The Arnoux–Yoccoz Teichmüller disc

We prove that the Teichmüller disc stabilized by the Arnoux-Yoccoz pseudo-Anosov diffeomorphism contains at least two closed Teichmüller geodesics. This proves that the corresponding flat surface does not have a cyclic Veech group. In addition, we prove that this Teichmüller disc is dense inside the hyperelliptic locus of the connected component (2,2) . The proof uses Ratner’s theorems. Rephrasing our results in terms of quadratic differentials, we show that there exists a holomorphic quadratic differential, on a genus 2 surface, with the two following properties:

Catalyzed Methanolysis of Five Membered Ring Phosphoenolates

Abstract

Alkyl cyclic enediolphosphates, 1, have been widely investigated to probe nucleophilic catalysis in the phosphorylation of alcohols. Hexacoordinated species have been supposed to participate into the process¹. The same type of intermediates has been recently considered in the solvolysis of halogenophosphorus derivatives, activated by nucleophiles².     

Triisopropoxysilyl-functionalized oxide nanoparticles using a di-tert-butyl phosphonate ester as the surface grafting agent

The synthesis of a bifunctional coupling reagent possessing a triisopropoxysilyl group and a tert-butyl phosphonate ester is described. The tert-butyl phosphonate ester was used as an efficient and selective grafting reagent for the anchoring of the triisopropoxysilyl group at the surface of TiO₂ and SnO₂ nanoparticles under mild conditions. The triisopropoxysilyl group remained intact and did not react at the surface of the oxide nanoparticles. The reactivity of the triisopropoxysilyl group was then further investigated.     

Intramolecular nitrogen ligand stabilization of phenyl-imidazolidine derived silicon species

The synthesis of some new functional aminoarylsilanes with the aromatic ring substituted in the ortho-position by a 2-(1,3-dimethyl)imidazolidine ligand is presented. The donating properties of the imidazolidine fragment, in which the two coordinating nitrogen atoms are located on the same side of the silicon center induce a specific chemical behavior of the organosilicon species. Thus, only one Si–H bond of ArSiH₃ was found to react with an excess of organic acids and heterocumulenes. NMR studies showed that, if in imidazolidinylphenyldihydrosilanes containing a strong electronegative substituent, the silicon center is pentacoordinated by forming one additional N→Si bond, only a small activation energy is sufficient to exchange the two donating nitrogen atoms. The reason for this easy exchange is probably the small distance between the two donor centers and the rigidity caused by the bridging ethylene unit.     

Kinetics of solvolysis reactions of pentaarylantimony compounds in 2-octanol

Tetraphenyl-p-tolylantimony, m-chlorophenyltetraphenylantimony and p-methoxyphenyltetraphenylantimony have been prepared and subjected to solvolysis in 2-octanol at temperatures ranging from 50–65°. First order rate constants have been determined, and a plot of log k X 10⁵ vs. σ has been found to be linear, with p = 1.12. The value for the specific rate constant of the pentaphenylantimony reaction cannot be measured directly owing to solubility problems, but it can be calculated by use of the Hammett equation. Analysis of the rate data by the method of parallel first-order reactions gives results which are in agreement with experimental data for the reaction period extending from the time at which a homogeneous solution is formed to the end of the reaction. Partial rate factors for formation of benzene and the substituted benzene have been calculated for each reaction, and these data plus the activation parameters have been used as the basis for suggested mechanisms of the solvolysis reactions. Preliminary studies have also been carried out on the effects of 2-octanoxide anion on the solvolysis reactions. In the case of the p-methoxyphenyltetraphenylantimony reaction, second order kinetics were observed (first order with respect to the pentaarylantimony compound and first order with respect to the 2-octanoxide anion). Although precise rates could not be obtained for the reactions of the other pentaarylantimony compounds with sodium 2-octanoxide, qualitative evidence indicated that the anion exerts a major influence in each case.     

Analogies between silicon and phosphorus stereochemistry—I : Influence of the leaving group on the stereochemistry of nucleophilic displacement at phosphorus

Stereochemistry of cyclic halogenophosphates has been studied by adding aryloxides, in THF. All extra parameters being equal, the fluoro substituent which is of the more electronegative (and the more apicophilic) is displaced with the more predominant retention F>Cl≈Br. Such behaviour cannot be explained with the usual concepts of phosphorus stereochemistry and, in particular, the generally accepted view of apical attack giving the more stable P^V intermediate. By contrast, strong analogies with the stereochemistry observed at silicon are clearly evidenced. Like for silicon compounds, front-side attack could explain predominant retention, particularly in P-F bond cleavage. Trigonal bipyramidal intermediates with the entering group in equatorial position and the leaving group in apical position, or square-pyramidal geometries may be envisaged.     

Silicon-phosphorus analogies : Participation of external nucleophiles to activated processes of racemization and hydrolysis of chlorophosphono derivatives

Kinetic and stereochemical studies show nucleophilic assistance by dimethylformamide (DMF), dimethylacetainide (DMA), hexamethylphosphotriamide (HMPT) and N-methylimidazole (NMI) in racemization and solvolysis of menthylchloro(phenyl)phosphonate, 1a, and O-ethylchloro(phenyl)thiophosphonate, 2. Similar orders of nucleophilic reactivity (Nu = NMI?HMPT>DMF>DMA), and identical rate-laws (v_rac=k [M-Cl] [Nu]² and v_H2O = k' [M-Cl] [H₂O] [Nu]) are consistent with a common mechanism, governed by entropy (?60 u.e< ΔS^≠<?40u.e). Analogies between reaction mechanisms at silicon and phosphorus are clearly evidenced. A two-step process, involving rate-determining attack on a pentacoordinate complex is discussed.