by variable‐temperature UV/Vis and NMR spectroscopies. Depending on the metal ion, rather different behaviors are observed. Complex 2 has been found to be one of the few examples so far reported to exhibit the coexistence of two thermally induced electron transfer processes, ligand‐to‐metal (IET^LM) and ligand‐to‐ligand (IET^LL). IET^LL was only found to take place in complex 3 , and no IET was observed for complex 4 . Such experimental studies have been combined with ab initio wavefunction‐based CASSCF/CASPT2 calculations. Such a strategy allows one to solicit selectively the speculated orbitals and to access the ground states and excited‐spin states, as well as charge‐transfer states giving additional information on the different IET processes.     

Polyglycerol-derived amphiphiles for the solubilization of single-walled carbon nanotubes in water: a structure-property study

A series of nonionic amphiphiles derived from polyglycerol dendrons were studied for their ability to solubilize and isolate single-walled carbon nanotubes. The amphiphiles possessed differently sized polar head groups, hydrophobic tail units, and various aromatic and non-aromatic groups between the head and tail groups. Absorbance analysis revealed that amphiphiles with anchor groups derived from pyrene were far inferior to those that possessed simple linear aliphatic tail groups. Absorbance and near-infrared fluorescence analyses revealed a weak dependence on the dendron size of the head group, but a strong positive trend in suspended nanotube density and fluorescence intensity for amphiphiles with longer tail units. Variations in the moieties linking the head and tail groups led to a range of effects on the suspensions, with linkers imparting flexibility and a bent shape that gave improved performance overall. This was illustrated most dramatically by a pair of benzamide-containing amphiphiles, the para isomer of which showed evidence in the fluorescence data of increased nanotube aggregate formation when compared with the meta isomer. In addition, statistical AFM was used to illustrate more directly the microscopic differences between amphiphiles that were effective at nanotube bundle disruption and those that were not.     

Phenyliodine(III) bis(trifluoroacetate) (PIFA)-promoted synthesis of Bodipy dimers displaying unusual redox properties

Phenyliodine(III) bis(trifluoroacetate) (PIFA) in conjunction with a Lewis acid promotes C-C coupling of Bodipy monomers leading to mixtures of various oligomers. When a single position is blocked with an iodo or phenyl group, formation of the dimer is favored. These dimers display two successive oxidation and two reduction waves separated on average by 260 and 130 mV, respectively, corresponding to each Bodipy subunit.     

Quasi-classical trajectory study of the S + OH → SO + H reaction: from reaction probability to thermal rate constant

First quasi-classical trajectory calculations have been carried out for the S((3)P) + OH(X?(2)Π) → SO(X?(3)Σ(-)) + H((2)S) reaction on an ab initio global potential energy surface for the ground electronic state, X?(2)A', of HSO. Cross sections, computed for collision energies up to 1 eV, show no energy threshold and decrease with the increasing collision energy. Rate constants have been calculated in the 5-500 K temperature range. The thermal rate constant is in good agreement with approximate quantum results, while a disagreement is found at 298 K with the experimental data. Product energy distributions have also been reported at four collision energies from 0.001 to 0.5 eV. The shapes of the rovibrational and angular distributions suggest the formation of an intermediate complex that is more and more long-lived as the collision energy increases.