Synthetic, spectral and catalytic activity studies of ruthenium bipyridine and terpyridine complexes: Implications in the mechanism of the ruthenium(pyridine-2,6-bisoxazoline)(pyridine-2,6-dicarboxylate)-catalyzed asymmetric epoxidation of olefins utilizing H2O2

Various Ru(L₁)(L₂) (1) complexes (L₁ = 2,2′-bipyridines, 2,2′:6′,2″-terpyridines, 6-(4S)-4-phenyl-4,5-dihydro-oxazol-2-yl-2,2′-bipyridinyl or 2,2′-bipyridinyl-6-carboxylate; L₂ = pyridine-2,6-dicarboxylate, pyridine-2-carboxylate or 2,2′-bipyridinyl-6-carboxylate) have been synthesized (or in situ generated) and tested on epoxidation of olefins utilizing 30% aqueous H₂O₂. The complexes containing pyridine-2,6-dicarboxylate show extraordinarily high catalytic activity. Based on the stereoselective performance of chiral ruthenium complexes containing non-racemic 2,2′-bipyridines including 6-[(4S)-4-phenyl-4,5-dihydro-oxazol-2-yl]-[2,2′]bipyridinyl new insights on the reaction intermediates and reaction pathway of the ruthenium-catalyzed enantioselective epoxidation are proposed. In addition, a simplified protocol for epoxidation of olefins using urea hydrogen peroxide complex as oxidizing agent has been developed.     

Delay-induced oscillatory dynamics in humoral mediated immune response with two time delays

A mathematical model for the quantitative analysis of cancer immune interaction, considering the role of humoral (antibody) mediated immune response with two time delays, namely maturation and interaction delays has been proposed in this paper. The aim of this work is to assess the effect of time delays on the interaction between cancerous cells and the antibodies. After categorizing the parametric plane into different regions based on the existence of equilibria, we investigate both analytically and through simulations, the stability of equilibria and the onset of sustained oscillations through Hopf bifurcations. The direction and stability of the Hopf bifurcation which occurs at the positive interior equilibrium point of the system have also been studied. It is observed that both the delays play an important role in stability switching. Appropriate therapy with a proper choice of system parameters are suggested to obtain cancer free equilibrium.     

Polymers with self-avoiding interaction in random medium: a localization-delocalization transition

In this paper we investigate the problem of a long self-avoiding polymer chain immersed in a random medium. We find that in the limit of a very long chain and when the self-avoiding interaction is weak, the conformation of the chain consists of many “blobs” with connecting segments. The blobs are sections of the molecule curled up in regions of low potential in the case of a Gaussian distributed random potential or in regions of relatively low density of obstacles in the case of randomly distributed hard obstacles. We find that as the strength of the self-avoiding interaction is increased the chain undergoes a delocalization transition in the sense that the appropriate free energy per monomer is no longer negative. The chain is then no longer bound to a particular location in the medium but can easily wander around under the influence of a small perturbation. For a localized chain we estimate quantitatively the expected number of monomers in the “blobs” and in the connecting segments. Received 13 November 2002 Published online 14 March 2003     

An efficient biomimetic Fe-catalyzed epoxidation of olefins using hydrogen peroxide

A new, environmentally benign and practical epoxidation method was developed using inexpensive and efficient Fe catalysts. FeCl3.6H2O in combination with commercially available pyridine-2,6-dicarboxylic acid and amines showed excellent reactivity and selectivity towards aromatic olefins and moderate reactivity towards 1,3-cyclooctadiene utilizing H2O2 as the terminal oxidant.     

Biomimetic iron-catalyzed asymmetric epoxidation of aromatic alkenes by using hydrogen peroxide

A novel and general biomimetic non-heme Fe-catalyzed asymmetric epoxidation of aromatic alkenes by using hydrogen peroxide is reported herein. The catalyst consists of ferric chloride hexahydrate (FeCl(3)6 H(2)O), pyridine-2,6-dicarboxylic acid (H(2)(pydic)), and readily accessible chiral N-arenesulfonyl-N'-benzyl-substituted ethylenediamine ligands. The asymmetric epoxidation of styrenes with this system gave high conversions but poor enantiomeric excesses (ee), whereas larger alkenes gave high conversions and ee values. For the epoxidation of trans-stilbene (1 a), the ligands (S,S)-N-(4-toluenesulfonyl)-1,2-diphenylethylenediamine ((S,S)-4 a) and its N'-benzylated derivative ((S,S)-5 a) gave opposite enantiomers of trans-stilbene oxide, that is, (S,S)-2 a and (R,R)-2 a, respectively. The enantioselectivity of alkene epoxidation is controlled by steric and electronic factors, although steric effects are more dominant. Preliminary mechanistic studies suggest the in situ formation of several chiral Fe-complexes, such as [FeCl(L*)(2)(pydic)]HCl (L*=(S,S)-4 a or (S,S)-5 a in the catalyst mixture), which were identified by ESIMS. A UV/Vis study of the catalyst mixture, which consisted of FeCl(3)6 H(2)O, H(2)(pydic), and (S,S)-4 a, suggested the formation of a new species with an absorbance peak at lambda=465 nm upon treatment with hydrogen peroxide. With the aid of two independent spin traps, we could confirm by EPR spectroscopy that the reaction proceeds via radical intermediates. Kinetic studies with deuterated styrenes showed inverse secondary kinetic isotope effects, with values of k(H)/k(D)=0.93 for the beta carbon and k(H)/k(D)=0.97 for the alpha carbon, which suggested an unsymmetrical transition state with stepwise O transfer. Competitive epoxidation of para-substituted styrenes revealed a linear dual-parameter Hammett plot with a slope of 1.00. Under standard conditions, epoxidation of 1 a in the presence of ten equivalents of H(2) (18)O resulted in an absence of the isotopic label in (S,S)-2 a. A positive nonlinear effect was observed during the epoxidation of 1 a in the presence of (S,S)-5 a and (R,R)-5 a.     

Exploring the dynamics of dimer crossing over a Kramers type potential

We explore the escape rate of a dimer crossing a potential barrier using both analytical and numerical approaches. We find that for small coupling strength k, the barrier hopping can be well approximated by a two step reaction scheme where one monomer hops over the barrier and is then followed by the other. In this regime the escape rate increases with k showing that the cooperativity between monomers enhances the crossing rate. However, in the limit of large coupling strength, applying the method of adiabatic elimination, we find that the escape rate is a decreasing function of k. Thus, we find that the escape rate is a non-monotonic function of the spring constant which is peaked at an optimal coupling strength. Furthermore, in the presence of a weak periodic signal, we show that the system response to the periodic signal is pronounced at a particular spring constant showing the dimer can be transported rapidly across the reaction coordinate in a half period.     

Nonclassical Features of Intra-Cavity and Transmitted Fields in a Coherently-Pumped Correlated-Emission Laser with Injected Thermal Light†

Journal of Russian Laser Research - We discuss effects of phase fluctuations and thermal light on the entanglement, squeezing, and intensity of the two-mode intra-cavity and transmitted fields...     

3,3,6,6‐Tetra­methyl‐1,2,4,5‐tetroxane: a twinned crystal structure

The title compound, C₆H₁₂O₄, also known as dimeric acetone peroxide, Me₂(C₂O₄)Me₂, has crystallographically imposed inversion symmetry and adopts a chair conformation in the solid state. This structure contrasts with that of the sulfur homologue Me₂(C₂S₄)Me₂, which has crystallographically imposed symmetry and crystallizes in a twist‐boat conformation. Crystals of the title compound are twinned along the reciprocal c* axis.