Characterization Theorem for Best Polynomial Spline Approximation with Free Knots,Variable Degree and Fixed Tails

In this paper, we derive a necessary condition for a best approximation by piecewise polynomial functions of varying degree from one interval to another. Based on these results, we obtain a characterization theorem for the polynomial splines with fixed tails, that is the value of the spline is fixed in one or more knots (external or internal). We apply nonsmooth nonconvex analysis to obtain this result, which is also a necessary and sufficient condition for inf-stationarity in the sense of Demyanov–Rubinov. This paper is an extension of a paper where similar conditions were obtained for free tails splines. The main results of this paper are essential for the development of a Remez-type algorithm for free knot spline approximation.     

Mobilité conformationnelle et migration des liaisons π dans le [24]annulène

Conformational Mobility and Migration of the π Bonds of the [24]annulene. The configuration and the conformation of [24]annulene have been determined after a detailed analysis of its ¹H-NMR spectrum recorded at −95°. At this temperature, molecular dynamics is practically frozen, and the spectrum can be correctly simulated considering eight magnetic sites with the relevant couplings. The [24]annulene exhibits alternation of the double and the single bonds with the CTTTCTTTCTTT sequence (C=cis, T=trans) expressing the connectivity of the double bonds. The signal of the 9 protons pointing inside the ring is 7.72 ppm at lower field than the signal of the 15 outer protons; this indicates a marked paramagnetic ring current. Molecular dynamics is revealed by the dependence of the spectrum upon the temperature; the simulation of the line shape of these spectra indicates that the [24]annulene in solution exists as an equilibrium of two conformers A and B ( B / A ≤0.05), both having the same configuration. Each of these conformers undergoes two isodynamic processes: a migration of the π bonds on the adjacent single bonds (bond shift) described by V and a conformational mobility described by K. The two conformers interconvert extremely rapidely. Conformer A complies with C_3h symmetry, conformer B with C₃ symmetry. The enthalpy, entropy, and free energy of activation for the processes described by V and K in the major conformer A have been determined: these processes are slower than those observed in [16]annulene. From their values, we could deduce that the resonance energy in the [24]-7³annulene is negative and of the order of −9 to −10 kcal⋅mol⁻¹.     

Phosphonated Near‐Infrared Fluorophores for Biomedical Imaging of Bone

The conventional method for creating targeted contrast agents is to conjugate separate targeting and fluorophore domains. A new strategy is based on the incorporation of targeting moieties into the non‐delocalized structure of pentamethine and heptamethine indocyanines. Using the known affinity of phosphonates for bone minerals in a model system, two families of bifunctional molecules that target bone without requiring a traditional bisphosphonate are synthesized. With peak fluorescence emissions at approximately 700 or 800 nm, these molecules can be used for fluorescence‐assisted resection and exploration (FLARE) dual‐channel imaging. Longitudinal FLARE studies in mice demonstrate that phosphonated near‐infrared fluorophores remain stable in bone for over five weeks, and histological analysis confirms their incorporation into the bone matrix. Taken together, a new strategy for creating ultra‐compact, targeted near‐infrared fluorophores for various bioimaging applications is described.     

Elongated Bacterial Pili as a Versatile Alignment Medium for NMR Spectroscopy

In NMR spectroscopy, residual dipolar couplings (RDCs) have emerged as one of the most exquisite probes of biological structure and dynamics. The measurement of RDCs relies on the partial alignment of the molecule of interest, for example by using a liquid crystal as a solvent. Here, we establish bacterial type 1 pili as an alternative liquid-crystalline alignment medium for the measurement of RDCs. To achieve alignment at pilus concentrations that allow for efficient NMR sample preparation, we elongated wild-type pili by recombinant overproduction of the main structural pilus subunit. Building on the extraordinary stability of type 1 pili against spontaneous dissociation and unfolding, we show that the medium is compatible with challenging experimental conditions such as high temperature, the presence of detergents, organic solvents or very acidic pH, setting it apart from most established alignment media. Using human ubiquitin, HIV-1 TAR RNA and camphor as spectroscopic probes, we demonstrate the applicability of the medium for the determination of RDCs of proteins, nucleic acids and small molecules. Our results show that type 1 pili represent a very useful alternative to existing alignment media and may readily assist the characterization of molecular structure and dynamics by NMR.     

trans-cis Photoisomerization of the styrylpyridine Ligand in [Re(CO)3(2,2'-bipyridine)(t-4-styrylpyridine)]+: role of the metal-to-ligand charge-transfer excited states

The trans-cis isomerization of the styrylpyridine carbon-carbon double bond induced by visible light irradiation in fac-[Re(CO)(3)(bpy)(stpy)](+) (bpy = 2,2'-bipyridine; stpy = t-4-styrylpyridine) has been investigated by means of quantum-chemical methods. The structures of the various cis and trans conformers of [Re(CO)(3)(bpy)(stpy)](+) have been optimized at the density functional theory (DFT) level. Three rotational conformers for the most stable trans isomer lie within 2.3 kJ mol(-1) each other. The energy difference between the cis and trans isomers is 27.0 kJ mol(-1). The electronic spectroscopy of the most stable conformers has been investigated by time-dependent DFT (TD-DFT) and complete active space self-consistent field/CAS second order perturbation theory (CASSCF/CASPT2) calculations. The lowest absorption bands are dominated by metal-to-ligand charge-transfer (MLCT, d(Re)-->pi*(bpy)) transitions calculated at about 25,000 cm(-1) and by a strong intraligand (1)IL (pi(stpy)-->pi*(stpy)) transition in the near UV region. On the basis of CASSCF potential energy curves (PECs) calculated as a function of the torsion angle of the C=C bond of the styrylpyridine ligand, it is shown that the role of the low-lying MLCT states is important in the photoisomerization mechanism. In contrast to the free organic ligand, in which the singlet mechanism is operational via the (1)IL (S(1)) and electronic ground (S(0)) states, coordination to the rhenium steers the isomerization to the triplet PEC corresponding to the (3)IL state. From the (3)IL(t) (t = trans) the system evolves to the perpendicular intermediate (3)IL(p) (p = perpendicular) following a 90 degrees rotation around the styrylpyridine C=C bond. The metal center acts as a photosensitizer because of the presence of photoactive MLCT states under visible irradiation. The position of the crossing between the (3)IL and electronic ground state PEC determines the quantum yield of the isomerization process.     

Analysis of the essential oil from aerial parts of Eupatorium cannabinum subsp. corsicum (L.) by gas chromatography with electron impact and chemical ionization mass spectrometry

Eupatorium cannabinum subsp. corsicum (L.), an aromatic plant, is an endemic subspecies from Corsica. The essential oil from aerial parts of E. cannabinum subsp. corsicum was studied by GC, GC/MS and 13C NMR. One hundred and forty-seven components were identified representing 93.6% of the total amount. The main constituents are germacrene D (28.5%), alpha-phellandrene (19.0%) and para-cymene (5.2%). A particularity of this essential oil is the presence of monoterpene esters derived from nerol, lavandulol, borneol, thymol and 8,9-dehydrothymol. These compounds have been investigated using GC/MS in different ionization modes like electron impact (EI), positive chemical ionization (PCI) and negative chemical ionization (NCI).     

Photophysics of a Ruthenium 4H‐Imidazole Panchromatic Dye in Interaction with Titanium Dioxide

The photophysics of bis(4,4′‐di‐tert‐butyl‐2,2′‐bipyridine‐κ²N,N′)[2‐(4‐carboxyphenyl)‐4,5‐bis(p‐tolylimino‐κN)imidazolato]ruthenium(II) hexafluorophosphate is investigated, both in solution and attached to a nanocrystalline TiO₂ film. The studied substitution pattern of the 4H‐imidazole ligand is observed to block a photoinduced structural reorganization pathway within the 4H‐imidazole ligand that has been previously investigated. Protonation at the 4H‐imidazole ring decreases the excited‐state lifetime in solution. When the unprotonated dye is anchored to TiO₂, photoinduced electron injection occurs from thermally nonrelaxed triplet metal‐to‐ligand charge transfer (³MLCT) states with a characteristic time constant of 0.5 ps and an injection efficiency of roughly 25 %. Electron injection from the subsequently populated thermalized ³MLCT state of the dye does not take place. The energy of this state seems to be lower than the conduction band edge of TiO₂.     

In‐ and Out‐of‐Cavity Interactions by Modulating the Size of Ruthenium Metallarectangles

Cationic (arene)ruthenium‐based tetranuclear complexes of the general formula [Ru₄(η⁶‐p‐cymene)₄(μ‐N∩N)₂(μ‐OO∩OO)₂]⁴⁺ were obtained from the dinuclear (arene)ruthenium complexes [Ru₂(η⁶‐p‐cymene)₂(μ‐OO∩OO)₂Cl₂] (p‐cymene=1‐methyl‐4‐(1‐methylethyl)benzene, OO∩OO=5,8‐dihydroxy‐1,4‐naphthoquinonato(2?), 9,10‐dihydroxy‐1,4‐anthraquinonato(2?), or 6,11‐dihydroxynaphthacene‐5,12‐dionato(2?)) by reaction with pyrazine or bipyridine linkers (N∩N=pyrazine, 4,4′‐bipyridine, 4,4′‐[(1E)‐ethene‐1,2‐diyl]bis[pyridine]) in the presence of silver trifluoromethanesulfonate (CF₃SO₃Ag) (Scheme). All complexes 4 – 12 were isolated in good yield as CF₃SO salts, and characterized by NMR and IR spectroscopy. The host–guest properties of the metallarectangles incorporating 4,4′‐bipyridine and (4,4′‐[(1E)‐ethene‐1,2‐diyl]bis[pyridine] linkers were studied in solution by means of multiple NMR experiments (1D, ROESY, and DOSY). The largest metallarectangles 10 – 12 incorporating (4,4′‐[(1E)‐ethene‐1,2‐diyl]bis[pyridine] linkers are able to host an anthracene, pyrene, perylene, or coronene molecule in their cavity, while the medium‐size metallarectangles 7 – 9 incorporating 4,4′‐bipyridine linkers are only able to encapsulate anthracene. However, out‐of‐cavity interactions are observed between these 4,4′‐bipyridine‐containing rectangles and pyrene, perylene, or coronene. In contrast, the small pyrazine‐containing metallarectangles 4 – 6 show no interaction in solution with this series of planar aromatic molecules.     

Acid-induced degradation of phosphorescent dopants for OLEDs and its application to the synthesis of tris-heteroleptic iridium(III) bis-cyclometalated complexes

Investigations of blue phosphorescent organic light emitting diodes (OLEDs) based on [Ir(2-(2,4-difluorophenyl)pyridine)(2)(picolinate)] (FIrPic) have pointed to the cleavage of the picolinate as a possible reason for device instability. We reproduced the loss of picolinate and acetylacetonate ancillary ligands in solution by the addition of Br?nsted or Lewis acids. When hydrochloric acid is added to a solution of a [Ir(C^N)(2)(X^O)] complex (C^N = 2-phenylpyridine (ppy) or 2-(2,4-difluorophenyl)pyridine (diFppy) and X^O = picolinate (pic) or acetylacetonate (acac)), the cleavage of the ancillary ligand results in the direct formation of the chloro-bridged iridium(III) dimer [{Ir(C^N)(2)(μ-Cl)}(2)]. When triflic acid or boron trifluoride are used, a source of chloride (here tetrabutylammonium chloride) is added to obtain the same chloro-bridged iridium(III) dimer. Then, we advantageously used this degradation reaction for the efficient synthesis of tris-heteroleptic cyclometalated iridium(III) complexes [Ir(C^N(1))(C^N(2))(L)], a family of cyclometalated complexes otherwise challenging to prepare. We used an iridium(I) complex, [{Ir(COD)(μ-Cl)}(2)], and a stoichiometric amount of two different C^N ligands (C^N(1) = ppy; C^N(2) = diFppy) as starting materials for the swift preparation of the chloro-bridged iridium(III) dimers. After reacting the mixture with acetylacetonate and subsequent purification, the tris-heteroleptic complex [Ir(ppy)(diFppy)(acac)] could be isolated with good yield from the crude containing as well the bis-heteroleptic complexes [Ir(ppy)(2)(acac)] and [Ir(diFppy)(2)(acac)]. Reaction of the tris-heteroleptic acac complex with hydrochloric acid gives pure heteroleptic chloro-bridged iridium dimer [{Ir(ppy)(diFppy)(μ-Cl)}(2)], which can be used as starting material for the preparation of a new tris-heteroleptic iridium(III) complex based on these two C^N ligands. Finally, we use DFT/LR-TDDFT to rationalize the impact of the two different C^N ligands on the observed photophysical and electrochemical properties.