Dynamic chemical devices: modulation of photophysical properties by reversible, ion-triggered, and proton-fuelled nanomechanical shape-flipping molecular motions

The terpy-derived (terpy=terpyridine) ligand 1 has an extended W shape in which the two appended photoactive pyrenyl groups are held apart. On binding of a zinc(II) ion with a terpy group, ligand 1 is converted into complex 2 whereby it adopts a U shape, thus stacking the aromatic units. This structural modification leads to a very pronounced change in photophysical properties: from a highly fluorescent free ligand to a very weakly emitting complex. The W/U structural switching can be reversibly induced by the addition of a competitive tren ligand, which binds and releases a zinc(II) ion under protonation/deprotonation cycles, thus leading to oscillations in light emission. Therefore, the present system performs periodic modulation of optical output through a nanomechanical shape-flipping motion, triggered by metal ion binding and fuelled by acid-base neutralisation energy. Overall, it represents an ion-triggered opto-mechanical supramolecular device.     

Protonic modulation of redox properties in ionisable [2 x 2] grid-like metalloarrays

The oxidation state of the cobalt centres can be controlled by modification of the protonation state in [2 x 2] grid-like arrays based on ionisable bis(hydrazone) ligands, allowing conversion of the paramagnetic Co(II)(4) into the diamagnetic Co(III)(4) grid.     

Solid state and solution 43Ca NMR of calcium peroxides involved in the disproportionation of hydrogen peroxide by calcium hydroxide

In order to get some insight into the mechanism of the disproportionation of hydrogen peroxide catalyzed by calcium hydroxide, 43Ca NMR spectra of enriched samples of calcium peroxides and of their precursors have been studied in both solution and solid state. This study demonstrates that no well-defined peroxidized calcium species are formed in solution, showing that the catalytic role of calcium is likely restricted to the solid state. Most of the calcium compounds that could be involved in the catalytic process have been investigated with solid state NMR. The shift and quadrupolar parameters of Ca(OH)2, CaO2.8H2O and CaO2.2H2O2 are reported for the first time. These parameters are different enough to allow the quantitative analysis of a complex mixture of these compounds by NMR.     

Re-based heterogeneous catalysts for olefin metathesis prepared by surface organometallic chemistry: reactivity and selectivity

Herein we describe the catalytic activity of 1, a well-defined Re alkylidene complex supported silica, in the reaction of olefin metathesis. This system is highly active for terminal and internal olefins with initial rates up to 0.7 mol per mol Re per s. It also catalyses the self-metathesis of methyl oleate (MO) without the need of co-catalysts. The turnover numbers can reach up to 900 for MO, which is unprecedented for a heterogeneous Re-based catalyst. Moreover the use of silica as a support can bring major advantages, such as the possibility to use branched olefins like isobutene, which are usually incompatible with alumina-based supports; therefore, the formation of isoamylene from the cross-metathesis of propene and isobutene can be performed. All these results are in sharp contrast to what has been found for other silica- or alumina-supported rhenium oxide systems, which are either completely inactive (silica system) or typically need co-catalysts when functionalised olefins are used. Finally the initiation step corresponds to a cross-metathesis reaction to give a 3:1 mixture of 3,3-dimethylbutene and trans-4,4-dimethylpent-2-ene, and make this catalyst the first generation of well-defined Re-based heterogeneous catalysts.     

Differential equations over polynomially bounded o-minimal structures

We investigate the asymptotic behavior at of non-oscillatory solutions to differential equations a$">, where is definable in a polynomially bounded o-minimal structure. In particular, we show that the Pfaffian closure of a polynomially bounded o-minimal structure on the real field is levelled.

     

À propos de l’indice de composition des nombres

 We define the index of composition λ(n) of an integer n ⩾ 2 as λ(n) = log n/log γ(n), where γ(n) stands for the product of the primes dividing n, and first establish that λ and 1/λ both have asymptotic mean value 1. We then establish that, given any ɛ > 0 and any integer k ⩾ 2, there exist infinitely many positive integers n such that . Considering the distribution function F(z,x) := #{n < x : λ(n) > z}, we prove that, given 1 < z < 2 and ɛ > 0, then, if x is sufficiently large,

Azido-, hydroxo-, and oxo-bridged copper(II) dimers: spin population analysis within broken-symmetry, density functional methods

Within the general context of homometallic spin-coupled Cu(II) dimers, we propose to relate the antiferromagnetic part of the exchange coupling constant, J _AF, to the quantity ΔP ²(Cu), the difference of copper squared spin populations as calculated for the high-spin (i.e. triplet) and broken-symmetry spin states, through J _AF≈−UΔP ²(Cu), where U is interpreted as the covalent–ionic term. This proportionality is illustrated for three “bare” Cu(II) dimers (i.e. without peripheral ligation, so as to enhance the antiferromagnetic contribution) bridged by azido, hydroxo, or oxo groups. This provides an alternative quantifier of the exchange phenomenon to that usually used, i.e. Δ², the square of the singly occupied molecular orbital splitting in the triplet state. Moreover, and quite interestingly, the quantity ΔP ²(Cu) can become negative (i.e. induce ferromagnetism) without apparently affecting the proportionality relation. Received: 17 September 1999 / Accepted: 9 March 2000 / Published online: 21 June 2000     

Radiative decay ofJ/ψ into γ π+ π−

The radiative decayJ/ψ → γ π⁺ π^? has been studied using the 8.6 millionJ/ψ produced in the DM2 experiment at the DCIe ⁺e^? storage rings at Orsay. The π⁺ π^? mass spectrum shows a cleanf ₂ (1270) signal, and the possible presence of two other states at thef ₂ (1720) andf ₄ (2030) masses. For thef ₂ (1270), the branching ratio BR(J/ψ →γf)xBR(f→π⁺ π^?) is measured to be (7.50±0.30±1.12)×10^?4, and the spin analysis prefers theJ=2 assignment, with helicity parametersx=0.83±0.06 andy=0.01±0.06. The existence of higher mass states is discussed.     

Volume approximation of smooth convex bodies by three-polytopes of restricted number of edges

For a given convex body K in \Bbb R³{\Bbb R}^3 with C ² boundary, let P ^c _n be the circumscribed polytope of minimal volume with at most n edges, and let P ⁱ _n be the inscribed polytope of maximal volume with at most n edges. Besides presenting an asymptotic formula for the volume difference as n tends to infinity in both cases, we prove that the typical faces of P ^c _n and P ⁱ _n are asymptotically regular triangles and squares, respectively, in a suitable sense.