Complexity index for the linear mechanisms of chemical reactions

A complexity measure is proposed for the kinetic models of chemical reactions with linear mechanisms. The index is related to the structure of fractional-rational kinetic laws for chemical reactions, as well as to the structure of cyclic graphs used to describe them. The complexity index is shown to be closely related to the detailed hierarchical classification and to the code of linear reaction mechanisms, recently introduced. A number of index properties are proved for two- and three-reaction routes. They reflect the influence of the various classification criteria, such as the number of reaction routes and intermediates, the type, class and subclasses of the mechanism, and the number of intermediates in each reaction route. Hierarchical levels of mechanisms with the same complexity (isocomplex mechanisms) are specified. Standard tables are presented with complexity indices for all topologically distinct linear reaction mechanisms having one to three reaction routes, two to six intermediates, and reversible elementary steps.[/p]     

Measurement of the absolute cross section of the 3He(4He, γ)7Be reaction at Ec.m. = 525 keV

The cross section for the radiative capture reaction ³He(⁴He, γ)⁷Be has been measured at 525 keV in the centre-of-mass by detection of prompt capture γ- rays. The targets were ³He-implanted Nb foils that allowed us to circumvent the experimental difficulties inherent in the use of extended gas cells for absolute measurements. The results give an inferred zero-energy cross-section factor of S₃₄(0) = 0.47 ± 0.04 keV · b. The present result is compared with results from previous capture γ-ray yield and ⁷Be-activity methods of measuring the cross-section factor.     

A weak Grothendieck compactness principle for Banach spaces with a symmetric basis

The Grothendieck compactness principle states that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. In Dowling et al. (J Funct Anal 263(5):1378–1381, 2012), an analogue of the Grothendieck compactness principle for the weak topology was used to characterize Banach spaces with the Schur property. Using a different analogue of the Grothendieck compactness principle for the weak topology, a characterization of the Banach spaces with a symmetric basis that are not isomorphic to $\ell ^1$ and do not contain a subspace isomorphic to $c_0$ is given. As a corollary, it is shown that, in the Lorentz space $d(w,1)$ , every weakly compact set is contained in the closed convex hull of the rearrangement invariant hull of a norm null sequence.     

Chloropolyfluorodiethyl ethers

Fluorination of 2-chlorodiethyl ether by cobalt trifluoride at 110–150 °C afforded isomers of 2-chloro-pentafluoro-, -hexafluoro-, and -heptafluorodiethyl ethers. Chlorine was lost in similar fluorinations of 2-chloro-2,2-difluoroethyl ethyl ether, the only products isolated being a heptaand a hexa-fluoro diethyl ether. Structures were established spectroscopically.     

Co desorption and adsorption on Pt(111)

The kinetics of the desorption of CO from a Pt(111) crystal between 419 and 505 K is reported using a Low-Energy Molecular-Beam-Scattering (LEMS) technique with a helium probe beam and a CO dosing beam. The resulting first-order Arrhenius rate constant is $\text{k = 2.7 × 10}{}^{13}\text{exp(?31.1}\text{kcal}\text{mole}\text{· RT) s}{}^{\mathrm{?1}}$. We also report a study of the equilibriumadsorbed CO between 400 and 600 K using LEMS. These results, fitted to a Temkin isotherm model, indicate that the adsorption energy decreases linearly with surface coverage with the average value equal to $\text{31.1 + 1.2}\text{kcal}\text{mole}$ over the coverage range 0 < θ ? 0.5. The average harmonic oscillator frequency of the adsorbed CO molecules is 191 ± 76 cm^?1.     

Quantification of the Magnetic Anisotropy of a Single-Molecule Magnet from the Experimental Electron Density

Reported here is an entirely new application of experimental electron density (EED) in the study of magnetic anisotropy of single-molecule magnets (SMMs). Among those SMMs based on one single transition metal, tetrahedral Co^II-complexes are prominent, and their large zero-field splitting arises exclusively from coupling between the d and d_xy orbitals. Using very low temperature single-crystal synchrotron X-ray diffraction data, an accurate electron density (ED) was obtained for a prototypical SMM, and the experimental d-orbital populations were used to quantify the d_xy-d coupling, which simultaneously provides the composition of the ground-state Kramers doublet wave function. Based on this experimentally determined wave function, an energy barrier for magnetic relaxation in the range 193–268 cm⁻¹ was calculated, and is in full accordance with the previously published value of 230 cm⁻¹ obtained from near-infrared spectroscopy. These results provide the first clear and direct link between ED and molecular magnetic properties.