自伴算子代数上的某些*-自同态的σ-弱混合性

设A是希尔伯特空间H上的自伴算子代数,α是A上的*-自同态.如果存在单位向量e∈H,使得对任意α∈A和单位向量h∈H,有lim_(n→∞)〈α~n(a)h,h〉=〈αe,e〉成立,那么称α是A上的σ-弱混合的*-自同态.本文研究了这一有趣性质,并得到了一个*-自同态是σ-弱混合的充分条件.     

Design of a new molecule that exhibits observable CD spectra under σ-σ* excitation: 2,6-Disilyl-2,6-disilaspiro[3.3]heptanes

Abstract

We previously designed and prepared the first molecules to exhibit observable CD spectra by n-σ* excitation, 2,6-dithiaspiro[3.3]heptane 2,6-dioxide. Spiro[3.3]heptane frameworks possess axial asymmetry due to puckering of 2 four-membered rings; the ring bonds are rich in p-character due to acute bond angles, which lowers the σ* energy levels. In contrast, the lone pairs are rich in s-character, which results in a good donor with conformational fixation. We expected that, instead of lone pairs as donating orbitals, the use of σ-electron-donating Si-Si bonds should result in UV absorption in the observable range (>180?nm), so that the Cotton effect could appear, at least partially, in that range. We designed 2,6-disilyl-2,6-disilaspiro[3.3]heptanes as models, and performed theoretical calculations to confirm our idea.     

σ2 Hessian方程的Pogorelov型C2 内估计及应用

提出利用拉格朗日乘子法重新证明σ2算子的最优凹性,并定义了一个凸锥Γ3?=λ=(λ1,λ2,?,λn)∈Rn:σ1(λ)>0,σ2(λ|i)>0,1≤i≤n。利用σ2算子的最优凹性，给出了σ2Hessian方程Pogorelov型C2内估计，进而证明了σ2(D2u(x))=1,x∈Rn的满足二次多项式增长条件的Γ3?-凸整解为二次多项式。     

Factors affecting the strengths of σ-hole electrostatic potentials

A σ-hole is a region of diminished electronic density on the extension of a covalent bond to an atom. This region often exhibits a positive electrostatic potential, which allows attractive noncovalent interactions with negative sites. In this study, we have systematically examined the dependence of σ-hole potentials upon (a) the atom having the σ-hole, and (b) the remainder of the molecule. We demonstrate that not only relative electron-attracting powers need to be considered, but also relative charge capacities (or polarizabilities), and that other factors can also have significant roles.     

σ-Aromaticity-Induced Stabilization of Heterometallic Supertetrahedral Clusters [Zn6Ge16]4− and [Cd6Ge16]4−

In this work, the largest heterometallic supertetrahedral clusters, [Zn₆Ge₁₆]⁴⁻ and [Cd₆Ge₁₆]⁴⁻, were directly self-assembled through highly-charged [Ge₄]⁴⁻ units and transition metal cations, in which 3-center–2-electron σ bonding in Ge₂Zn or Ge₂Cd triangles plays a vital role in the stabilization of the whole structure. The cluster structures have an open framework with a large central cavity of diameter 4.6 Å for Zn and 5.0 Å for Cd, respectively. Time-dependent HRESI-MS spectra show that the larger clusters grow from smaller components with a single [Ge₄]⁴⁻ and ZnMes₂ units. Calculations performed at the DFT level indicate a very large HOMO–LUMO energy gap in [M₆Ge₁₆]⁴⁻ (2.22 eV), suggesting high kinetic stability that may offer opportunities in materials science. These observations offer a new strategy for the assembly of heterometallic clusters with high symmetry.     

Stabilities,Electronic Structures,and Bonding Properties of Iron Complexes (E1E2)Fe(CO)2(CNArTripp2)2 (E1E2=BF,CO, N2, CN−, or NO+)**

The coordination of 10-electron diatomic ligands (BF, CO N₂) to iron complexes Fe(CO)₂(CNAr^Tripp2)₂ [Ar^Tripp2=2,6-(2,4,6-(iso-propyl)₃C₆H₂)₂C₆H₃] have been realized in experiments very recently (Science, 2019 , 363, 1203–1205). Herein, the stability, electronic structures, and bonding properties of (E₁E₂)Fe-(CO)₂(CNAr^Tripp2)₂ (E₁E₂=BF, CO, N₂, CN⁻, NO⁺) were studied using density functional (DFT) calculations. The ground state of all those molecules is singlet and the calculated geometries are in excellent agreement with the experimental values. The natural bond orbital analysis revealed that Fe is negatively charged while E₁ possesses positive charges. By employing the energy decomposition analysis, the bonding nature of the E₂E₁–Fe(CO)₂(CNAr^Tripp2)₂ bond was disclosed to be the classic dative bond E₂E₁→Fe(CO)₂(CNAr^Tripp2)₂ rather than the electron-sharing double bond. More interestingly, the bonding strength between BF and Fe(CO)₂(CNAr^Tripp2)₂ is much stronger than that between CO (or N₂) and Fe(CO)₂(CNAr^Tripp2)₂, which is ascribed to the better σ-donation and π back-donations. However, the orbital interactions in CN⁻→Fe(CO)₂(CNAr^Tripp2)₂ and NO⁺→Fe(CO)₂(CNAr^Tripp2)₂ mainly come from σ-donation and π back-donation, respectively. The different contributions from σ donation and π donation for different ligands can be well explained by using the energy levels of E₁E₂ and Fe(CO)₂(CNAr^Tripp2)₂ fragments.     

过渡金属-配体σ键键能在碳-氢键活化中的应用

过渡金属催化的碳-氢(C-H)键活化因其优异的原子经济性及步骤简便性在过去几十年间蓬勃发展,已成为当前构建复杂化合物最常用的策略之一.对该过程中活性中间体的热力学研究有助于加深人们对反应机理的理解,指导新催化剂、新反应的理性设计.然而,近年来该领域的发展颇为缓慢,相应的报道十分零散,缺少系统的归纳和总结.本综述简要梳理...     

The Bifurcated σ-Hole···σ-Hole Stacking Interactions

The bifurcated σ-hole···σ-hole stacking interactions between organosulfur molecules, which are key components of organic optical and electronic materials, were investigated by using a combined method of the Cambridge Structural Database search and quantum chemical calculation. Due to the geometric constraints, the binding energy of one bifurcated σ-hole···σ-hole stacking interaction is in general smaller than the sum of the binding energies of two free monofurcated σ-hole···σ-hole stacking interactions. The bifurcated σ-hole···σ-hole stacking interactions are still of the dispersion-dominated noncovalent interactions. However, in contrast to the linear monofurcated σ-hole···σ-hole stacking interaction, the contribution of the electrostatic energy to the total attractive interaction energy increases significantly and the dispersion component of the total attractive interaction energy decreases significantly for the bifurcated σ-hole···σ-hole stacking interaction. Another important finding of this study is that the low-cost spin-component scaled zeroth-order symmetry-adapted perturbation theory performs perfectly in the study of the bifurcated σ-hole···σ-hole stacking interactions. This work will provide valuable information for the design and synthesis of novel organic optical and electronic materials.     

The Phosphorus Bond,or the Phosphorus-Centered Pnictogen Bond: The Covalently Bound Phosphorus Atom in Molecular Entities and Crystals as a Pnictogen Bond Donor

The phosphorus bond in chemical systems, which is an inter- or intramolecular noncovalent interaction, occurs when there is evidence of a net attractive interaction between an electrophilic region associated with a covalently or coordinately bonded phosphorus atom in a molecular entity and a nucleophile in another, or the same, molecular entity. It is the second member of the family of pnictogen bonds, formed by the second member of the pnictogen family of the periodic table. In this overview, we provide the reader with a snapshot of the nature, and possible occurrences, of phosphorus-centered pnictogen bonding in illustrative chemical crystal systems drawn from the ICSD (Inorganic Crystal Structure Database) and CSD (Cambridge Structural Database) databases, some of which date back to the latter part of the last century. The illustrative systems discussed are expected to assist as a guide to researchers in rationalizing phosphorus-centered pnictogen bonding in the rational design of molecular complexes, crystals, and materials and their subsequent characterization.     

非合作n人投标报价服从N(μ,σ~2)分布时局中人投标报价策略的研究

推导了矩阵对策模型 ,对非合作 n人投标报价的分布进行 x2 检验。当非合作 n人投标报价服从N (μ,σ2 )分布时 ,根据参数区间公式 ,估计非合作 n人有效报价平均数的范围 ,局中人 最佳报价可根据矩阵对策模型来确定。该方法确定的报价与最佳标底的误差能控制在较小的范围内 ,适用于招标中合成标底的评标办法 ,对确定报价具有一定的实用价值。