On the cube problem of Las Vergnas

We prove a conjecture of Las Vergnas in dimensions d7: The matroid of the d-dimensional cube C ^d has a unique reorientation class. This extends a result of Las Vergnas, Roudneff and Salaün in dimension 4. Moreover, we determine the automorphism group G ^d of the matroid of the d-cube C ^d for arbitrary dimension d, and we discuss its relation to the Coxeter group of C ^d . We introduce matroid facets of the matroid of the d-cube in order to evaluate the order of G ^d . These matroid facets turn out to be arbitrary pairs of parallel subfacets of the cube. We show that the Euclidean automorphism group W ^d is a proper subgroup of the group G ^d of all matroid symmetries of the d-cube by describing genuine matroid symmetries for each Euclidean facet. A main theorem asserts that any one of these matroid symmetries together with the Euclidean Coxeter symmetries generate the full automorphism group G ^d . For the proof of Las Vergnas' conjecture we use essentially these symmetry results together with the fact that the reorientation class of an oriented matroid is determined by the labeled lower rank contractions of the oriented matroid. We also describe the Folkman-Lawrence representation of the vertex figure of the d-cube and a contraction of it. Finally, we apply our method of proof to show a result of Las Vergnas, Roudneff, and Salaün that the matroid of the 24-cell has a unique reorientation class, too.     

Synthesis of new tren-based tris-macrocycles. Anion cluster assembling inside the cavity generated by a bowl-shaped receptor

The synthesis of three new tris-macrocycles, containing three [12]aneN(4) (L1), [12]aneN(3)O (L2), or [14]aneN(4) (L3) moieties appended to a tren unit, is reported. The crystal structure of the [(Na(ClO(4))(6)) subset L1(2)H(13)]Na(6)Cl(2)(ClO(4))(12) compound shows the anionic cluster [Na(ClO(4))(6)](5)(-) assembled inside the cavity defined by two bowl-shaped polyammonium receptors, held by multiple charge-charge and hydrogen bond interactions.     

The deprotonation of benzyl alcohol radical cations: a mechanistic dichotomy in the gas phase as in solution

The gas-phase acidity of ionized benzyl alcohol and of some of its derivatives with selected reference bases has been studied by Fourier Transform Ion Cyclotron Resonance (FT-ICR) mass spectrometry. The aim was to relate the gas-phase reactivity to the behavior in aqueous solution of the radical cations of benzyl alcohols bearing methoxy substituent(s) on the phenyl ring which are known to undergo deprotonation at both the CH2 and OH groups. The dual reactivity behavior is confirmed in the gas phase, in which the prototypical ion, C6H5CH2OH*+, is deprotonated at both the CH2 and OH groups, whereas the ring hydrogens are not involved. An increasing extent of O-deprotonation is shown as the strength of the base increases. Appropriate methyl substitution, as in the radical cations of C6H5C(Me)2OH and C6H5CH2OMe, allows only O- or C-acidity. The two processes are characterized by comparable thermodynamic features with a Gas-phase Basicity (GB) value of 852 kJ mol(-1) for the cumyloxyl radical and 850 kJ mol(-1) for the alpha-methoxybenzyl radical. The possible origin of the observed mechanistic dichotomy is discussed.     

Anilinepropylsilica xerogel used as a selective Cu (II) adsorbent in aqueous solution

The metal ion adsorption properties of the microporous hybrid anilinepropylsilica xerogel were studied using divalent copper, zinc, and cadmium ions in aqueous solutions in concentrations ranging from 10(-4) up to 5x10(-3) moll(-1). At low concentrations the surface of the solid phase presents selectivity for Cu (II), even in competitive conditions. This preferential sorption ability for copper in relation to zinc and cadmium ions was interpreted by considering the xerogel morphology.     

Synthesis, structure and properties of N-acetylated derivatives of methyl 5-amino-1H-[1,2,4]triazole-3-carboxylate

Methyl 5-amino-1H-[1,2,4]triazole-3-carboxylate hydrochloride (1). and free ester (2). were obtained and 2 was reacted with Ac(2)O to give the acetylated products 3-6. Compounds 1-6 were studied using HPLC, GC-MS, FTIR and multinuclear NMR spectroscopy, including the cross-polarisation magic angle spinning (CPMAS) technique. The results of the acetylation of 2 were compared to those of the acetylation of 5-amino-1H-[1,2,4]triazole, and for 2 a significant decrease in the susceptibility to acetylation was found. The reaction of 2 with Ac(2)O at 20 degrees C, regardless of the amount and the concentration of the latter, including neat Ac(2)O, proceeds fully regioselectively and leads to one product: methyl 1-acetyl-5-amino-1H-[1,2,4]triazole-3-carboxylate (3). In sharp contrast to 5-amino-1H-[1,2,4]triazole, neither an additional monoacetylated isomer, whether annular or exocyclic, nor any diacetylated derivative could be detected. The diacetylation of 2 requires the process to be carried out in neat boiling Ac(2)O and, as in the case of 5-amino-1H-[1,2,4]triazole, gives two diacetylated isomers. These are methyl 1-acetyl-3-(acetylamino)-1H-[1,2,4]triazole-5-carboxylate (4) and 1-acetyl-5-(acetylamino)-1H-[1,2,4]triazole-3-carboxylate (5). Hypothetical pathways of their formation have been suggested. A mixture of 4 and 5 upon hydrolysis of the ring acetyl group gives the monoacetylated derivative methyl 5-(acetylamino)-1H-[1,2,4]triazole-3-carboxylate (6). The spectroscopic, structural and conformational characteristics of compounds 1-6 have been given and methods for their preparation have been provided.