A Generalized Unpaired Electron Spin Density Equation and Organic Hyperconjugation Mechanism

A large class of stereochemcial and related interactions in organic chemistry are repulsive and others are attractive, but the relative orientation of two methyl groups and the amount of energy required to twist one relative to the other (the hindered rotation energy barriers), or the alignment of such a group with respect to a conjugated ring to which it is attached (widely attributed to a mechanism called “hyperconjugation”) are estimated to be small in compared with the total energy of the molecule. We used theories of both isotropic and anisotropic proton hyperfine interactions in the π‐electron systems developed in the early sixties. They are approximated by the magnetic dipole nteractions between each proton and an electron spin magnetization that is distributed in 2s and 2p Slater atomic orbitals center on carbon atoms. We have extended these theories to the non‐planar olefinic cation radicals, which are very important in biochemistry as well as in petroleum catalysis. A three dimensional electron spin density equation has been developed in this paper to handle some Jahn‐Teller vibronic molecules. The new electron spin density equation related the observed proton hyperfine splittings to the non‐planar structures of the open‐chain alkene cation radicals generated by radiolysis and various chemical oxidation methods. The spin densities and the conformational calculations based on valence bond theory and symmetry principles are compared with some more elaborated molecular orbital calculations in the literature. The localized valence bond approaches are better in accord with our experimental results. The anomalous line‐width effect of the four methyl groups observed in the 2,3‐dimethyl‐2‐butene cation radicals also confirmed the positive sign of the electron‐proton hyperfine constant of hyper‐conjugation mechanism. A methyl substituent attached to a conjugated molecule often behaves as if it formed part of the region of conjugation; the charge appears to flow from the methyl group into the π electron system and it may also give rise to an appreciable dipole moment. Methylation also gives rise to an appreciable dipole moment, and the resultant red shift of electronic absorption bands is of some importance in the design of dye molecules.     

Approximation bounds for quadratic maximization and max-cut problems with semidefinite programming relaxation

In this paper,we consider a class of quadratic maximization problems.For a subclass of the problems,we show that the SDP relaxation approach yields an approximation solution with the ratio is dependent on the data of the problem with α being a uniform lower bound.In light of this new bound,we show that the actual worst-case performance ratio of the SDP relaxation approach (with the triangle inequalities added) is at least α δd if every weight is strictly positive,where δd ＞ 0 is a constant depending on the problem dimension and data.     

高能核碰撞中带电多重数快度与能量和中心度的关系

用强子–弦级联模型JPCIAE及相应的Monte Carlo事例产生器研究相对论性核–核碰撞中带电粒子多重数的赝快度密度对能量和中心度的依赖关系.无需另调任何模型参数的条件下,此模型可以同时较好地描述相对论性pp实验数据及PHOBOS和PHENIX实验组的Au+Au实验数据.本文指出:因〈N_part〉并非严格定义的物理量,致使实验上和理论上确定〈N_part〉有一定任意性,从而使得每参加者核子对的带电粒子赝快度密度随着〈N_part〉的增加可能逐渐增大,也可能逐渐减小,因此用它来区分粒子产生机制是欠妥的.     

Ab-initio simulation of elastic constants for some ceramic materials

Athermal elasticity for some ceramic materials (α-Al₂O₃, SiC (α and β phases), TiO₂ (rutile and anatase), hexagonal AlN and TiB₂, cubic BN and CaF₂, and monoclinic ZrO₂) have been investigated via density functional theory. Energy-volume equation-of-state computations to obtain the zero pressure equilibrium volume and bulk modulus as well as computations of the full elastic constant tensor of these ceramics at the experimental zero pressure volume have been performed. The present results for the single crystal elasticity are in good agreement with experiments both for the aggregate properties (bulk and shear modulus) and the elastic anisotropy. In contrast, a considerable discrepancy for the zero pressure bulk modulus of some ceramics evaluated from the energy-volume fit to the computational zero pressure volume has been observed.     

Applications of density functional theory methods in millimeter‐wave spectroscopy

Density functional theory (DFT), using the most common functionals, and ab initio quantum chemistry methods are used to calculate the rotational constants and dipole moments of the astrophysically important molecules HCN, CH₃CN, CH₃CNH⁺, HCCCN, and HCCNC. As far as millimeter‐wave spectroscopy is of interest the DFT methods performed well with most functionals, giving results within ±1% of experiments for rotational constants and ±3% for dipole moments. Analyzing the results obtained with all theoretical models, it may be concluded that the Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Paar (B3LYP) and Becke's three‐parameter functional with Perdew–Wang correlational functional [B3PW91/6‐31G(d, p)] give the best performances. A detailed analysis of the electron correlation effects shows that HCCCN is more stable than is HCCNC, by 1.16 eV, with important contribution arising from triple excitations. This result is also compared with those obtained with DFT methods. Despite occasional difficulties, DFT with the currently available functionals are of great utility in quickly assessing spectroscopic parameters of astrophysical interest. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

First-principle studies on the electronic structure of Fe3O4(110) surface

The first-principle was employed to study the six possible models for the Fe₃O₄(110) surface, namely the AB-terminated surface (AB model), the AB-terminated with Fe_A vacancy (AB-Fe_A vac model), the AB-terminated with Fe_B vacancy (AB-Fe_B vac model), the B-terminated surface (B model), the B-terminated surface with Fe_B vacancy (B-Fe_B vac model) and the B-terminated surface with O vacancy (B-O vac model). The stability, the electronic structure and the magnetic properties of the six surface models were also calculated. The results predict that the B-O vac model is more stable than other types of surface models. The half-metallic property remain in the AB and B models, while the other four surface models exhibit metallic properties. At the same time, the AB, AB-Fe_A vac, AB-Fe_B vac, B and the B-Fe_B vac models have ferrimagnetic properties, while the B-O vac model has antiferromagnetic property.      

Charge density fluctuation of low frequency in a dusty plasma

The charge density fluctuation of low frequency in a dusty plasma, which is derived from the longitudinal dielectric permittivity of the dusty plasma, has been studied by kinetic theory. The results show that theP value, which describes the relative charge density on the dust in the plasma, and the charging frequency of a dust particle Ω _c , which describes the ratio of charge changing of the dust particles, determine the character of the charge density fluctuation of low frequency. For a dusty plasma ofP≪1, when the charging frequency Ω _c , is much smaller than the dusty plasma frequency ω_d, there is a strong charge density fluctuation which is of character of dust acoustic eigenwave. For a dusty plasma ofP≫1, when the frequency Ω _c , is much larger than ω _d there are weaker fluctuations with a wide spectrum. The results have been applied to the ionosphere and the range of radius and density of dust particles is found, where a strong charge density fluctuation of low frequency should exist.     

对数似然比与整值随机变量序列的一类强律

本文引进对数似然比作为整值随机变量序列相对于服从几何分布的独立随机变量序列的偏差的一种度量,并通过限制对数似然比给出了样本空间的一个子集.在此子集上得到了一类用不等式表示的强律,其中包含整值随机变量序列与相对熵密度及几何分布的熵函数有关的若干极限性质.     

Steady-state electrolysis at a grooved or ridged plane

This study concerns an infinite plane whose smoothness is marred by a single defect: either a groove or a ridge. The blemished plane serves as an electrode supporting a diffusion-controlled steady-state process. By using a convenient coordinate transformation, the local current density at all points on the surface is determined exactly. The results are found to confirm intuitive expectations. Thus, compared with normal values on the plane remote from a groove, the electron transfer rate is diminished within the groove but enhanced along its margins. Similarly, an abnormally large transfer rate is encountered high on the ridge but the rate is subnormal on its lower flanks. The total current is demonstrated to be unchanged by the presence of the blemish. Received: 27 September 1996 / Accepted: 11 March 1997