Springer basic sets and modular Springer correspondence for classical types

We define the notion of basic set data for finite groups (building on the notion of basic set, but including an order on the irreducible characters as part of the structure), and we prove that the Springer correspondence provides basic set data for Weyl groups. Then we use this to determine explicitly the modular Springer correspondence for classical types (defined over a base field of odd characteristic $p$, and with coefficients in a field of odd characteristic $?\ne p$): the modular case is obtained as a restriction of the ordinary case to a basic set. In order to do so, we compare the order on bipartitions introduced by Dipper and James with the order induced by the Springer correspondence. We provide a quick proof, by sorting characters according to the dimension of the corresponding Springer fibre, an invariant which is directly computable from symbols.     

计算代数方程组孤立奇异解的符号数值方法

求解代数方程组是计算代数几何的最基本问题之一,孤立奇异解的计算则是其中最具挑战性的课题之一,在科学与工程计算中有着广泛的应用,如机器人、计算机视觉、机器学习、人工智能、运筹学、密码学和控制论等.本文结合作者的研究成果,综述了符号数值方法在计算代数系统孤立奇异解、特别是近似奇异解精化与验证方面的研究进展,并对未来的研究方向提出了展望.     

Mechanistic Insights into C(sp2)−C(sp)N Reductive Elimination from Gold(III) Cyanide Complexes

A new family of phosphine-ligated dicyanoarylgold(III) complexes has been prepared and their reactivity towards reductive elimination has been studied in detail. Both, a highly positive entropy of activation and a primary ^12/13C KIE suggest a late concerted transition state while Hammett analysis and DFT calculations indicate that the process is asynchronous. As a result, a distinct mechanism involving an asynchronous concerted reductive elimination for the overall C(sp²)−C(sp)N bond forming reaction is characterized herein, for the first time, complementing previous studies reported for C(sp³)−C(sp³), C(sp²)−C(sp²), and C(sp³)−C(sp²) bond formation processes taking place on gold(III) species.     

Gold-Catalyzed Cross-Coupling Reactions: An Overview of Design Strategies,Mechanistic Studies,and Applications

Transition-metal-catalyzed cross-coupling reactions are central to many organic synthesis methodologies. Traditionally, Pd, Ni, Cu, and Fe catalysts are used to promote these reactions. Recently, many studies have showed that both homogeneous and heterogeneous Au catalysts can be used for activating selective cross-coupling reactions. Here, an overview of the past studies, current trends, and future directions in the field of gold-catalyzed coupling reactions is presented. Design strategies to accomplish selective homocoupling and cross-coupling reactions under both homogeneous and heterogeneous conditions, computational and experimental mechanistic studies, and their applications in diverse fields are critically reviewed. Specific topics covered are: oxidant-assisted and oxidant-free reactions; strain-assisted reactions; dual Au and photoredox catalysis; bimetallic synergistic reactions; mechanisms of reductive elimination processes; enzyme-mimicking Au chemistry; cluster and surface reactions; and plasmonic catalysis. In the relevant sections, theoretical and computational studies of Au^I/Au^III chemistry are discussed and the predictions from the calculations are compared with the experimental observations to derive useful design strategies.     

NO分子宏观气体热力学性质的理论研究

采用量子统计系综理论,研究了基态NO分子宏观气体摩尔熵、摩尔内能、摩尔热容等热力学性质.首先应用课题组前期建立的变分代数法(variational algebraic method, VAM)计算获得了基态NO分子的完全振动能级,得到的VAM振动能级作为振动部分,结合欧拉-麦克劳林渐进展开公式的转动贡献,应用于经典的热力学与统计物理公式中,从而计算得到了1000-5000 K温度范围内NO宏观气体的摩尔内能、摩尔熵和摩尔热容.将不同方法计算得到的摩尔热容结果分别与实验值进行比较,结果表明基于VAM完全振动能级获得的结果优于其他方法获得的理论结果.振动部分采用谐振子模型对无限能级求和计算热力学性质的方法有一定的局限性,应当使用有限的完全振动能级进行统计求和.     

Reactions with a Metalloid Tin Cluster {Sn10[Si(SiMe3)3]4}2−: Ligand Elimination versus Coordination Chemistry

Chemistry that uses metalloid tin clusters as a starting material is of fundamental interest towards understanding the reactivity of such compounds. Since we identified {Sn₁₀[Si(SiMe₃)₃]₄}^2? 7 as an ideal candidate for such reactions, we present a further step in the understanding of metalloid tin cluster chemistry. In contrast to germanium chemistry, ligand elimination seems to be a major reaction channel, which leads to the more open metalloid cluster {Sn₁₀[Si(SiMe₃)₃]₃}^? 9 , in which the Sn core is only shielded by three Si(SiMe₃)₃ ligands. Compound 9 is obtained through different routes and is crystallised together with two different countercations. Besides the structural characterisation of this novel metalloid tin cluster, the electronic structure is analysed by ¹¹⁹Sn Mössbauer spectroscopy. Additionally, possible reaction pathways are discussed. The presented first step into the chemistry of metalloid tin clusters thus indicates that, with respect to metalloid germanium clusters, more reaction channels are accessible, thereby leading to a more complex reaction system.     

Experimental and Theoretical Mechanistic Study on the Thermal Decomposition of 3,3-diphenyl-4-(trichloromethyl)-5-nitropyrazoline

The present paper is a continuation of comprehensive study regarding to synthesis and properties of pyrazoles and their derivatives. In its framework an experimental and theoretical studies of thermal decomposition of the 3,3-diphenyl-4-(trichloromethyl)-5-nitropyrazoline were performed. It was found, that the decompositions of the mentioned pyrazoline system in the solution and at the melted state proceed via completely different molecular mechanisms. These mechanisms have been explained in the framework of the Molecular Electron Density Theory (MEDT) with the computational level of B3LYP/6-31G(d). A Bonding Evolution Theory (BET) examination of dehydrochlorination of the 3,3-diphenyl-4-(trichloromethyl)-5-nitropyrazoline permits elucidation of the molecular mechanism. It was found, that on the contrary for most known HCl extrusion processes in solution, this reaction is realised via single-step mechanism.