Convergence of delay differential equations driven by fractional Brownian motion

In this note, we prove an existence and uniqueness result of solution for stochastic differential delay equations with hereditary drift driven by a fractional Brownian motion with Hurst parameter H > 1/2. Then, we show that, when the delay goes to zero, the solutions to these equations converge, almost surely and in L ^p , to the solution for the equation without delay. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann–Stieltjes integral.     

Three-dimensional six-connecting organic building blocks based on polychlorotriphenylmethyl units--synthesis, self-assembly, and magnetic properties

The synthesis of a three-dimensional, six-connecting, organic building block based on a robust, rigid, and open-shell polychlorotriphenylmethyl (PTM) unit (radical 1) is reported, and its self-assembly properties are described in detail. The tendencies of this highly polar molecule and its hydrogenated precursor, compound 4, to form hydrogen bonds with oxygenated solvents ([1THF(6)] and [4THF(6)]) were reduced by replacing THF with diethyl ether in the crystallization process to yield two-dimensional (2D) hydrogen-bonded structures ([1(Et(2)O)(3)] and [4(Et(2)O)(3)]). The presence of direct hydrogen bonds between the radicals in the latter phase of 1 gives rise to very weak ferromagnetic intermolecular interactions at low temperatures, whereas when the radicals are isolated by THF molecules these interactions are antiferromagnetic and very weak. The role played by the carboxylic groups not only in the self-assembly properties but also in the transmission of the magnetic interactions has been illustrated by determination of the crystal structure and measurement of the magnetic properties of the corresponding hexaester radical 6, in which the close packing of molecular units gives rise to weak antiferromagnetic intermolecular interactions. Attempts to avoid solvation of the molecules in the solid state and to increase the structural and magnetic dimensionality were pursued by recrystallization of both compounds 1 and 4 from concentrated nitric acid, affording two three-dimensional (3D) robust hydrogen-bonded structures. While the structure obtained with compound 4 is characterized by the presence of polar channels and boxes containing water guest molecules along the c axis, radical 1 was oxidized to the corresponding fuchsone 10, which presented a completely different close-packed, guest-free structure.     

Stereoisomerism of molecular multipropellers. 1. Static stereochemistry of bis- and tris-triaryl systems

The static stereoisomerism of bis- and tris-triaryl systems has been analyzed by a systematic stereochemical analysis, and the resulting theoretical predictions have been experimentally confirmed by using reversed-phase HPLC and ESR and (1)H NMR spectroscopies with a family of seven distinct polychlorinated aromatic multipropellers. To analyze the static stereochemistry of these molecules, we have developed a specific procedure that uses a symmetry-adapted symbolic notation, allowing the theoretical prediction of both the number and symmetry of the isomers of the investigated molecules. Due to the steric hindrance introduced by the presence of bulky chlorine substituents, (all) conformational isomers can be characterized experimentally by several independent techniques confirming the theoretical stereochemical predictions. The different propeller moieties that constitute the molecule appear to be nearly independent of each other. Consequently, most of the observed isomers show comparable populations in solution at room temperature.     

Stereoisomerism of molecular multipropellers. 2. Dynamic stereochemistry of bis- and tris-triaryl systems

The dynamic stereochemistry of bis- and tris-triaryl systems, the most simple "molecular multipropellers", is discussed on the basis of an extension of a systematic stereochemical analysis based on a symmetry-adapted symbolic notation developed specifically for these molecules. A suitable theoretical basis for our study is provided by the classical hypotheses concerning the dynamics of simple triaryl systems as formulated by Mislow and co-workers (J. Am. Chem. Soc. 1973, 95, 1535-1547), which, once applied to molecular multipropellers, show the existence of two modes of rearrangement for each propeller. Interconversion graphs for all molecules under study, covering a wide span of structural complexity, are presented. A complete NMR study of a two- and a three-propeller molecule indicates that all experimentally observable exchange pathways are indeed predicted by theoretical analysis. Moreover, quantitative analysis of 2D-EXSY experiments affords the activation energy of the subset of pathways that give rise to observable interconversions on the NMR time scale. Assuming that two-ring flips are the threshold mechanism for individual propeller interconversion, the experimental evidence indicates a preference for the flip of the central ring and one of the outer rings over the flip of two outer rings.     

Novel fused D-A dyad and A-D-A triad incorporating tetrathiafulvalene and p-benzoquinone

Novel fused donor-acceptor dyad (TTF-Q or D-A) and acceptor-donor-acceptor triad (Q-TTF-Q or A-D-A) incorporating the donor tetrathiafulvalene (TTF) and the acceptor p-benzoquinone (Q) have been synthesized. The solution UV-vis spectra of these molecules display a low-energy absorption band that is attributed to an intramolecular charge transfer between both antagonistic units. The presence of reversible oxidation and reduction waves for the donor and acceptor moieties was shown by cyclic voltammetry, in agreement with the ratio TTF/quinone(s) units. The successive generation from these compounds of the cation radical and anion radical obtained upon (electro)chemical oxidation and reduction, respectively, was monitored by optical and ESR spectroscopies. The anion radical Q-TTF-Q(-.) triad was demonstrated to be a class II mixed-valence system with the existence of a temperature-dependent intramolecular electron transfer. The crystallographic tendency of these fused systems to overlap in mixed stacks of alternating A-D-A units is also discussed.     

Hydrogen-bonded self-assemblies in a polychlorotriphenylmethyl radical derivative substituted with six meta-carboxylic acid groups

The synthesis, self assembly and magnetic properties of a polychlorotriphenylmethyl radical, substituted with six meta-carboxylic groups, are reported showing that radical-radical hydrogen bonds in the solid state yield to very weak intermolecular ferromagnetic interactions.     

Multistability in a BEDT-TTF based molecular conductor

The low dimensional organic conductor (BEDT-TTF)(2)Br(1.3)I(1.1)Cl(0.6) [BEDT-TTF = bis(ethylenedithio)tertathiafulvalene] is shown to be a unique molecular solid that exists in three crystalline polymorphic forms (alpha'-, alpha' "-, beta' '-phase) and, surprisingly, is able to adopt the same metal-like beta' '-phase at both low (T < 185 K) and high (T > 395 K) temperatures. Several crystals of the alpha'- and alpha' "-phases have been studied using three different techniques: dc-conductivity measurements, ESR spectroscopy, and X-ray diffraction analysis. All these techniques show the existence of the reversible semiconductor <--> metal (alpha' " <--> beta' ') phase transition at both high and low temperatures as well as the alpha' <--> alpha' " phase transition at high temperatures. The phase transitions of these polymorphs are characterized by huge hysteresis and dramatic changes in the transport and magnetic properties. Based on ab initio calculations, it is suggested that dipole-dipole interactions can play a key role in the rich polymorphism of this molecular solid.