利用新构建势能面3A研究S(3P)+H2→HS+H反应含时波包量子散射

利用高精度从头算能量点构建三重态³A' 势能面. 单点能计算采用的方法是完全活性空间自洽场和多组态相互作用,计算中所用的基组是aug-cc-pV5Z,并利用多体展开方法结合AP函数形式对所有能量点进行了拟合. 在新构建的势能面基础上,在平动能0.8～2.2 eV进行了含时波包散射计算,计算中同时采用了离心突然近似和紧耦合方法. 另外还对初始振动态ν=0～3(j=0)情况下的总反应几率进行了计算,结果发现初始振动激发对该体系有很大的增强作用.     

计算平均力势的理论方法

提出了一个用于计算平均力势的普适性的理论框架,方法克服了以前的方法的缺陷,仅仅需要溶剂粒子在单个溶质粒子附近的密度分布作为输入.计算了两个大尺寸溶质粒子浸在小尺寸硬球溶剂浴中的平均力势,理论预言与可能的模拟数据符合.调查了溶剂-溶质相互作用势、溶剂密度、溶质粒子尺寸对过量平均力势的影响.结论是:溶剂粒子在单个溶质粒子附近的减少导致吸引的过量平均力势,而溶剂粒子在单个溶质粒子附近的聚集导致排斥的过量平均力势,高溶剂密度与大溶质粒子尺寸能强化这种趋势.讨论了这种空耗吸引-聚集排斥与生物学中的疏水吸引-水化排斥的联系.     

相互作用势对模拟计算单壁碳纳米管物理吸附储氢的影响

采用巨正则Monte Carlo方法模拟氢分子在单壁碳纳米管中的储存与分布,重点研究了Lennard-Jones势、Crowell-Brown势和Silvera- Goldman势对模拟计算单壁碳纳米管物理吸附储氢的影响.计算结果显示,碳纳米管与氢分子间的相互作用宜采用Lennard-Jones势描述;氢分子与氢分子间相互作用的描述则与碳纳米管的管径有关,管径较小时选Lennard-Jones势较佳,管径偏大时取七参数Silvera-Goldman 势更为合理,而三参数Silvera-Goldman势则不宜采用;并给出了相应的理论解释.     

von Neumann代数中套子代数上的Lie同构

本文给出因子von Neumann代数中的幂等算子在广义Lie积下的一个刻画; 得到因子von Neumann代数中套子代数的幂等算子在Lie积下的一个特征．作为应用, 研究了因子von Neumann代数中套子代数上的Lie同构,并证明因子von Neumann 代数中套子代数之间的Lie同构,要么是同构与广义迹之和,要么是负反同构与广义迹之和．     

The H2+ molecular ion: Low-lying states

Matching for a wavefunction the WKB expansion at large distances and Taylor expansion at small distances leads to a compact, few-parametric uniform approximation found in Turbiner and Olivares-Pilon (2011). The ten low-lying eigenstates of H₂⁺ of the quantum numbers (n,m,Λ,±)$(n,m,\Lambda ,\pm )$  with n=m=0$n=m=0$ at Λ=0,1,2$\Lambda =0,1,2$, with n=1$n=1$, m=0$m=0$ and n=0$n=0$, m=1$m=1$ at Λ=0$\Lambda =0$ of both parities are explored for all interproton distances R$R$. For all these states this approximation provides the relative accuracy ?10⁻⁵$?10^{-5}$ (not less than 5 s.d.) locally, for any real coordinate x$x$ in eigenfunctions, when for total energy E(R)$E\left(R\right)$ it gives 10-11 s.d. for R∈[0,50]$R\in [0,50]$  a.u. Corrections to the approximation are evaluated in the specially-designed, convergent perturbation theory. Separation constants are found with not less than 8 s.d. The oscillator strength for the electric dipole transitions E1$E1$ is calculated with not less than 6 s.d. A dramatic dip in the E1$E1$ oscillator strength f_{1sσg−3pσu}$f_{1s{\sigma }_g-3p{\sigma }_u}$ at R∼R_eq$R\sim R_{eq}$ is observed. The magnetic dipole and electric quadrupole transitions are calculated for the first time with not less than 6 s.d. in oscillator strength. For two lowest states (0,0,0,±)$(0,0,0,\pm )$ (or, equivalently, 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ states) the potential curves are checked and confirmed in the Lagrange mesh method within 12 s.d. Based on them the Energy Gap between 1sσ_g$1s{\sigma }_g$ and 2pσ_u$2p{\sigma }_u$ potential curves is approximated with modified Pade Re^−R[Pade(8/7)](R)$R{e}^{-R}\left[Pade(8/7)\right]\left(R\right)$ with not less than 4-5 figures at R∈[0,40]$R\in [0,40]$ a.u. Sum of potential curves E_1sσg+E_2pσu$E_{1s{\sigma }_g}+E_{2p{\sigma }_u}$ is approximated by Pade 1/R[Pade(5/8)](R)$1/R\left[Pade(5/8)\right]\left(R\right)$ in R∈[0,40]$R\in [0,40]$ a.u. with not less than 3-4 figures.     

Additive maps preserving the ascent and descent of operators

Let and be the algebras of all bounded linear operators on infinite dimensional complex Banach spaces X and Y, respectively. We characterize additive maps from onto preserving different quantities such as the nullity, the defect, the ascent, and the descent of operators.     

Operators associated with the Jacobi semigroup

The aim of this paper is to introduce some operators induced by the Jacobi differential operator and associated with the Jacobi semigroup, where the Jacobi measure is considered in the multidimensional case.In this context, we introduce potential operators, fractional integrals, fractional derivates, Bessel potentials and give a version of Carleson measures.We establish a version of Meyer’s multiplier theorem and by means of this theorem, we study fractional integrals and fractional derivates.Potential spaces related to Jacobi expansions are introduced and using fractional derivates, we give a characterization of these spaces. A version of Calderon’s Reproduction Formula and a version of Fefferman’s theorem are given.Finally, we present a definition of Triebel–Lizorkin spaces and Besov spaces in the Jacobi setting.     

应变速率和电位对应力腐蚀裂纹扩展的影响

以滑移-溶解-再钝化模型为基础,推导出应力腐蚀裂纹扩展速率与裂尖应变速率和电位之间的理论公式.计算表明,在裂纹扩展速率与裂尖应变速率的关系曲线中有两个特征区域.裂纹扩展速率在区域I随裂尖应变速率增加而增大,而在区域II不随裂尖应变速率的改变而变化.用慢应变速率拉伸技术（SSRT）测量了304L不锈钢的裂纹增长速率.当电位控制在区域II的阳极区时,理论计算的裂纹扩展速率与实验得到的结果比较吻合.