New Rare‐Earth Metal Germanides RE2Ge9 (RE = Nd,Sm) by Thermal Decomposition of High‐Pressure Phases REGe5

The rare‐earth metal germanides RE₂Ge₉ (RE = Nd, Sm) have been prepared by thermal decomposition of the metastable high‐pressure phases REGe₅ at ambient pressure. The compounds adopt an orthorhombic unit cell with a = 396.34(4) pm; b = 954.05(8) pm and c = 1238.4(1) pm for Nd₂Ge₉ and a = 395.46(7) pm; b = 946.4(2) pm and c = 1232.1(3) pm for Sm₂Ge₉. Crystal structure refinements reveal space group Pmmn (No. 59) for Nd₂Ge₉. The atomic pattern resembles an ordered defect variety of the pentagermanide motif REGe₅ (RE = La; Nd, Sm, Gd, Tb) comprising corrugated germanium layers. These condense into a three‐dimensional network interconnected by eight‐coordinated germanium atoms. The resulting framework channels along [100] enclose the neodymium atoms. With respect to the atomic arrangement of the pentagermanides, half of the interlayer germanium atoms are eliminated in an ordered way so that occupied and empty germanium columns alternate along [001]. The rare‐earth metal atoms of both types of compounds, REGe₅ and RE₂Ge₉, exhibit the electronic states 4f ³ and 4f ⁵ (oxidation state +3) for neodymium and samarium, respectively, evidencing that the modification of the germanium network leaves the electron configuration of the metal atoms unaffected.     

Nature of C60 and C70 fullerene encapsulation in a porphyrin- and metalloporphyrin-based cage: Insights from dispersion-corrected density functional theory calculations

The search for efficient synthetic hosts able to encapsulate fullerenes has attracted attention with regard to the purification and formation of ordered supramolecular architectures. This study of a porphyrin-based cage as an extension of the well-described ExCage⁶⁺ and BlueCage⁶⁺, involving viologen as sidearms, provides an interesting scenario where the oblate C₇₀ fullerene is preferred in comparison to the spherical C₆₀. Our results expose the nature of the fullerene-cage interaction involving ∼50% of dispersion-type interactions evidencing the strong π⋯π surface stacking, with a complementary contribution by the electrostatic and orbital polarization character produced by a charge reorganization with a charge accumulation facing the porphyrin macrocycles and a charge depletion along the equator formed by the viologens sidearms. Interestingly, the central N₄H₂ ring from each porphyrin contributes to the dispersion term via N-H⋯π interactions, which is decreased when the metallate N₄Zn is evaluated. Thus, the formation of stable and selective fullerene encapsulation can be achieved by taking into account two main driving forces, namely, (a) the extension of the π⋯π and X-H⋯π stacking surface and (b) charge reorganization over the fullerene surfaces, which can be used to control fine tuning of the encapsulation thanks to the introduction of more electron-deficient and electron-rich groups within the host cage.     

Frustration driven stock market dynamics: Leverage effect and asymmetry

By applying inverse statistics to financial data it has recently been found from empirical studies that indices exhibit a pronounced gain-loss asymmetry [M.H. Jensen, Phys. Rev. Lett. 83 (1999) 76; I. Simonsen, M.H. Jensen, A. Johansen, Eur. Phys. J. B 27 (2002) 583; M.H. Jensen, A. Johansen, I. Simonsen, Physica A 324 (2003) 338]. This gain-loss asymmetry appears to have some similarities with the stylized fact leverage effect and we investigate if they could be of same origin. For this purpose we introduce the Frustration Governed Market model which includes correlations in time between a model index and its individual stocks. It is shown that the model reproduces very well the empirical findings with respect to gain-loss asymmetry and leverage. In special cases, however, the model may produce leverage without a pronounced gain-loss asymmetry.     

Theoretical approach to cationic polymerization of alkenylfurans. II. Ab initio and semiempirical study of relevant steps in the reaction mechanism

SCF ab initio and AM1 semiempirical calculations with full geometry optimization have been carried out to model the initial steps of alkenylfuran cationic polymerization. Semiempirical procedures have been used to model propagation steps. Proton affinities of the relevant neutral species as well as the heats of formation of probable dimers were calculated. The results allow the explanation of the experimental behavior. The capabilities of the employed methods to describe these type of processes is discussed. It is confirmed that competition between vinyl and ring site attacks is the most important feature in these systems. © 1992 John Wiley & Sons, Inc.     

Sur la compatibilité des extensions ponctuelles d'un matroïde

A natural sufficient condition for a finite family of single element extensions of a matroid to be compatible is given. Characterizations of all the finite extensions N of a matroid M(E) are given for which the rank function satisfies

$\text{ρ}{}_{\mathrm{N}}\text{(X)=}\text{Min}\text{Z?E}\text{{ρ}{}_{\mathrm{M}}\text{(Z)+|X?}\text{Z}{}^{\mathrm{N}}\text{|}}$

or equivalently the closure operator satisfies $\text{X}{}^{\mathrm{N}}\text{=}\text{X}{}^{\mathrm{N}}\text{? E}{}^{\mathrm{N}}\text{? X}$. The single element extensions and the principal extensions are examples of such matroids. The notion of a sheaf of flats of M. Las Vergnas is used in the proof of a new necessary and sufficient condition for two single element extensions of a matroid to be compatible. An initial announcement of part of these results appeared in R. Cordovil (C. R. Acad. Sci. Paris. A284 (1977), 1249–1252).     

Kinetic study of the reaction between hydroxylated polybutadienes and isocyanates. 1. Reaction with tolylene diisocyanate (TDI)

A comparative kinetic study of the reaction of three different hydroxylated liquid polybutadienes (M _n ? 3000) — R - 45M, R-45HT, and H-034—and tolylene diisocyanate (TDI), was carried out in toluene solution. An analytical method was used to follow the kinetics of the reactions at four different temperatures. The reactions presented an apparent second-order rate law. In the second-order plots, a discontinuity was observed. The R-45M polybutadiene was about twice more reactive than R-45HT and H-034; these latter two polybutadienes presented similar reactivities.     

3-Aryl-4-Isoquinolinone Derivatives An Efficient Oxidative Preparation

A comparative study of the oxidation of 3-aryl-4-hydroxytetrahydroisoquinolines has been carried out. A modification of the Jones conditions turn out to be the best methodology for the regioselective preparation of target 4-isoquinolinone derivatives.