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1.
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. 相似文献
2.
Yuji Naruse Atsushi Takamori Itsuki Nagasawa 《Phosphorus, sulfur, and silicon and the related elements》2020,195(7):523-525
AbstractWe 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. 相似文献
3.
缪正武 《浙江大学学报(理学版)》2019,46(6):680-685
提出利用拉格朗日乘子法重新证明σ 2 ![]()
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算子的最优凹性,并定义了一个凸锥Γ 3 ? = λ = ( λ 1 , λ 2 , ? , λ n ) ∈ R n : σ 1 ( λ ) > 0 , σ 2 ( λ | i ) > 0 , 1 ≤ i ≤ n ![]()
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。利用σ 2 ![]()
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算子的最优凹性,给出了σ 2 H e s s i a n 方 程 P o g o r e l o v ![]()
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型C 2 ![]()
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内估计,进而证明了σ 2 ( D 2 u ( x ) ) = 1 , x ∈ R n ![]()
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的满足二次多项式增长条件的Γ 3 ? - ![]()
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凸整解为二次多项式。 相似文献
4.
《Journal of computational science》2014,5(4):590-596
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. 相似文献
5.
Hong-Lei Xu Dr. Ivan A. Popov Nikolay V. Tkachenko Dr. Zi-Chuan Wang Prof. Dr. Alvaro Muñoz-Castro Prof. Dr. Alexander I. Boldyrev Prof. Dr. Zhong-Ming Sun 《Angewandte Chemie (Weinheim an der Bergstrasse, Germany)》2020,132(39):17439-17443
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. 相似文献
6.
Gerui Pei Dr. Pei Zhao Song Xu Xintian Zhao Prof. Chuncai Kong Prof. Zhimao Yang Prof. Masahiro Ehara Prof. Tao Yang 《ChemistryOpen》2020,9(11):1195-1201
The coordination of 10-electron diatomic ligands (BF, CO N2) to iron complexes Fe(CO)2(CNArTripp2)2 [ArTripp2=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(CNArTripp2)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(CNArTripp2)2 bond was disclosed to be the classic dative bond E2E1→Fe(CO)2(CNArTripp2)2 rather than the electron-sharing double bond. More interestingly, the bonding strength between BF and Fe(CO)2(CNArTripp2)2 is much stronger than that between CO (or N2) and Fe(CO)2(CNArTripp2)2, which is ascribed to the better σ-donation and π back-donations. However, the orbital interactions in CN−→Fe(CO)2(CNArTripp2)2 and NO+→Fe(CO)2(CNArTripp2)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(CNArTripp2)2 fragments. 相似文献
7.
8.
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. 相似文献
9.
Pradeep R. Varadwaj Arpita Varadwaj Helder M. Marques Koichi Yamashita 《Molecules (Basel, Switzerland)》2022,27(5)
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. 相似文献
10.
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。 相似文献