New strapped porphyrins as hosts for fullerenes: synthesis and complexation study

New strapped porphyrin-based hosts with different π-conjugated moieties and linkers have been prepared and their ability to bind with fullerenes was studied in dilute solution. We found that the ability of these hosts to bind with fullerenes strongly depends on their chemical nature and more precisely on the substitution pattern of the porphyrin deck. As expected, the more electron-rich hosts containing either an exTTF or a porphyrin unit as the strap bind fullerenes more efficiently with association constants of up to 3.9 × 10(5) M(-1). The results clearly demonstrate the potential of such hosts as a supramolecular scaffold for surface immobilization of pristine fullerenes.     

The photodissociation of NO(2) by visible and ultraviolet light

We present velocity map images of the NO, O((3)P(J)) and O((1)S(0)) photofragments from NO(2) excited in the range 7.6 to 9.0 eV. The molecule was initially pumped with a visible photon between 2.82-2.95 eV (440-420 nm), below the first dissociation threshold. A second ultraviolet laser with photon energies between 4.77 and 6.05 eV (260-205 nm) was used to pump high-lying excited states of neutral NO(2) and/or probe neutral photoproducts. Analysis of the kinetic energy release spectra revealed that the NO photofragments were predominantly formed in their ground electronic state with little kinetic energy. The O((3)P(J)) and O((1)S(0)) kinetic energy distributions were also dominated by kinetically 'cold' fragments. We discuss the possible excitation schemes and conclude that the unstable photoexcited states probed in the experiment were Rydberg states coupled to dissociative valence states. We compare our results with recent time-resolved studies using similar excitation and probe photon energies.     

New bis(aryloxy)-Ti(iv) complexes and their use for the selective dimerization of ethylene to 1-butene

New titanium complexes of general formula [(ArO)(n)Ti(Oi-Pr)((4-n))] were synthesized and used as pre-catalysts for the selective dimerization of ethylene to 1-butene. The complexes were prepared in cyclohexane using [Ti(Oi-Pr)(4)] and one or two equivalents of the corresponding phenols (ArOH) at room temperature. In this work, both monodentate and chelating phenols were evaluated. For alkyl-substituted phenols, it was demonstrated that large steric hindrance at both ortho and ortho' positions selectively yielded the mono-substituted complexes [(ArO)Ti(Oi-Pr)(3)]. Substitution at only one of the ortho positions allowed both the mono- and the di-substituted Ti complexes to be isolated. When a heteroatom was introduced on the phenol backbone, di-substitution systematically occurred except with phenols presenting a hemilabile -CH(2)NR(2) group at the ortho position. Upon activation with 3 equiv. of AlEt(3) at 20 bar and 60 °C, all the complexes selectively dimerized ethylene to 1-butene (>86% of butenes among which 99% of 1-butene). An increase of the steric bulk at the ortho position of the ligand or the introduction of a functional group led to decreased activity compared to [Ti(Oi-Pr)(4)].     

Algebraic leaves of algebraic foliations over number fields

Summary — We prove an algebraicity criterion for leaves of algebraic foliations defined over number fields. Namely, consider a number field K embedded in C, a smooth algebraic variety X over K, equipped with a K-rational point P, and F an algebraic subbundle of the its tangent bundle T_X, defined over K. Assume moreover that the vector bundle F is involutive, i.e., closed unter Lie bracket. Then it defines an holomorphic foliation of the analytic mainfold X(C), and one may consider its leaf ℱ through P. We prove that ℱ is algebraic if the following local conditions are satisfied: i) For almost every prime ideal p of the ring of integers 𝒪_K of the number field K, the p-curvature of the reduction modulo p of the involutive bundle F vanishes at P (where p denotes the characteristic of the residue field 𝒪_K / p ). ii) The analytic manifold ℱ satisfies the Liouville property; this arises, in particular, if ℱ is the image by some holomorphic map of the complement in a complex algebraic variety of a closed analytic subset. This algebraicity criterion unifies and extends various results of D. V. and G. V. Chudnovsky, André, and Graftieaux, and also admits new consequences. For instance, applied to an algebraic group G over K, it shows that a K-Lie subalgebra h of Lie G is algebraic if and only if for almost every non-zero prime ideal p of 𝒪_K , of residue characteristic p, the reduction modulo p of h is a restricted Lie subalgebra of the reduction modulo p of Lie G (i.e., is stable under p-th powers). This solves a conjecture of Ekedahl and Shepherd-Barron. The algebraicity criterion above follows from a more basic algebraicity criterion concerning smooth formal germs in algebraic varieties over number fields. The proof of the latter relies on “transcendence techniques”, recast in a modern geometric version involving elementary concepts of Arakelov geometry, and on some analytic estimates, related to the First Main Theorem of higher-dimensional Nevanlinna theory.

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Résumé — Nous établissons un critère d'algébricité concernant les feuilles des feuilletages algébriques définis sur un corps de nombres. Soit en effet K un corps de nombres plongé dans C, X une variété algébrique lisse sur K, munie d'un point K-rationnel P, et F un sous-fibré du fibré tangent T_X, défini sur K. Supposons de plus que le fibré vectoriel F soit involutif, i.e.., stable par crochet de Lie. Il définit alors un feuilletage holomorphe de la variété analytique X(C) et l'on peut considérer la feuille ℱ de ce feuilletage passant par P. Nous montrons que ℱ est algébrique lorque les conditions locales suivantes son satisfaites: i) Pour presque tout idéal premier p de l'annneau des entiers 𝒪_K de K, la réduction modulo p du fibré F est stablé par l'opération de puissance p-ième (où p désigne la caractéristique du corps résiduel 𝒪_K / p ). ii) La variété analytique ℱ satisfait à la propriété de Liouville; cela a lieu, par exemple, lorsque ℱ est l'image par une application holomorphe du complémentaire d'un sous-ensemble analytique fermé dans une variété algébrique. Ce critère d'algébricité unifie et généralise divers résultats de D. V. and G. V. Chudnovsky, André et Graftieaux. Il conduit aussi à de nouvelles conséquences. Par exemple, appliqué à un groupe algébrique G sur K, il montre qu'une sous-algèbre de Lie h de Lie G, définie sur K, est algébrique si et seulement si, pour presque tout idéal premier p de 𝒪_K , de caractéristique résiduelle p, la réduction modulo p de h est une sous-p-algèbre de Lie de la réduction modulo p de Lie G (i.e., est stable par puissance p-ième). Cet énoncé résout une conjecture d'Ekedahl et Shepherd-Barron. Le critère d'algébricité ci-dessus découle d'un critère d'algébricité plus général, concernant les germes de sous-variétés formelles des variétés sur les corps de nombres. La démonstration de ce dernier repose sur des “techniques de transcendance”, reformulées dans une version géométrique utilisant diverses notions élémentaires de géométrie d'Arakelov, et sur des estimations analytiques reliées au premier théorème fondamental de la théorie de Nevanlinna en dimension supérieure.

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Manucsrit re?u le 27 septembre 2000.