Stability and Computation of Topological Invariants of Solids in ${\Bbb R}^n$

In this work one proves that under quite general assumptions one can deduce the topology of a bounded open set in from an approximation of it. For this, one introduces the weak feature size (wfs) that extends for nonsmooth objects the notion of local feature size. Our results apply to open sets with positive wfs. This class includes subanalytic open sets which cover many cases encountered in practical applications. The proofs are based upon the study of distance functions to closed sets and their critical points. The notion of critical point is the same as the one used in riemannian geometry [22], [9], [20] and nonsmooth analysis [10]. As an application, one gives a way to compute the homology groups of open sets from noisy samples of points on their boundary.     

Diverse strategies toward indenol and fulvene derivatives: Rh-catalyzed C-H activation of aryl ketones followed by coupling with internal alkynes

The synthesis of indenols and fulvenes was achieved through Rh-catalyzed C-H bond activation of simple and diverse aryl ketone derivatives and subsequent coupling with internal alkynes. The process was found to involve either an α or γ dehydration step, depending on the substrate disposition and representing diverse pathways toward functionalized fulvenes.     

Ergodic actions of mapping class groups on moduli spaces of representations of non-orientable surfaces

Let M be a non-orientable surface with Euler characteristic χ(M) ≤ −2. We consider the moduli space of flat SU(2)-connections, or equivalently the space of conjugacy classes of representations

A large‐volume gas cell for high‐energy X‐ray reflectivity investigations of interfaces under pressure

A cell for the investigation of interfaces under pressure is presented. Given the pressure and temperature specifications of the cell, P≤ 100 bar and 253 K ≤T≤ 323 K, respectively, high‐energy X‐rays are required to penetrate the thick Al₂O₃ windows. The CH₄(gas)/H₂O(liquid) interface has been chosen to test the performance of the new device. The measured dynamic range of the high‐energy X‐ray reflectivity data exceeds 10^?8, thereby demonstrating the validity of the entire experimental set‐up.     

Formation of Tc metal in 12 M HCl using Zn as a reductant

Amorphous TcO₂ and NH₄TcO₄ solubilized into 12 M HCl will spontaneously convert to hexachlorotechnetate (TcCl₆ ^2?). This process is accelerated upon heating but species lower than Tc(IV) are not generated by this action. TcCl₆ ^2? is kinetically unstable with regards to formation in solutions of low concentrations of HCl and will spontaneously convert back to soluble and insoluble forms of Tc(IV) in water. TcCl₆ ^2? in 12 M HCl placed in contact with the reducing metal Zn at elevated temperatures (90 °C) forms a black precipitate that contains amorphous Tc metal, TcO₂, and oxy-chlorides of Tc. Powder X-ray diffraction indicates the presence of Tc metal after thermal treatment where X-ray absorption fine structure spectroscopy indicates the presence of hexagonal Tc metal and amorphous TcO₂ in the precipitate after rinsing with 12 HCl but before thermal treatment. The resulting solution contains a mixture of Tc chlorides and oxy-chlorides following reduction where TcCl₆ ^2? is completely consumed resulting primarily in Tc₂OCl₁₀ ^4? dominating the UV–visible spectra. Reducing the solution volume and reconstituting the products into 12 M HCl while boiling the mixed solution (>24 h) will slowly convert all soluble Tc back to TcCl₆ ^2?. Expanding on previous efforts made in this laboratory to recover Tc metal from aqueous solution, we investigate its synthesis when Tc(IV) and Tc(VII) in 12 M HCl is placed in contact with the reducing metal (i.e., Zn) at elevated temperatures.     

Investigations of acidity and nucleophilicity of diphenyldithiophosphinate ligands using theory and gas-phase dissociation reactions

Diphenyldithiophosphinate (DTP) ligands modified with electron-withdrawing trifluoromethyl (TFM) substitutents are of high interest because they have demonstrated potential for exceptional separation of Am (3+) from lanthanide (3+) cations. Specifically, the bis( ortho-TFM) (L 1 (-)) and ( ortho-TFM)( meta-TFM) (L 2 (-)) derivatives have shown excellent separation selectivity, while the bis( meta-TFM) (L 3 (-)) and unmodified DTP (L u (-)) did not. Factors responsible for selective coordination have been investigated using density functional theory (DFT) calculations in concert with competitive dissociation reactions in the gas phase. To evaluate the role of (DTP + H) acidity, density functional calculations were used to predict p K a values of the free acids (HL n ), which followed the trend of HL 3 < HL 2 < HL 1 < HL u. The order of p K a for the TFM-modified (DTP+H) acids was opposite of what would be expected based on the e (-)-withdrawing effects of the TFM group, suggesting that secondary factors influence the p K a and nucleophilicity. The relative nucleophilicities of the DTP anions were evaluated by forming metal-mixed ligand complexes in a trapped ion mass spectrometer and then fragmenting them using competitive collision induced dissociation. On the basis of these experiments, the unmodified L u (-) anion was the strongest nucleophile. Comparing the TFM derivatives, the bis( ortho-TFM) derivative L 1 (-) was found to be the strongest nucleophile, while the bis( meta-TFM) L 3 (-) was the weakest, a trend consistent with the p K a calculations. DFT modeling of the Na (+) complexes suggested that the elevated cation affinity of the L 1 (-) and L 2 (-) anions was due to donation of electron density from fluorine atoms to the metal center, which was occurring in rotational conformers where the TFM moiety was proximate to the Na (+)-dithiophosphinate group. Competitive dissociation experiments were performed with the dithiophosphinate anions complexed with europium nitrate species; ionic dissociation of these complexes always generated the TFM-modified dithiophosphinate anions as the product ion, showing again that the unmodified L u (-) was the strongest nucleophile. The Eu(III) nitrate complexes also underwent redox elimination of radical ligands; the tendency of the ligands to undergo oxidation and be eliminated as neutral radicals followed the same trend as the nucleophilicities for Na (+), viz. L 3 (-) < L 2 (-) < L 1 (-) < L u (-).     

Detailed characterisation of the flow resistance of commercial sub-2 micrometer reversed-phase columns

The pressure-drop characteristics of six sub-2 microm columns of three different manufacturers but with the same surface chemistry (C(18)) have been studied using the recently introduced total pore blocking method for the determination of the external porosity and by using scanning electron microscopy pictures to measure the actual size of the particles. Having used the Sauter-mean particle size to correctly account for the particle size spread, and having corrected for the influence of the intra-particle porosity, it was found that all columns yielded Kozeny-Carman constant (f(KC)) values close to 180, in agreement with the theory. This agreement could subsequently be used to quantify how the different system parameters such as mean particle size, packing density and intra-particle porosity (all tending to vary significantly from manufacturer to manufacturer) each contributes to the observed total bed permeability. Small (upward) deviations from the f(KC)=180-value could be correlated to a larger width of the particle size distribution, and more notably to the existence of a high size ratio of the largest to the smallest particles present in the particle batches.     

Atom tunneling in organic transformations

There and gone: atoms, such as hydrogen or deuterium, commonly disappear and reappear at different locations in molecular structures. For example, carboxylic acids and hydroxycarbenes isomerize through atom tunneling events. It could happen in your reaction!     

Multi-configurational quantum chemical studies of the Tc2X8(n-) (X = Cl, Br; n = 2, 3) anions. Crystallographic structure of octabromoditechnetate(3-)

The [Cs((2 + x))][H(3)O((1 - x))]Tc(2)Br(8)·4.6H(2)O (x = 0.221) salt has been synthesized and characterized by single crystal XRD. Multi-configurational quantum chemical calculations on Tc(2)X(8)(n-) (X = Cl, Br; n = 2, 3) have been performed and indicate the π component in the Tc-Tc bond to be stronger for n = 3.