The W algorithm and the D transformation for the numerical evaluation of three‐center nuclear attraction integrals

Three‐center nuclear attraction integrals over exponential‐type functions are required for ab initio molecular structure calculations and density functional theory (DFT). These integrals occur in many millions of terms, even for small molecules, and they require rapid and accurate numerical evaluation. The use of a basis set of B functions to represent atomic orbitals, combined with the Fourier transform method, led to the development of analytic expressions for these molecular integrals. Unfortunately, the numerical evaluation of the analytic expressions obtained turned out to be extremely difficult due to the presence of two‐dimensional integral representations, involving spherical Bessel integral functions. % The present work concerns the development of an extremely accurate and rapid algorithm for the numerical evaluation of these spherical Bessel integrals. This algorithm, which is based on the nonlinear D transformation and the W algorithm of Sidi, can be computed recursively, allowing the control of the degree of accuracy. Numerical analysis tests were performed to further improve the efficiency of our algorithm. The numerical results section demonstrates the efficiency of this new algorithm for the numerical evaluation of three‐center nuclear attraction integrals. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Comparison study of several numerical integration schemes used in calculations of density functional theory

Several numerical integration schemes for the evaluation of matrix elements in density functional theory calculations have been studied and compared by computational practice. The best scheme was found to be the combination of the atomic partition function proposed by Becke with the scaled generalized Gauss-Laguerre quadrature formula for radial integration suggested by Yang, which achieve the highest convergence rate to the numerical integration. With the same number of integration points, the accuracy of the calculated results by this scheme is higher by 1 to 2 orders of magnitudes than that by other schemes. The reason for achieving higher accuracy by this scheme has been proposed preliminarily.     

Electrochemically Induced Iron Release of Adsorbed Horse Spleen Ferritin: Quantitation of Iron Using Long Optical Path Length Thin‐Layer Spectroelectrochemistry

In this work, long optical path length thin‐layer electrochemical cell was constructed using indium‐tin oxide on glass as the electrode material. Iron release from ferritin adsorbed on the electrode was induced by applying a negative potential sweep in the presence of 1,10‐phenanthroline. The usefulness of spectroelectrochemistry as a means of determining the quantity of iron released from an adsorbed layer of ferritin is demonstrated.     

On the influence of nuclear fluctuations on calculated NMR shieldings of benzene and ethylene: a Feynman path integral–ab initio investigation*

The absolute magnetic shieldings of benzene and ethylene have been theoretically studied under the conditions of thermal equilibrium, i.e., under explicit consideration of the nuclear degrees of freedom. For this purpose we have combined the Feynman path integral quantum Monte Carlo (PIMC) formalism with the gauge‐including atomic orbital (GIAO) approach in the Hartree–Fock (HF) approximation. The HF operator has been employed to derive the NMR parameters of the two hydrocarbons via an ensemble averaging over large sets of molecular configurations that are populated in thermal equilibrium. The nuclear fluctuations are responsible for a deshielding of the nuclei relative to the shieldings at the vibrationless minimum of the potential energy surface (PES). The influence of the nuclear degrees of freedom is largest for the isotropic part of the ¹³C shielding tensor. The theoretical results can be explained on the basis of simple geometrical considerations. The bond lengths in thermal equilibrium are larger than the bond lengths at the minimum of the PES. This length enhancement is the prerequisite for a deshielding of the nuclei in thermal equilibrium. The vibrational corrections of the nuclear magnetic resonance (NMR) parameters of benzene and ethylene are quantum driven; classical thermal degrees of freedom of the nuclei are of minor importance. Conceptual problems of theoretical studies of NMR parameters on the basis of a single molecular geometry are emphasized. The influence of the spatial uncertainty of the nuclei becomes decisive in molecules with light atoms. It is pointed out that the combination of the PIMC formalism with electronic Hamiltonians of state‐of‐the‐art quality renders possible accurate determinations of NMR parameters. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem 86: 280–296, 2002     

Theoretical Study on Photoisomerization of 2-Methylfuran to 3-Methylfuran

1 INTRODUCTION 2-Methylfuran belongs to the basic heteroaromatic compounds relevant to many fields of modern che- mistry, ranging from the study of natural products and biologically active substances to the develop- ment of building blocks for organic synthesis and conducting polymers[1]. Since the photochemistry ofR-furan was gradually recognized in 1960s[2～7], lots of interest has been aroused. Herein we only study one branch of photoche- mistry of R-furan: the isomerization of 2-methy…     

PWM/PFM双模调制的高效率DC/DC开关电源

利用根据负载电流的大小改变调制模式的方法实现了一种降压型高转换效率的DC/DC开关电源,并采用二次集成的方式在芯片内部集成了功率p-M O SFET。当控制电压占空比小于20%时,采用PFM(Pu lse-F requency M odu lation)模式调制;占空比大于20%时,采用PWM(Pu lse-W idth M odu lation)模式调制,平均转换效率约为93%,输出电流范围可以从0.01 A到3.0 A。当输出驱动电流为3.0 A时,整个调制控制电路的功耗仅为6.0 mW。输入电压为5 V时,负载调整率小于1.5%;负载电流为0.01 A时,线性调整率小于0.5%。     

基于图形理论的Ad Hoc网络容量研究

网络容量是评估无线Ad Hoc网络性能的重要参数。本文的目的是研究如何使Ad Hoc网络容量达到最大。文章从一个全新的角度考虑Ad Hoc网络的建模，核心思想是Ad Hoc网络节点间的传输具有有限资源（包括带宽、功率等），在同等条件下若能使网络传输消耗资源最小，则网络容量迭到最大。建立了资源消耗的线性规划方程，利用图论的方法对问题求解并对算法进行改进，得到相应的路由策略。由仿真试验说明修改后的算法更加高效。     

基于亲水表面处理的GaAs/GaN晶片直接键合

对晶片进行亲水表面处理,在氮气保护下500℃热处理10min,成功实现GaAs与GaN晶片的直接键合,键合质量较好.扫描电子显微镜观测结果表明,键合界面没有空洞.光致发光谱观测结果表明,键合工艺对晶体内部结构的影响很小.可见光透射谱测试结果表明,键合界面具有良好的透光特性.GaAs与GaN晶片直接键合的成功,为实现GaAs和GaN材料的集成提供了实验依据.     

运用模糊数解决非确定环境下的路由问题

本文基于模糊数学的有关原理,论述了网络环境不确定的条件下路由问题的求解.本文假定网络链路延迟是模糊数,给出了路径延迟小于端到端延迟约束的可信度的定义,提出了路径可信度判定(Path Reliability Decision:PRD),最优可信度路由(Most Optimal Reliability Path:MORP),最优路径分解(Path Optimal Partition:POP),及最优分解路径(Most Optimal Partition Path:MOPP)等问题.本文证明,PRD是多项式可解的,POP可以用等可信度分解实现,一般情况下,MORP和MOPP是等价的.在所有链路延迟的宽度都相同时,MORP转化为约束为跳数的最短路径问题,因此是多项式可解的.最后我们给出了MORP的近似算法,算法的时间复杂度为O(log(ε)^-1(vlog(v)+e)).     

高能闪光照相中影响光程确定的几个因素

 利用闪光照相基本原理和成像原理，在直接记录法和转换屏记录法的情况下，研究了闪光照相中影响X射线在材料中光程确定的主要因素。结果表明，影响光程确定的几个因素是：散射效应、光源角分布效应、立体角效应和能谱效应。对于高能闪光照相，散射效应是影响光程确定的最主要因素，散射的存在使光程的测量值比实际值降低20%～40%。因此必须在做CT之前，对散射的影响进行修正。