A q-analogue of the FKG inequality and some applications

Let L be a finite distributive lattice and μ: L → ℝ⁺ a log-supermodular function. For functions k: L → ℝ⁺ let

Perfect Matchings in Total Domination Critical Graphs

A graph is total domination edge-critical if the addition of any edge decreases the total domination number, while a graph with minimum degree at least two is total domination vertex-critical if the removal of any vertex decreases the total domination number. A 3 _t EC graph is a total domination edge-critical graph with total domination number 3 and a 3 _t VC graph is a total domination vertex-critical graph with total domination number 3. A graph G is factor-critical if G − v has a perfect matching for every vertex v in G. In this paper, we show that every 3 _t EC graph of even order has a perfect matching, while every 3 _t EC graph of odd order with no cut-vertex is factor-critical. We also show that every 3 _t VC graph of even order that is K _1,7-free has a perfect matching, while every 3 _t VC graph of odd order that is K _1,6-free is factor-critical. We show that these results are tight in the sense that there exist 3 _t VC graphs of even order with no perfect matching that are K _1,8-free and 3 _t VC graphs of odd order that are K _1,7-free but not factor-critical.     

Ex situ generation of stoichiometric and substoichiometric 12CO and 13CO and its efficient incorporation in palladium catalyzed aminocarbonylations

A new technique for the ex situ generation of carbon monoxide (CO) and its efficient incorporation in palladium catalyzed carbonylation reactions was achieved using a simple sealed two-chamber system. The ex situ generation of CO was derived by a palladium catalyzed decarbonylation of tertiary acid chlorides using a catalyst originating from Pd(dba)(2) and P(tBu)(3). Preliminary studies using pivaloyl chloride as the CO-precursor provided an alternative approach for the aminocarbonylation of 2-pyridyl tosylate derivatives using only 1.5 equiv of CO. Further design of the acid chloride CO-precursor led to the development of a new solid, stable, and easy to handle source of CO for chemical transformations. The synthesis of this CO-precursor also provided an entry point for the late installment of an isotopically carbon-labeled acid chloride for the subsequent release of gaseous [(13)C]CO. In combination with studies aimed toward application of CO as the limiting reagent, this method provided highly efficient palladium catalyzed aminocarbonylations with CO-incorporations up to 96%. The ex situ generated CO and the two-chamber system were tested in the synthesis of several compounds of pharmaceutical interest and all of them were labeled as their [(13)C]carbonyl counterparts in good to excellent yields based on limiting CO. Finally, palladium catalyzed decarbonylation at room temperature also allowed for a successful double carbonylation. This new protocol provides a facile and clean source of gaseous CO, which is safely handled and stored. Furthermore, since the CO is generated ex situ, excellent functional group tolerance is secured in the carbonylation chamber. Finally, CO is only generated and released in minute amounts, hence, eliminating the need for specialized equipment such as CO-detectors and equipment for running high pressure reactions.     

Hydrogen spillover in Pt-single-walled carbon nanotube composites: formation of stable C-H bonds

Using in situ electrical conductivity and ex situ X-ray photoelectron spectroscopy (XPS) measurements, we have examined how the hydrogen uptake of single-walled carbon nanotubes (SWNTs) is influenced by the addition of Pt nanoparticles. The conductivity of platinum-sputtered single-walled carbon nanotubes (Pt-SWNTs) during molecular hydrogen exposure decreased more rapidly than that of the corresponding pure SWNTs, which supports a hydrogenation mechanism facilitated by "spillover" of dissociated hydrogen from the Pt nanoparticles. C 1s XPS spectra indicate that the Pt-SWNTs store hydrogen by means of chemisorption, that is, covalent C-H bond formation: molecular hydrogen charging at elevated pressure (8.27 bar) and room temperature yielded Pt-SWNTs with up to 16 ± 1.5 at. % sp(3)-hybridized carbon atoms, which corresponds to a hydrogen-storage capacity of 1.2 wt % (excluding the weight of Pt nanoparticles). Pt-SWNTs prepared by the Langmuir-Blodgett (LB) technique exhibited the highest Pt/SWNT ratio and also the best hydrogen uptake.     

Increased fraction of low-density structures in aqueous solutions of fluoride

X-ray absorption spectroscopy (XAS) and small angle x-ray scattering (SAXS) were utilized to study the effect of fluoride (F(-)) anion in aqueous solutions. XAS spectra show that F(-) increases the number of strong H-bonds, likely between F(-) and water in the first hydration shell. SAXS data show a low-Q scattering intensity increase similar to the effect of a temperature decrease, suggesting an enhanced anomalous scattering behavior in F(-) solutions. Quantitative analysis revealed that fluoride solutions have larger correlation lengths than chloride solutions with the same cations but shorter compared to pure water. This is interpreted as an increased fraction of tetrahedral low-density structures in the solutions due to the presence of the F(-) ions, which act as nucleation centers replacing water in the H-bonding network and forming stronger H-bonds, but the presence of the cations restricts the extension of strong H-bonds.     

Fulleropyrrolidine end-capped molecular wires for molecular electronics--synthesis, spectroscopic, electrochemical, and theoretical characterization

In continuation of previous studies showing promising metal-molecule contact properties a variety of C(60) end-capped "molecular wires" for molecular electronics were prepared by variants of the Prato 1,3-dipolar cycloaddition reaction. Either benzene or fluorene was chosen as the central wire, and synthetic protocols for derivatives terminated with one or two fullero[c]pyrrolidine "electrode anchoring" groups were developed. An aryl-substituted aziridine could in some cases be employed directly as the azomethine ylide precursor for the Prato reaction without the need of having an electron-withdrawing ester group present. The effect of extending the π-system of the central wire from 1,4-phenylenediamine to 2,7-fluorenediamine was investigated by absorption, fluorescence, and electrochemical methods. The central wire and the C(60) end-groups were found not to electronically communicate in the ground state. However, the fluorescence of C(60) was quenched by charge transfer from the wire to C(60). Quantum chemical calculations predict and explain the collapse of coherent electronic transmission through one of the fulleropyrrolidine-terminated molecular wires.     

Understanding thermodynamic properties at the molecular level: multiple temperature charge density study of ribitol and xylitol

X-ray diffraction data of high quality measured to high resolution on crystals of the two pentitol epimers ribitol (centric) and xylitol (acentric) at 101, 141, and 181 K and data on the two compounds previously recorded at 122 K have formed the basis for multipole refinements with the VALRAY system. Our analysis showed that it is possible to obtain a reliable crystal electron density for an acentric compound (xylitol) from X-ray diffraction data and that the thermal motion can be deconvoluted from the static density in this temperature range. The Bader-type topological analysis of the static electron densities revealed virtually identical intramolecular interactions as well as very similar hydrogen bond interactions of ribitol and xylitol; the only minor differences are found in the weaker intermolecular interactions. The high-level periodic DFT calculations are in accordance with the thermodynamic measurements that show that the two pentitols have identical sublimation energies. A rigid body normal coordinate analysis was performed on the atomic displacement parameters obtained at the four different temperatures. The translational and librational mean square deviations derived through this analysis were used in a quantum statistical approach to derive frequencies of the corresponding harmonic oscillators. The analysis showed a consistent vibrational model for all temperatures. The frequencies were subsequently used to calculate crystal entropies assuming an Einstein-type behavior. These calculations show that the crystal entropy of ribitol is 8 J K(-1) mol(-1) higher than the crystal entropy of xylitol, confirming that it is a difference in the entropy of the two compounds that causes the difference in their free energy. Our results presented in this Article show the potential to use X-ray diffraction data to obtain physicochemical properties of crystals.     

A novel catalyst of WO2 nanorod for the counter electrode of dye-sensitized solar cells

Tungsten dioxide (WO(2)) nanorods were synthesized, which showed excellent catalytic activity for the reduction of triiodide to iodide. The dye-sensitized solar cell (DSC) using WO(2) as a counter electrode (CE) reached a high energy conversion efficiency of 7.25%, which can match the performance of the DSC based on a Pt CE.