Does a Reinforced Kinetic Macrocyclic Effect Exist? The Demetallation in Strong Acid of Copper(II) Complexes with Open and Cyclic Tetramines Containing a Piperazine Fragment

The demetallation in acidic solution of the Cu(II) complexes with open-chain and cyclic tetramines containing a piperazine unit (2 and 3) has been investigated in terms of its kinetic aspects and compared with the behaviour of unsubstituted counterparts (tetramines 1 and 4). The presence of the piperazine fragment slows demetallation of the open-chain-ligand complex owing to the activation barrier associated with the conformational change from boat-to-half-boat; however, it does not affect the demetallation of the macrocyclic complex, which involves the spontaneous boat-to-twist conformational change. Thus, lateral reinforcement of a cyclam-like ligand does not add any further contribution to the typical inertness in demetallation of macrocyclic complexes.     

Ruthenium-catalyzed [3 + 2] intramolecular cycloaddition of alk-5-ynylidenecyclopropanes promoted by the "first-generation" Grubbs carbene complex

The well-known "first generation" Grubbs metathesis complex is capable of catalyzing the intramolecular [3 + 2] cycloaddition of alk-5-ynylidenecyclopropanes. It appears that the species responsible for the catalysis is a ruthenium complex generated in situ from the Grubbs carbene in the presence of the substrate.     

Formation of benzynes from 2,6-dihaloaryllithiums: mechanistic basis of the regioselectivity

The key elimination step for the formation of 3-chloro- and 3-fluorobenzyne from 2-chloro-6-fluorophenyllithium displays a pronounced solvent-dependent regioselectivity. 6Li and 13C NMR spectroscopic studies on 2-chloro-6-fluorophenyllithium reveal a single monomeric aryllithium, suggested by DFT computational studies to be a trisolvate. Rate studies indicate that the elimination of LiCl and LiF proceeds via trisolvated and disolvated monomers, respectively.     

Dynamics of alkoxy-oligothiophene ground and excited states in nanochannels

Two oligothiophenes, 4,4'-dipentoxy-2,2'-dithiophene and 4,4"-dipentoxy-2,2':5',2":5",2' '-tetrathiophene, have been included in the nanochannels of the autoassembling host TPP (tris-o-phenylenedioxycyclotriphosphazene). The effect of the confinement on the structure and properties of the two dyes, as conformational arrangements, dynamics, and photophysical behavior, was addressed by the combination of high spinning speed solid-state NMR and time-resolved EPR spectroscopy. We compared the conformations of the dyes in their ground and photoexcited triplet states and described in detail the dynamics of the supramolecular adducts from 4 K to room temperature. Above 200 K surprisingly fast spinning rates of the dithiophene core were discovered, while the side chains show far slower reorientation motion, being in bulky gauche-rich conformations. These lateral plugs keep the planar core as appended in the space like a nanoscale gyroscope, allowing a reorientation in the motion regime of liquids and a long triplet lifetime at unusually high temperature. The nuclear magnetic properties of the guest dyes are also largely affected by the aromatic rings of the neighboring host, imparting an impressive magnetic susceptibility effect (2 ppm proton shift). The high mobility is due to the formation of a nanocage in a channel where aliphatic and aromatic functions isolate the thiophene moieties. Instead, two conformers of the tetrathiophene twisted on the central bond are stabilized by interaction with the host. They interconvert fast enough to be averaged in the NMR time scale.     

Acetylene to vinylidene rearrangements on electron rich d6 metal centers: a density functional study

The acetylene to vinylidene isomerization on several Ru(II) d(6) metal fragments with different electron richness of the metal center has been investigated by means of density functional theory calculations. We considered the [(eta(5)-C(5)Me(5))Ru(dippe)](+), [(eta(5)-C(5)Me(5))Ru(dmpe)](+), [(eta(5)-C(5)H(5))Ru(PMe(3))(2)](+), [(eta(6)-C(6)Me(6))(PMe(3))ClRu](+), [(eta(5)-C(5)H(5))Ru(CO)(PPh(3))](+) and [eta(6)-C(6)H(6))(PMe(3))ClRu](+), species which are quite common in the chemistry of cationic Ru(II) complexes and span a wide range of electron-richness. For each of the considered fragments, the minima on the potential energy surfaces for the two possible isomerization mechanisms, i.e. through a direct 1,2-hydrogen shift or through a hydrido-alkynyl intermediate, have been localized. A linear correlation has been found between the C=C stretching frequencies of the vinylidene complexes, as an estimate of the electron richness, and the stability of the corresponding hydrido-alkynyl intermediates. For the most electron-rich among the considered fragments, [(Cp*)(dippe)Ru(HCCH)](+), the hydrido-alkynyl species has been found essentially isoenergetic with the alkyne complex (only 1.9 kcal mol(-1) higher), in agreement with the experimental evidence showing for this system an equilibrium between these two species. For the same [(Cp*)(dippe)Ru](+) fragment, a detailed analysis of the reaction profiles for the two possible acetylene rearrangement pathways has been performed. Our results show that once the eta(2)-C-H coordinated acetylene intermediate is accessed, the system can easily evolve towards a hydrido-alkynyl intermediate, this process being kinetically favored with respect to the direct 1,2-shift leading to the vinylidene product.     

Matrix Christoffel Functions

We introduce and study matrix Christoffel functions for a matrix weight W. We find an explicit expression of the matrix Christoffel functions in terms of any sequence of orthonormal matrix polynomials with respect to W. An extremal property related to the matrix moment problem defined by W is established for the matrix Christoffel functions. We finally find the relative asymptotic behavior of the matrix Christoffel functions associated to matrix weights in the matrix Nevai class.     

Isoperimetric inequalities in crystallography

Given a cubic space group (viewed as a finite group of isometries of the torus ), we obtain sharp isoperimetric inequalities for -invariant regions. These inequalities depend on the minimum number of points in an orbit of and on the largest Euler characteristic among nonspherical -symmetric surfaces minimizing the area under volume constraint (we also give explicit estimates of this second invariant for the various crystallographic cubic groups ). As an example, we prove that any surface dividing into two equal volumes with the same (orientation-preserving) symmetries as the A. Schoen minimal Gyroid has area at least (the conjectured minimizing surface in this case is the Gyroid itself whose area is ).

     

Entropy and degree of polarization for nonlinear optical waves

I show that the usual definitions of entropy and degree of polarization are not relevant for nonlinear optical waves, because they would lead to the erroneous conclusion that a genuine process of reversible propagation would be characterized by an irreversible process of entropy production. To circumvent this problem, I propose appropriate definitions of entropy and degree of polarization that depend on all the statistical moments of the nonlinear wave, so that they exhibit the satisfactory property to be conserved during a reversible propagation process.     

Spectral Talbot-like phenomena in one-dimensional photonic bandgap structures

Using numerical simulations, we report the observation of a new effect--a spectral Talbot-like effect--in one-dimensional photonic bandgap structures, particularly sampled chirped fiber Bragg gratings. We derive the general conditions for which spectral Talbot-like phenomena, namely, integer and fractional spectral self-imaging, can be observed and relate them to the physical grating parameters.