Recyclable Mn(I) Catalysts for Base-Free Asymmetric Hydrogenation: Mechanistic,DFT and Catalytic Studies

We report here a mechanistic, DFT and catalytic study on a series of Mn(I) complexes 1 , 2 ( a – d ), 3 , 4 . The studies apprehended the requirements for Mn(I) complexes to be active in both asymmetric direct ( AH ) and transfer hydrogenations ( ATH ). The investigations disclosed 6 vital factors accelerating the formation of a resting species, which plays a significant role in lowering the activities of the Mn(I) complex 1 in ATH and AH , respectively. In addition, we also report here a base free Mn(I) catalyzed ATH of aryl alkyl ketones with high enantioselectivity (up to 98 % ee) and improved activity. More significantly, a novel and simple single-step process for recycling the resting species from the catalytic leftover has been discovered. Notably, the studies provide evidence for the existence of two different temperature dependent mechanisms for AH and ATH , in contrast to previous studies on related systems.     

A general study on random integro-differential equations of arbitrary order

Here the broad study is depending on random integro-differential equations (RIDE) of arbitrary order. The fractional order is in terms of $\psi$-Hilfer fractional operator. This work reveals the dynamical behaviour such as existence, uniqueness and stability solutions for RIDE involving fractional order. Thus initial value problem (IVP), boundary value problem (BVP), impulsive effect and nonlocal conditions are taken in account to prove the results.     

Bounds on Lifting Continuous-State Markov Chains to Speed Up Mixing

It is often possible to speed up the mixing of a Markov chain \(\{ X_{t} \}_{t \in \mathbb {N}}\) on a state space \(\Omega \) by lifting, that is, running a more efficient Markov chain \(\{ \widehat{X}_{t} \}_{t \in \mathbb {N}}\) on a larger state space \(\hat{\Omega } \supset \Omega \) that projects to \(\{ X_{t} \}_{t \in \mathbb {N}}\) in a certain sense. Chen et al. (Proceedings of the 31st annual ACM symposium on theory of computing. ACM, 1999) prove that for Markov chains on finite state spaces, the mixing time of any lift of a Markov chain is at least the square root of the mixing time of the original chain, up to a factor that depends on the stationary measure of \(\{X_t\}_{t \in \mathbb {N}}\). Unfortunately, this extra factor makes the bound in Chen et al. (1999) very loose for Markov chains on large state spaces and useless for Markov chains on continuous state spaces. In this paper, we develop an extension of the evolving set method that allows us to refine this extra factor and find bounds for Markov chains on continuous state spaces that are analogous to the bounds in Chen et al. (1999). These bounds also allow us to improve on the bounds in Chen et al. (1999) for some chains on finite state spaces.     

A Duality for Spin Verlinde Spaces and Prym Theta Functions

The paper proves canonical isomorphisms between Spin Verlindespaces, that is, spaces of global sections of a determinantline bundle over the moduli space of semistable Spin_n-bundlesover a smooth projective curve C, and the dual spaces of thetafunctions over Prym varieties of unramified double covers ofC.     

Galactose Grafted Two-Dimensional Nanosheets as a Scaffold for the In Situ Synthesis of Silver Nanoparticles: A Potential Catalyst for the Reduction of Nitroaromatics

Two major hurdles in NP-based catalysis are the aggregation of the NPs and their recycling. Immobilization of NPs onto a 2D support is the most promising strategy to overcome these difficulties. Herein, amphiphilicity-driven self-assembly of galactose-hexaphenylbenzene-based amphiphiles into galactose-decorated 2D nanosheet is reported. The extremely dense decoration of reducing sugar on the surface of the sheets is used for the in situ synthesis and immobilization of ultrafine catalytically active AgNPs by using Tollens’ reaction. The potential of the system as a catalyst for the reduction of various nitroaromatics is demonstrated. Enhanced catalytic activity is observed for the immobilized AgNPs when compared to the corresponding discrete AgNPs. Recovery of the catalytic system from the reaction mixture by ultrafiltration and its subsequent recycling for several cycles without dropping its activity is shown. This is the first report demonstrating the in situ synthesis and immobilization of ultrafine AgNPs onto a 2D nanosheet that exhibits excellent catalytic performance for the reduction of nitroaromatics.     

Viscoelasticity and diffusion in miscible blends of saturated hydrocarbon polymers

Linear viscoelasticity and tracer diffusion were investigated as functions of temperature, component molecular weight and blend composition for entangled, single-phase blends of nearly monodisperse poly(ethylene-alt-propylene) (PEP) and head-to-head polypropylene (HHPP). Both components are non-polar and, despite evidence for slight differences of component glass temperatures in their blends, the viscoelastic data obey time-temperature superposition rather well. The properties of the blends were compared at constant T-T _g (blend) with predictions of the tube-model theories. The composition dependence of viscosity agrees best with the double-reptation prediction, as had been found earlier for molecular weight blends. The variation in plateau modulus with composition is consistent with reptation, but the changes are too small to provide a definitive test. The tracer diffusion coefficients, D ^* _PEP and D ^* _HHPP are nearly independent of composition, consistent with the reptation prediction and in sharp contrast with tracer diffusion for blends with specific associations. Results for the recoverable compliance depart from this pattern, varying differently and much less strongly with composition than the predictions of either single or double reptation. It thus seems that microstructural blends may behave in significantly more complex ways than molecular weight blends even for components with only weak dispersive interactions and rather modest differences in glass temperature and plateau modulus.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.     

On the Mechanism of the Dehydroaromatization of Hexane to Benzene by an Iridium Pincer Catalyst

The developments in the area of transition‐metal pincer complexes have opened up new avenues for conversion of saturated hydrocarbons to more useful aromatic compounds under homogeneous reaction conditions. In the backdrop of an interesting series of conversions of unbranched alkanes to benzene, toluene, and xylene (known as the BTX family aromatics) reported by Goldman and co‐workers (Nature Chem. 2011 , 3, 167), we herein present a comprehensive mechanistic picture obtained by using density functional computations. The reaction involves an iridium–PCP‐pincer‐catalyzed dehydroaromatization of hexane to benzene (in which PCP=η³‐C₆H₃(iPrP)₂‐1,3) by using tert‐butylethylene (TBE) as a sacrificial acceptor. The most energetically preferred pathway for a sequence of dehydrogenations is identified to begin with a terminal C? H bond activation of n‐hexane leading to the formation of hex‐1‐ene. Although the initial dehydrogenation of n‐hexane was found to be endergonic, the accompanying exoergic hydrogenation of TBE to tert‐butylethane (TBA) compensates the energetics to keep the catalytic cycle efficient. Subsequent dehydrogenations provide a hexa‐1,3‐diene and then a hexa‐1,3,5‐triene. The pincer bound triene is identified to undergo cyclization to furnish cyclohexadiene. Eventually, dehydrogenation of cyclohexa‐1,3‐diene offers benzene. In the most preferred pathway, the Gibbs free energy barrier for cyclization leading to the formation of cyclohexa‐1,3‐diene is found to exhibit the highest barrier (21.7 kcal mol^?1).