QTAIM analysis of the HF, HCl, HBr, and HOH elimination reactions of halohydrocarbons and halohydroalcohols

The 1,2-HX elimination reaction (where X = F, Cl, Br, OH) has been established as an important reaction in the degradation of compounds introduced into the upper atmosphere, including common CFC replacement compounds. By analyzing the electron densities of the transition state geometries of these reactions using QTAIM, we see that we can divide these reactions into two types. For HF and HOH elimination, the transition state is a complete ring of bonds, and neither the C-H nor the C-X bonds have been broken at the maximum of energy. There is very little accumulation of electron density on the X atom, with the majority of charge being lost by the hydrogen atom undergoing elimination, being transferred on to the two carbon atoms. In HCl and HBr elimination, a similar loss of electron density of the hydrogen atom is accompanied by significant accumulation of electron density on the X atom and a smaller change in electron density on the carbon atoms. The C-X bond is broken in the transition state geometry, with no ring critical point being present. This may explain the relative stabilities of halohydrocarbons and haloalcohols with respect to loss of H-X.     

The combination of living radical polymerization and click chemistry for the synthesis of advanced macromolecular architectures

Since its introduction, click chemistry has received a considerable amount of interest. In this contribution, the term click chemistry and the reactions that fall under this term are briefly explained. The main focus of this review is on the application of click chemistry in conjunction with living radical polymerization for the synthesis of advanced macromolecular architectures. Therefore the most powerful living radical polymerization (LRP) techniques are discussed and an overview of click chemistry in the different synthetic schemes is given. A large number of examples are shown that include the synthesis of block copolymers, star-shaped polymers, surface modified particles, and polymer-protein conjugates. The enormous potential of LRP/click chemistry is probably best exemplified by the synthesis of different miktoarm star copolymers, to which a separate section is dedicated.     

Synthesis of (hetero)arylated pyridazin-3(2H)-ones via Negishi reaction involving zincated pyridazin-3(2H)-ones

Zincated pyridazin-3(2H)-ones generated via bromine-magnesium exchange followed by transmetalation using ZnCl(2) or via lactam-directed ortho C4-H zincation with TMPZnCl·LiCl have been synthesized. These in situ created organometallics can be used in Negishi reactions with iodo(hetero)arenes delivering a new approach toward (hetero)arylpyridazin-3(2H)-ones.     

Protonation of the oxygen axial ligand in galactose oxidase model compounds as seen with high resolution X-ray emission experiments and FEFF simulations

X-ray Emission Spectroscopy (XES) crossover peaks were shown to be sensitive to the protonation state of solvent molecules in the Zn protein carbonic anhydrase and its model compounds. Here we extend such studies to galactose oxidase models i.e. Cu(ii) open d-shell systems, illustrating that XES combined with FEFF8 simulations reflect changes in the protonation state of the phenolate ligand for the copper center.     

On longest cycles and strongly linking vertex sets

Let G be a simple non-hamiltonian graph, let C be a longest cycle in G, and let p be a positive integer. By considering a special form of connectivity, we obtain a sufficient condition on degrees for the nonexistence of (p - 1)-path-connected components in G - C.     

Tail behavior of conditional sojourn times in Processor-Sharing queues

We investigate the tail behavior of the sojourn-time distribution for a request of a given length in an M/G/1 Processor-Sharing (PS) queue. An exponential asymptote is proven for general service times in two special cases: when the traffic load is sufficiently high and when the request length is sufficiently small. Furthermore, using the branching process technique we derive exact asymptotics of exponential type for the sojourn time in the M/M/1 queue. We obtain an equation for the asymptotic decay rate and an exact expression for the asymptotic constant. The decay rate is studied in detail and is compared to other service disciplines. Finally, using numerical methods, we investigate the accuracy of the exponential asymptote. AMS 2000 Subject Classifications Primary:60K25,Secondary: 60F10,68M20,90B22