Numerical calculation of overlap and kinetic integrals in prolate spheroidal coordinates. II

The efficient algorithm calculating the overlap and the kinetic integrals for the numerical atomic orbitals is presented. On the basis of the prolate spheroidal coordinates, the overlap and the kinetic integral are reduced to the integral over the rectangular domain. The integration over the rectangular domain is performed by the adaptive integration scheme. The developed algorithm is applied to calculate the integrals for the pairs of hydrogen and gallium eigenfunctions. It is demonstrated that high accuracy can be obtained for small number of integrand evaluations what guarantees the efficiency of the presented algorithm. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

On the computation of molecular auxiliary functions A n and B n

Molecular auxiliary functions A _n (p) and B _n (pt), arising in the Hartree-Fock-Roothaan (HFR) approximation for molecules, Ewald’s crystal lattice theory, electromagnetic stopping theory, and other approximate methods, are evaluated and analysed in the range of 17≤n≤60 and 25≤pt≤60.     

An atomic linear Stark shift violating P but not T arising from the electroweak nuclear anapole moment

We propose a direct method of detection of the nuclear anapole moment. It is based on the existence of a linear Stark shift for alkali atoms in their ground state perturbed by a quadrupolar interaction of uniaxial symmetry around a direction and a magnetic field. This shift is characterized by the T-even pseudoscalar ( ^. )(∧ ^. )/B ². It involves on the one hand the anisotropy of the hyperfine interaction induced by the quadrupolar interaction and, on the other, the static electric dipole moment arising from electroweak interactions inside the nucleus. The case of ground state Cs atoms trapped in a uniaxial (hcp) phase of solid ⁴He is examined. From an explicit evaluation of both the hyperfine structure anisotropy and the static dipole deduced from recent empirical data about the Cs nuclear anapole moment, we predict the Stark shift. It is three times the experimental upper bound to be set on the T-odd Stark shift of free Cs atoms in order to improve the present limit on the electron EDM. Received 20 December 2000     

键能的分子轨道理论研究2: 键能与Mulliken布居对键强度的 判断的比较

用键能E~A~B和Mulliken布居对化学键强度的判别进行了分析比较。结果表明,键能判据比Mulliken布居判据所得结论更符合实际情况。作为衡量原子间化学键强度的尺度,不仅应考虑原子轨道间的布居因素,还应考虑分子轨道(或原子轨道)的能量因素。     

C-H 键和C-C 键核自旋偶合常数的理论研究

利用PM3级别最大重迭对称性分子轨道法和最大键级杂化轨道方法,计算了系列烃类化合物的杂化轨道和电荷分布,拟合出计算C-H及C-C偶合常数的简单关系式. 研究了各种烃类分子中不同的C-H键和C-C键偶合常数,理论计算值和实验数据都较为符合. 进一步验证了直接键连¹J_CX偶合常数主要取决于偶合作用中的Fermi接触项,为从简单价键理论角度解释和计算¹J_CH和¹J_CC提供了一种简便直观的方法.     

EFFECT OF Z-PINS＇ DIAMETER, SPACING AND OVERLAP LENGTH ON CONNECTING PERFORMANCE OF CMC SINGLE LAP JOINT

The effect of through-thickness reinforcement by composite pins （Z-pins） on the static tensile strength and failure mechanisms of the joints made from ceramic matrix composite （CMC） is investigated. Overlap length of the single lap joint is 15 mm, 20 mm, 23 mm, 37 mm, and 60 mm, respectively. The experimental results indicate that the final failure modes of the joints can be divided into two groups, （a） the bond-line stops debonding until crack encounters Z-pins; and then the adherends break at the location of Z-pins, when overlap length is more than 20 mm; （b） the bond-line detaches entirely and Z-pins are drawn from adherends, when overlap length is equal to 15 mm. A simple efficient computational approach is presented for analyzing the benefit of through-thickness pins for restricting failure in the single lap joints. Here, the mechanics problem is simplified by representing the effect of the pins by tractions acting on the fracture surfaces of the cracked bond-line. The tractions are prescribed as functions of the crack displacement, which are available in simple forms that summarize the complex deformations to a reasonable accuracy. The resulting model can be used to track the evolution of complete failure mechanisms, for example, bond-line initial delamination and ultimate failure associated with Z-pin pullout, ultimate failure of the adherends. The paper simulates connecting performance of the single lap joints with different Z-pins＇ diameter, spacing and overlap length; the numerical results agree with the experimental results; the numerical results indicate enlarging diameter and decreasing spacing of Z-pins are in favor of improving the connecting performance of the joints. By numerical analysis method, the critical overlap length that lies between two final failure modes is between 18 mm and 19 mm, when Z-pins＇ diameter and spacing are 0.4 mm, 5 mm, respectively.     

Mulliken布居对键强度判断的经验修正

Ｍｕｌｌｉｋｅｎ布居是Ｍｕｌｌｉｋｅｎ[1]提出的表示电荷在各组成原子之间分布情况的方法 .Ｍｕｌｌｉｋｅｎ指出 ,成键原子Ａ和Ｂ间的总重叠电荷ｎ(Ａ ,Ｂ)反映Ａ和Ｂ原子间形成共价键的程度 ,若ｎ(Ａ ,Ｂ)很大 ,则Ａ和Ｂ原子间有共价键存在 ,若ｎ(Ａ ,Ｂ)很小 ,则表示Ａ和Ｂ原子间不存在化学键或离子键 .但是 ,Ｍｕｌｌｉｋｅｎ的方法也有一些严重的缺陷 ,使得Ｍｕｌｌｉｋｅｎ布居分析在某些情况下得到的数值不合理 ,影响了其应用 .为克服Ｍｕｌｌｉｋｅｎ布居的这些缺陷 ,有人提出将重叠区电荷在两原子间加权分配[2 ],Ｐｏｌｌａｋ等…     

On Evaluation of Overlap Integrals with Noninteger Principal Quantum Numbers

By use of complete orthonormal sets of ψ^α exponential-type orbitals (ψ^α-ETOs,α=1,0,-1,-2,...) the series expansion formulas for the noninteger n Slater-type orbitals (NISTOs) in terms of integer n Slater-type orbitals (ISTOs) are derived. These formulas enable us to express the overlap integrals with NISTOs through the overlap integrals over ISTOs with the same and different screening constants. By calculating concrete cases the convergence of the series for arbitrary values of noninteger principal quantum numbers and screening constants of NISTOs and internuclear distances is tested. The accuracy of the results is quite high for quantum numbers, screening constants and location of STOs.     

Evaluation of expansion coefficients for translation of Slater‐type orbitals using complete orthonormal sets of exponential‐type functions

By the use of exponential‐type functions (ETFs) the simpler formulas for the expansion of Slater‐type orbitals (STOs) in terms of STOs at a displaced center are derived. The expansion coefficients for translation of STOs are presented by a linear combination of overlap integrals. The final results are of a simple structure and are, therefore, especially useful for machine computations of arbitrary multielectron multicenter molecular integrals over STOs that arise in the Hartree–Fock–Roothaan approximation and also in the Hylleraas correlated wave function method for the determination of arbitrary multielectron properties of atoms and molecules. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 126–129, 2001     

对称性轨道的构造

提出1种以配体轨道的旋转性质为基础,并利用群生成元表示矩阵来构造对称性轨道的新方法。讨论了对称性系数之间的相互关系,同时给出群重迭积分的计算过程。