Electrostatics and Polarization in σ- and π-Hole Noncovalent Interactions: An Overview

The energetics of σ- and π-hole interactions can be described very well in terms of electrostatics and polarization, consistent with their Coulombic natures. When both of these components are taken into account, very good correlations with quantum-chemically computed interaction energies are obtained. If polarization is only minor, as when the interactions are quite weak, then electrostatics can suffice, as represented by the most positive electrostatic potential associated with the σ- or π-hole. For stronger interactions, the combination of electrostatics plus polarization is very effective even for interaction energies considerably greater in magnitude than what is normally considered noncovalent bonding. Several procedures for treating polarization are summarized, including the use of point charges and the direct inclusion of electric fields.     

Computational analysis of relative stabilities of polyazine N-oxides

There is considerable interest in polyazine N-oxides as potential frameworks for energetic compounds with relatively high enthalpies of formation and crystal densities. The N⁺→O^? linkages, if appropriately located, may diminish the destabilization associated with nitrogen catenation. We have computationally characterized 40 N-oxides of the isomeric diazines, triazines, and tetrazines in terms of their geometries, relative energies, and (for a representative selection) electrostatic potentials. The presence of N⁺→O^? linkages does partially counteract the destabilizing effects of nitrogen catenation, although the isomers with complete catenation remain the least stable. The stabilizing influence of N⁺→O^? groups, and the accompanying changes in bond lengths, can be understood in terms of resonance charge delocalization to the polyazine rings. The N(O)–N(O) bonds between nitrogens that both bear oxygens tend to be relatively weak. The electrostatic potentials above the polyazine rings become increasingly positive as there are more nitrogens and oxygens; eventually they are positive above all of the carbons and nitrogens and possibly even the oxygens, with negative regions only on the peripheries of the molecules. However, the nitrogens that bear oxygens always have more positive potentials than those that do not.     

Halogen Bonding: An Interim Discussion

Halogen bonding is a noncovalent interaction that is receiving rapidly increasing attention because of its significance in biological systems and its importance in the design of new materials in a variety of areas, for example, electronics, nonlinear optical activity, and pharmaceuticals. The interactions can be understood in terms of electrostatics/polarization and dispersion; they involve a region of positive electrostatic potential on a covalently bonded halogen and a negative site, such as the lone pair of a Lewis base. The positive potential, labeled a σ hole, is on the extension of the covalent bond to the halogen, which accounts for the characteristic near‐linearity of halogen bonding. In many instances, the lateral sides of the halogen have negative electrostatic potentials, allowing it to also interact favorably with positive sites. In this discussion, after looking at some of the experimental observations of halogen bonding, we address the origins of σ holes, the factors that govern the magnitudes of their electrostatic potentials, and the properties of the resulting complexes with negative sites. The relationship of halogen and hydrogen bonding is examined. We also point out that σ‐hole interactions are not limited to halogens, but can also involve covalently bonded atoms of Groups IV–VI. Examples of applications in biological/medicinal chemistry and in crystal engineering are mentioned, taking note that halogen bonding can be “tuned” to fit various requirements, that is, strength of interaction, steric factors, and so forth.     

A look at bonds and bonding

Structural Chemistry - Even after roughly a century of quantum theory, there is still debate, sometimes rather contentious, as to the nature of the chemical bond—or is it bonds, or is it...     

Synthesis of Novel Chiral Diol Ligands for the Enantioselective Reactions

The chiral diols ((,(,((,((-Tetraaryl-1,3-dioxolane-4,5-dimethanols) have been used for the formation of cyclic titanates and similar derivatives of Mg, Al and Zr. These complexes of oxophilic metal centers were employed in catalytic and stiochiometric enantioselective reactions such as enantioselective addition reactions of carbon-centered nucleophiles to aldehydes1, [2+2] cycloadditions2, and Diels-Alder reactions3. So far, the two hydrogen atoms of all this type of diols are in trans form…     

Enhanced detonation sensitivities of silicon analogs of PETN: reaction force analysis and the role of σ–hole interactions

Si-pentaerythritol tetranitrate (PETN), Si[CH₂ONO₂]₄, is a silicon analog of the widely used explosive PETN, C[CH₂ONO₂]₄. Si-PETN is extremely sensitive to impact, much more so than PETN. This was attributed by Liu et al. to Si-PETN having a much lower activation barrier to decomposition, via a facile rearrangement that is not as readily available to PETN, and which releases considerable energy that can promote further steps. We have investigated computationally why the barrier to the rearrangement is so much lower for Si-PETN than for PETN, using 5, (H₃C)₃C–CH₂ONO₂, and 6, (H₃C)₃Si–CH₂ONO₂, as models for PETN and Si-PETN. Reaction force analysis shows that most of the difference between the rearrangement barriers for 5 and 6 comes about in the initial (reactant) stages of the processes, in which 6 benefits from a 1,3 electrostatic interaction involving a positive σ–hole on the silicon and the negative linking oxygen. The analogous interaction is weaker in 5, since the central carbon does not have positive σ–holes; furthermore, this carbon is less able than silicon to temporarily expand its coordination sphere. A similar explanation involving a positive silicon σ–hole and a linking oxygen is proposed for Si-PETN. The greater exothermicity of the rearrangement of 6 (and also Si-PETN) can be rationalized, following Liu et al., in terms of the formation of the strong Si–O bond.     

基于箭形累积损伤的裂纹尖端力学:奇异性分级和多尺度分段

在适度的空间和时间尺度组合下,裂纹既可在几个月中蠕变几个纳米,也能在几秒钟内扩展10km.虽然裂纹的尖端没有实际的质量,但是它能通过激活周围的物质而处于高能量状态.依赖于材料的损伤方向,激活质量的减少和增加可发生在尺度转变之前或之后.每个尺度区的分段阈值被假定为与裂纹尖端速度的平方a~2和激活质量密度M的乘积有关:W=M_(↓↑)a_(↑↓)~2和D=M~(↓↑)a_(↑↓)~2.W和D分别被称为直接吸收和自耗散能量密度.正如下标/上标符号所示,激活的质量密度M_(↓↑)和M~(↓↑)与裂纹尖端速度a变化趋势相反,既可增加也可减少.a~2和M的互补效应隐含着常用于宇宙物理学建模的膨胀和/或收缩的物理过程.在用于尺度敏感的裂纹尖端的行为时,激活的质量密度有相同的解释.分段时的多尺度可以由…皮观、纳观、微观和宏观…组成.因此,形象地说,材料损伤过程可以通过裂纹扩展过程中非均匀的总体和局部能量的传递来模拟.疲劳裂纹扩展引起的材料损伤被用来阐释由大到小和由慢到快的尺度/时间序,热力学中的冷→热和有序→无序转换.这一过程正巧与宇宙演化的箭形方向相反,宇宙演化遵循小→大和快→慢,而热力学相反,遵循热→冷和无序→有序.为了表示由损伤萌生所造成的类裂缝型缺陷的不均匀性,提出了一个被称为裂纹尖端力学(crack tip mechanics,CTM)的新模式.涉及的范围是模拟原子列之间的界面裂纹或连续体中分叉的切口.假如需要的话,尺寸和时间的范围可以复盖从皮观到宏观甚至更大.虽然采用疲劳裂纹来说明CTM的基本原理,在宇宙物理学背景中与直接吸收和自耗散相关的膨胀和收缩的情况可以描述裂纹周围激活质量的行为,它们可看为能量的汇或源.奇异性被用来捕获能量的源或汇的特性,物理上,两者作为界面的一部分,从数学上看则是不连续的线的一部分.能量从一种形式变为另一种形式取决于能量吸收或耗散的箭形损伤时间,这之中牵涉到尺度分段和奇异性强度的联合应用.材料组分随时间的劣化是根据指定的设计寿命导出的,从而使材料的响应与加载率的时间历史匹配.2024-T3铝板的皮观/纳观/微观/宏观开裂模型用来说明什么地方可以增加结构的寿命部分.皮观/纳观/微观/宏观/结构系统的性能随时间劣化可以用9个尺度转变物理参数来描述:纳观/微观区有3个(μ_(na/mi)~*,σ_(na/mi)~*,d_(na/mi)~*),微观/宏观区有3个(μ_(mi/ma)~*,σ_(mi/ma)~*,d_(mi/ma)~*),皮观/纳观区有3个(μ_(pi/na)~*,σ_(pi/na)~*,d_(pi/na)~*).下标pi,na,mi,ma和struc分别表示皮观、纳观、微观、宏观和结构.只要知道两个相连的尺度敏感参数,在较低尺度的时间相关的局部物理参数就完成了分析连续体的形式论,虽然它们并不需要用实验来知道.更具体地说,根据皮观→纳观→微观→宏观分别有1.25/1.00/0.75/0.50的λ奇异性强度,皮观裂纹、纳观裂纹、微观裂纹和宏观裂纹的转变特征是从时间箭形的指定的寿命预期来确定的.附加的0.25强度的奇异性可用于结构元件.回想起来,λ=0.5相应于断裂力学中的应力分量与r~(0.5)成反比,r是与宏观裂纹尖端的距离.微观裂纹、纳观裂纹和皮观裂纹分别赋予r~(-0.75),r~(-1.0),r~(-1.25)的奇异性.箭形时间(以年为单位)取决于问题的定义.设备的关键部件可用1.5~±/2.5~±/3.5~±/5.5~±寿命分布和总寿命为13~±年(a)的皮观/纳观/微观/宏观尺度来设计运行.上标±表示多于或少于实际运行的时间.累进损伤被假定为发生在皮观→纳观→微观→宏观方向.同样的方案用于20年总寿命的2024-T3铝板的疲劳损伤,按照1.5~±/2.5~±/3.5~±/5.5~±/7.0~±的方式将它的寿命分布在皮观、纳观、微观、宏观和结构的尺度上,这样的指定只是满足在每个尺度范围内损伤内部材料结构所用的能量匹配,因此可以强制执行在总寿命的跨度内精确的时间相关的材料性能劣化过程.     

Correlations of peaks of Gaussian random fields

The high peaks of a Gaussian random field are studied. Asymptotic expansions, appropriate for high peak thresholds and large spatial separations, are developed for theN-point correlation functions of the number density of high peaks, in terms of the two-point correlation of the underlying Gaussian field. Similar expressions are derived for the correlations of points, not necessarily the positions of peaks, where the field exceeds a high threshold.Work supported in part by U.S. Department of Energy under contract DEAC03-81-ER40050.KFAS Graduate FellowAlfred P. Sloan Foundation Fellow and supported in part by U.S. Department of Energy Outstanding Junior Investigator Program under contract No. DE-FG03-84 ER40172     

The diffraction of elastic waves by an imperfect fusion bond

We consider diffraction by a semi-infinite crack located alonga fusion interface between two differing elastic media. Twotypes of crack, namely open and partially closed cracks, areinvestigated. An open crack is modelled by a stress-free contactboundary condition and a partially closed crack is modelledby a spring contact boundary condition. For the latter, thejump in the stress across the crack is assumed to be proportionalto the jump in the displacement across the crack. This situationarises in, for example, a K-weld where the fine grain of theparent material (for example, ferritic or forged austeniticsteel) is in stark contrast with the coarse-grained weld metal(for example, austenitic weld metal). In the metal weld thedirection of the grain axis varies through the metal. However,diffraction is a local phenomenon and so the austenitic steelis assumed to have a zonal axis so that it may be modelled bya transversely isotropic composite. The ferritic or forged austeniticsteel will be modelled as an isotropic material.     

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