Insights into Sonogashira cross-coupling by high-throughput kinetics and descriptor modeling

A method is presented for the high-throughput monitoring of reaction kinetics in homogeneous catalysis, running up to 25 coupling reactions in a single reaction vessel. This method is demonstrated and validated on the Sonogashira reaction, analyzing the kinetics for almost 500 coupling reactions. First, one-pot reactions of phenylacetylene with a set of 20 different meta- and para-substituted aryl bromides were analyzed in the presence of 17 different Pd-phosphine complexes. In addition, the temperature-dependent Sonogashira reactions were examined for 21 different ArX (X=Cl, Br, I) substrates, and the corresponding activation enthalpies and entropies were determined by means of Eyring plots: ArI (DeltaH(not equal)=48-62 kJ mol(-1); DeltaS(not equal)=-71--39 J mol(-1) K; NO(2)-->OMe), ArBr (DeltaH(not equal)=54-82 kJ mol(-1), DeltaS(not equal)=-55-11 J mol(-1) K), and ArCl (DeltaH(not equal)=95-144 kJ mol(-1), DeltaS(not equal)=-6-100 J mol(-1) K). DFT calculations established a linear correlation of DeltaH( not equal) and the Kohn-Sham HOMO energies of ArX (X=Cl, Br, I) and confirmed their involvement in the rate-limiting step. However, despite different C--X bond energies, aryl iodides and electron-deficient aryl bromides showed similar activation parameters.     

Asymptotic revenue equivalence of asymmetric auctions with interdependent values

We prove an asymptotic revenue equivalence among weakly asymmetric auctions with interdependent values, in which bidders have either asymmetric utility functions or asymmetric distributions of signals.     

Large auctions with risk-averse bidders

We study private-value auctions with n risk-averse bidders, where n is large. We first use asymptotic analysis techniques to calculate explicit approximations of the equilibrium bids and of the seller’s revenue in any k-price auction (k = 1, 2, . . .). These explicit approximations show that in all large k-price auctions the effect of risk-aversion is O(1/n ²) small. Hence, all large k-price auctions with risk-averse bidders are O(1/n ²) revenue equivalent. The generalization, that all large auctions are O(1/n ²) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as ${n\longrightarrow \infty }We study private-value auctions with n risk-averse bidders, where n is large. We first use asymptotic analysis techniques to calculate explicit approximations of the equilibrium bids and of the seller’s revenue in any k-price auction (k = 1, 2, . . .). These explicit approximations show that in all large k-price auctions the effect of risk-aversion is O(1/n ²) small. Hence, all large k-price auctions with risk-averse bidders are O(1/n ²) revenue equivalent. The generalization, that all large auctions are O(1/n ²) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as n? ￥{n\longrightarrow \infty } with risk-averse bidders is strictly below the risk-neutral limit. Therefore, these auction mechanisms are not revenue equivalent to large k-price auctions even to leading-order as n? ￥{n\longrightarrow \infty }.     

多阶强度非线性条件下的光束传输研究 *

研究了多阶强度非线性综合作用情况下光束传输的统计行为方程 ,给出了其中的守恒量和二阶矩随传输轴的二阶导数 ,从而得出了傍轴情况下光束的多阶非线性传输满足的微分方程组 ,进而得到了广义光束质量因子和相应的q -参数 ,并将ABCD定律推广至傍轴情况下任意阶强度非线性光束传输的情况 .以超Gauss光束为例子 ,比较了多阶非线性效应与三阶非线性效应 .     

Existence of nondetermined sets for some two person games over reals

Various two person games with perfect information over reals are shown to have a nondetermined set. A game formulated by Mycielski is solved. This is a part of the author’s Ph.D. thesis, prepared at the Hebrew University under the supervision of Professor Azriel Levy, to whom the author wishes to express his warm thanks.     

Tracking chemical kinetics in high-throughput systems

Combinatorial chemistry and high‐throughput experimentation (HTE) have revolutionized the pharmaceutical industry—but can chemists truly repeat this success in the fields of catalysis and materials science? We propose to bridge the traditional “discovery” and “optimization” stages in HTE by enabling parallel kinetic analysis of an array of chemical reactions. We present here the theoretical basis to extract concentration profiles from reaction arrays and derive the optimal criteria to follow (pseudo)first‐order reactions in time in parallel systems. We use the information vector f and introduce in this context the information gain ratio, χ_r, to quantify the amount of useful information that can be obtained by measuring the extent of a specified reaction r in the array at any given time. Our method is general and independent of the analysis technique, but it is more effective if the analysis is performed on‐line. The feasibility of this new approach is demonstrated in the fast kinetic analysis of the carbon–sulfur coupling between 3‐chlorophenylhydrazonopropane dinitrile and β‐mercaptoethanol. The theory agrees well with the results obtained from 31 repeated C? S coupling experiments.     

Copper-catalyzed Suzuki cross-coupling using mixed nanocluster catalysts

A small library of copper and noble metal nanoclusters is designed and synthesized. These clusters are tested as catalysts in the Suzuki cross-coupling of various aryl halides with phenylboronic acid. It is found that copper and copper/noble metal combination nanoclusters are active catalysts for this reaction, the most active being the combined copper/palladium clusters. Iodo-, bromo-, and chloroarenes can be used. In the case of p-nitrobromobenzene, a one-pot cross-coupling and selective hydrogenation is achieved.