Structural Diversity of Copper(I)–N‐Heterocyclic Carbene Complexes; Ligand Tuning Facilitates Isolation of the First Structurally Characterised Copper(I)–NHC Containing a Copper(I)–Alkene Interaction

The preparation of a series of imidazolium salts bearing N‐allyl substituents, and a range of substituents on the second nitrogen atom that have varying electronic and steric properties, is reported. The ligands have been coordinated to a copper(I) centre and the resulting copper(I)–NHC (NHC=N‐heterocyclic carbene) complexes have been thoroughly examined, both in solution and in the solid‐state. The solid‐state structures are highly diverse and exhibit a range of unusual geometries and cuprophilic interactions. The first structurally characterised copper(I)–NHC complex containing a copper(I)–alkene interaction is reported. An N‐pyridyl substituent, which forms a dative bond with the copper(I) centre, stabilises an interaction between the metal centre and the allyl substituent of a neighbouring ligand, to form a 1D coordination polymer. The stabilisation is attributed to the pyridyl substituent increasing the electron density at the copper(I) centre, and thus enhancing the metal(d)‐to‐alkene(π*) back‐bonding. In addition, components other than charge transfer appear to have a role in copper(I)–alkene stabilisation because further increases in the Lewis basicity of the ligand disfavours copper(I)–alkene binding.     

Ni‐Catalyzed [4+3+2] Cycloaddition of Ethyl Cyclopropylideneacetate and Dienynes: Scope and Mechanistic Insights

A detailed study of the Ni‐catalyzed [4+3+2] cycloaddition reaction between ethyl cyclopropylideneacetate and dienynes has been conducted, resulting in the development of a new method for the synthesis of compounds containing nine‐membered rings. We studied the reactivity of various dienynes, together with their substituent and conformational effects. The mechanism of the reaction was probed by examining the stoichiometric reactions of the Ni complexes and dienynes.     

Aharonov–Bohm effect in non-uniform crater-like quantum dot with double rim

We study electron energies in a double concentric quantum ring with anisotropy in the rims heights in the presence of the external magnetic field applied along the symmetry axis. To this end, we consider a model in which the thickness grows linearly from the axis up to the inner rim with a slope different from one between the inner and the outer rims. The anisotropy in the rims heights originated by the presence in the structure of various valleys we simulate by periodic dependence of the slope on the radial direction. We show that the wave functions of the electron confined in such structure can be found analytically if the slopes in all radial directions are the same, and by using a simple exact diagonalization procedure otherwise. The behavior of the electron energies as functions of the magnetic field, rings radii and rims heights, as well as the number of the valleys and their depths is consistently described with our formalism. The entanglement of the states with different radial and orbital quantum numbers, the period and the amplitude of the Aharonov–Bohm oscillations are very sensible to any variations of the rims heights.     

Catalytic Synthesis of 8-Membered Ring Compounds via Cobalt(III)-Carbene Radicals

The metalloradical activation of o-aryl aldehydes with tosylhydrazide and a cobalt(II) porphyrin catalyst produces cobalt(III)-carbene radical intermediates, providing a new and powerful strategy for the synthesis of medium-sized ring structures. Herein we make use of the intrinsic radical-type reactivity of cobalt(III)-carbene radical intermediates in the [Co^II(TPP)]-catalyzed (TPP=tetraphenylporphyrin) synthesis of two types of 8-membered ring compounds; novel dibenzocyclooctenes and unprecedented monobenzocyclooctadienes. The method was successfully applied to afford a variety of 8-membered ring compounds in good yields and with excellent substituent tolerance. Density functional theory (DFT) calculations and experimental results suggest that the reactions proceed via hydrogen atom transfer from the bis-allylic/benzallylic C−H bond to the carbene radical, followed by two divergent processes for ring-closure to the two different types of 8-membered ring products. While the dibenzocyclooctenes are most likely formed by dissociation of o-quinodimethanes (o-QDMs) which undergo a non-catalyzed 8π-cyclization, DFT calculations suggest that ring-closure to the monobenzocyclooctadienes involves a radical-rebound step in the coordination sphere of cobalt. The latter mechanism implies that unprecedented enantioselective ring-closure reactions to chiral monobenzocyclooctadienes should be possible, as was confirmed for reactions mediated by a chiral cobalt-porphyrin catalyst.     

两共轴带电圆环的相互作用能和作用力

计算了两共轴均匀带电圆环的相互作用能,并求出它们之间的相互作用力,绘制出电场力的空间分布图,进而讨论了作用力和两圆环半径和中心距离等参量的关系.     

牛顿环实验测量结果不确定度的评定

详细分析了牛顿环实验中测量结果不确定度评定,由于干涉图样中各级暗环弦长左右读数的测量为不等精度测量,因此本文提出一种既简单又易操作的不确定度评定方法。     

多项式环的单位和稳定度的注记

称环R为广义2-素环,如果R的幂零元集与上诣零根一致.证明了R上的多项式为单位当且仅当它的常数项是R中的单位而其它系数是幂零的.因此,广义2-素环上的多项式环的稳定度大于一.     

具有卷积的中心自反环

本文研究了具有卷积的中心自反环的性质,定义并引入了中心-自反环,显然,中心-自反环是自反环、中心自反环和-自反环的推广.给出了这类环的一些特征,研究了相关的环扩张,包括平凡扩张,Dorroh扩张和多项式扩张.