Kinetics of gas-phase addition reactions of methyl radicals. I. Addition to ethylene,acetylene, and benzene

The reactions have been studied by a mass-balance method involving the photolysis of small amounts of biacetyl in the presence of a large excess of isobutane containing a small proportion of the unsaturated substrate. The following Arrhenius parameters have been derived:

The kinetics of the gas phase decomposition reactions of the hexafluoro-t-butoxy radical

Hexafluoro-t-butoxy radicals have been generated by reacting fluorine with hexafluoro-2-methyl isopropanol: Over the temperature range of 406–600 K the hexafluoro-t-butoxy radical decomposes exclusively by loss of a CF₃ radical [reaction (-2)] rather than by loss of a CH₃ radical [reaction (-1)]: (1) The limits of detectability of the product CF₃COCF₃, by gas-chromatographic analysis, place a lower limit on the ratio k_?2/k_-1 of ～80. The implications of this finding in relation to the reverse radical addition reactions to the carbonyl group are briefly discussed. A thermochemical kinetic calculation reveals a discrepancy in the kinetics and thermodynamics of the decomposition and formation reactions of the related t-butoxy radical:      

Quasisymmetric embeddings, the observable diameter, and expansion properties of graphs

It is shown that the edges of any n-point vertex expander can be replaced by new edges so that the resulting graph is an edge expander, and such that any two vertices that are joined by a new edge are at distance in the original graph. This result is optimal, and is shown to have various geometric consequences. In particular, it is used to obtain an alternative perspective on the recent algorithm of Arora et al. [Proceedings of the 36th Annual ACM Symposium on the Theory of Computing, 2004, pp. 222-231.] for approximating the edge expansion of a graph, and to give a nearly optimal lower bound on the ratio between the observable diameter and the diameter of doubling metric measure spaces which are quasisymmetrically embeddable in Hilbert space.     

Finite element simulations of tip-enhanced Raman and fluorescence spectroscopy

Finite element electromagnetic simulations of scanning probe microscopy tips and substrates are presented. The enhancement of the scattered light intensity is found to be as high as 10(12) for a 20 nm radius gold tip, and tip-substrate separation of 1 nm. Molecular resolution imaging (< 1 nm) is achievable, even with a relatively large radius tip (20 nm). We also make predictions for imaging in aqueous environments, noting a sizable red shift of the spectral peaks. Finally, we discuss signal levels, and predict that high-speed Raman mapping should be possible with gold substrates and a small tip-substrate separation (< 4 nm).     

Deterministic global optimization in ab-initio quantum chemistry

A large number of problems in ab-initio quantum chemistry involve finding the global minimum of the total system energy. These problems are traditionally solved by numerical approaches equivalent to local optimization. While these approaches are relatively efficient, they do not provide guarantees of global optimality unless a starting point sufficiently close to the global minimum is known apriori. Due to the enormous amount of computational effort required to solve these problems, more mathematically rigorous alternatives have so far received very little attention. Taking the above issue into consideration, this paper explores the use of deterministic global optimization in the context of Hartree-Fock theory, an important mathematical model applied in many quantum chemistry methods. In particular, it presents a general purpose approach for generating linear relaxations for problems arising from Hartree-Fock theory. This was then implemented as an extension to the ${{\tt COUENNE}}$ (Convex Over and Under ENvelopes for Nonlinear Estimation) branch and bound mixed integer non-linear programs solver. Proof of concept calculations that simultaneously optimise the orbital coefficients and the location of the nuclei in closed-shell Hartree-Fock calculations are presented and discussed.     

Mobile geometric graphs: detection, coverage and percolation

We consider the following dynamic Boolean model introduced by van den Berg et al. (Stoch. Process. Appl. 69:247–257, 1997). At time 0, let the nodes of the graph be a Poisson point process in ${\mathbb{R}^d}$ with constant intensity and let each node move independently according to Brownian motion. At any time t, we put an edge between every pair of nodes whose distance is at most r. We study three fundamental problems in this model: detection (the time until a target point—fixed or moving—is within distance r of some node of the graph); coverage (the time until all points inside a finite box are detected by the graph); and percolation (the time until a given node belongs to the infinite connected component of the graph). We obtain precise asymptotics for these quantities by combining ideas from stochastic geometry, coupling and multi-scale analysis.     

Bifunctional iminophosphorane superbases: Potent organocatalysts for enantio- and diastereoselective Michael addition reactions

Bifunctional iminophosphorane (BIMP) organocatalysts catalyze the enantio- and diastereoselective Michael additions of high pK_a cyclic malonamate ester pro-nucleophiles to nitroalkenes with reactivity profiles of up to 3 orders of magnitude greater than tertiary amine bifunctional Brønsted base/(thio)urea organocatalysts. The unrivalled performance of the BIMPs allows reaction times of challenging reactions to be slashed from weeks to minutes and has enabled new flow chemistry applications using polystyrene-supported versions contained within a flow reactor.     

Total Synthesis of (6R,10R,13R,14R,16R,17R,19S,20R,21R,24S, 25S,28S,30S,32R,33R,34R,36S,37S,39R)‐Azaspiracid‐3 Reveals Non‐Identity with the Natural Product

A convergent and stereoselective total synthesis of the previously assigned structure of azaspiracid‐3 has been achieved by a late‐stage Nozaki–Hiyama–Kishi coupling to form the C21?C22 bond with the C20 configuration unambiguously established from l ‐(+)‐tartaric acid. Postcoupling steps involved oxidation to an ynone, modified Stryker reduction of the alkyne, global deprotection, and oxidation of the resulting C1 primary alcohol to the carboxylic acid. The synthetic product matched naturally occurring azaspiracid‐3 by mass spectrometry, but differed both chromatographically and spectroscopically.     

Synthesis of natural products from the Indian neem tree Azadirachta indica

The synthesis of five natural products (3, 6, 7, 10, and 14), isolated from the Indian neem tree Azadirachta indica, is reported from a common intermediate (2). The judicious choice of transacetalization conditions allows efficient access to both the azadirachtinin (9 and 10) and the azadirachtin (3, 6, 7, and 14) skeletons.