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...     

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。     

Cross sections for (d–t) neutron interaction with germanium isotopes

The cross sections for (n,x)$(n,x)$ reactions with Ge isotopes were measured at (d–t) neutron energies around 14 MeV with the activation technique using metal discs of natural composition. Calculations of detector efficiency, incident neutron spectrum and correction factors were performed with the Monte Carlo technique (MCNP4C code). Cross sections data are presented for ⁷⁰Ge(n,2n$n,2n$)⁶⁹Ge, ⁷⁴Ge(n,α$n,\alpha$)^71mZn, ⁷⁶Ge(n,2n$n,2n$)^75(m + g)Ge, ⁷⁰Ge(n,p$n,p$)⁷⁰Ga and ⁷²Ge(n,2n$n,2n$)^71gGe reactions. The cross section results for ⁷²Ge(n,2n$n,2n$)^71gGe reaction were reported for the first time. Some other cross sections were obtained with higher precision, including the ⁷⁰Ge(n,p$n,p$)⁷⁰Ga reaction. Theoretical calculations of excitation functions were performed with the TALYS-1.0 code and compared with the experimental cross section values. Data were included in the EXFOR database.     

LK property for σ-ideals

An ideal J of subsets of a Polish space X has (LK) property whenever for every sequence (An) of analytic sets in X, if lim supn∈HAn∉J for each infinite H then _?n∈G∉J for some infinite G. In this note we present a new class of σ-ideals with (LK) property.     

On σ-commutativity in Menger algebras of n-place functions

We present an abstract characterization of various types of Menger algebras of n-place functions allowing certain permutations of variables.     

Prediction and characterisation of a chalcogen···π interaction with acetylene as a potential electron donor in XHS···HCCH and XHSe···HCCH (X = F,Cl, Br,CN, OH,OCH3, NH2, CH3) σ-hole complexes

It is well-known that many covalently bonded atoms of group VI have specific positive regions of electrostatic potential (σ-holes) through which they can interact with Lewis bases. This interaction is called ‘chalcogen bond’ by analogy with halogen bond and hydrogen bond. In this study, ab initio calculations are performed to predict and characterise chalcogen···π interactions in XHS···HCCH and XHSe···HCCH complexes, where X = F, Cl, Br, CN, OH, OCH₃, NH₂, CH₃. For the complexes studied here, XHS(Se) and HCCH are treated as a Lewis acid and a Lewis base, respectively. The CCSD(T)/aug-cc-pVTZ interaction energies of this type of σ-hole bonding range from ?1.18 to ?4.83 kcal/mol. The calculated interaction energies tend to increase in magnitude with increasing positive electrostatic potential on the extension of X–S(Se) bond. The stability of chalcogen···π complexes is attributed mainly to electrostatic and correlation effects. The nature of chalcogen···π interactions is unveiled by means of the atoms in molecules, natural bond orbital, and electron localisation function analyses.     

Tuning of carbon bonds by substituent effects: an ab initio study

ABSTRACT

An ab initio study, at the MP2/aug-cc-pVTZ level of theory, is performed to study σ-hole bond in binary XH₃C···CNY complexes, where X = CN, F, NO₂, CCH and Y = H, OH, NH₂, CH₃, C₂H₅, Li. This type of interaction is labelled as ‘carbon bond’, since a covalently bonded carbon atom acts as the Lewis acid in these systems. The geometrical and energetic parameters of the resulting complexes are analysed in details. The interaction energies of these complexes are between ?4.97 kJ/mol in (HCC)H₃C···CNH and ?23.07 kJ/mol in (O₂N)H₃C···CNLi. It is found that the electrostatic interaction plays a key role in the overall stabilisation of these carbon-bonded complexes. To deepen the understanding of the nature of the carbon-bonding, the molecular electrostatic potential, natural bond orbital, quantum theory of atoms in molecules and non-covalent interaction index analyses are also used. Our results indicate that the carbon bond is favoured over the C-H···C hydrogen bond in the all complexes considered and may suggest the possible important roles of the C···C interactions in the crystal growth and design.     

Is Lebesgue measure the only σ-finite invariant Borel measure?

S. Saks and recently R.D. Mauldin asked if every translation invariant σ-finite Borel measure on Rd is a constant multiple of Lebesgue measure. The aim of this paper is to investigate the versions of this question, since surprisingly the answer is “yes and no,” depending on what we mean by Borel measure and by constant. According to a folklore result, if the measure is only defined for Borel sets, then the answer is affirmative. We show that if the measure is defined on a σ-algebra containing the Borel sets, then the answer is negative. However, if we allow the multiplicative constant to be infinity, then the answer is affirmative in this case as well. Moreover, our construction also shows that an isometry invariant σ-finite Borel measure (in the wider sense) on Rd can be non-σ-finite when we restrict it to the Borel sets.