用诱导自洽方法计算振动力常数的研究

本文提出一种迭代方法计算振动力常数,可以比较清楚地显示基频与振动力常数之间的关系,从而能方便地选择合适的力常数限制条件,得到合理的结果.用本方法对一系列不同分子作了计算,结果比较满意,对计算中一些具体问题作了讨论.     

大型广义特征值问题的部分特征值和特征向量的块迭代求解

将求解标准特征值问题的Davidson方法推广到求解大型广义特征值问题, 并给出了相应的块迭代算法. 经过理论分析和数值计算发现, 如果迭代过程不发散, 则块迭代算法经过有限次迭代一定收敛. 设矩阵的维数为n, 要求的特征值和相应特征向量的个数为k, 初始的子空间大小为r(r≥k),迭代次数为m,则它们之间满足关系n=r+km. 通过调节子空间大小, 就得到迭代次数m的正整数解.     

POLYMATH软件在化工课程中的应用

以化学工程中的非线性方程、复杂函数的积分、离散数据点的处理、实验数据点的回归分析以及线性微分方程组求解为例,讨论POLYMATH软件在化学与化工课程中的应用。结果表明：利用POLYMATH求解计算问题稳定性好、方便快捷;能把学生从复杂的编程与调试中解脱出来,并能提高学生的学习效率以及分析问题和解决问题的能力。     

用Matlab求解化工原理计算问题的教学初探

以管路计算中的设计型问题和精馏过程计算中的操作型问题为例,分析了求解问题的思路,列出了详尽的Matlab计算源程序。计算过程及结果表明,利用Matlab求解化工原理计算问题具有数值稳定性好、使用方便、高效、快速等特点。     

自洽场迭代中的复对角位移法

本文把自洽场迭代的实对角位移公式推广到复数的场合,形成复对角位移公式。在理论上证明了该公式的收敛性,并且当自变量由复数退化为实数时,复对角位移公式就还原为实对角位移公式,从而论证了前者是后者的推广。复对角位移公式已被成功地应用到包括复数FOCK矩阵运算的MNDO/GIAO及INDO/GIAO核磁共振屏蔽常数的理论计算中去。全面收敛的结果表明,这是一种行之有效的解决复矩阵迭代收敛性的方法。     

十字交叉法的导出和运用

十字交叉法也称图解法,作为一种简化的解题方法,应用于二元混合体系具有平均值的计算问题,它具有简化思路、简便运算、计算速度快等显著优点。近年来,十字交叉法在中学化学计算中广泛使用,有许多高考题也可用此法快速求解。但是,到目前为止,一些书刊对该方法的介绍仅仅局限于简单推导、应用的范畴,且应用时始终把平均值放在“十字”的中间,而没有把通过十字交叉得到差值的比值的含义如何确定讲清楚,     

配位滴定终点误差的通用计算方法*

依据终点误差的体积比定义式,滴定分析中所加入滴定剂的体积与待测体系的初始体积之比是计算终点误差的关键。建立了配位滴定中关于体积比的一般方程,提出了求解该方程的迭代策略,并给出了终点误差的计算实例。结果表明,该方法具有适应范围广、计算精度高的特点。     

非交替烃HOMO、LUMO、LOMO能量计算

本文将前文~[1,2]建议的直接计算交替烃HOMO(最高占据分子轨道)、LUMO(最低未占分子轨道)能量的方法推广到非交替烃。在HMO近似内, 对非交替烃分子的邻接矩阵联合应用逆迭代和Rayleigh商, 只需迭代一次就能得到该分子HOMO(或LUMO)能量的足够精确的结果。文中提出了计算的格式, 说明了选择初始变分函数的原则。用这种方法, 计算了30个分子的前线轨道~[3]能量, 平均误差为0.002β。本文提出了计算LOMO(最低占据分子轨道)能量的拓扑公式, 它同时适用于交替烃和非交替烃, 其计算精度要优于文献中曾经报道过的结果。用例子说明了方法的应用。     

离子选择性电极分析中的多次标准加入法的一种非线性算法

离子选择电极分析的多次标准加入法的实验数据处理通常采用图解法或计算机解法。用计算机求解具有速度快、精度高等优点,目前被广泛采用。1970年Brand提出一种非线性最小二乘法求解C_x、S和E。的Fortran计算程序。其解法是用Taylor级数展开将非线性方程转化为线性法方程,用消元法解法方程,经过迭代计算求得结果。石守衡等人对Bra-ad解法进行改进,提出用共轭斜量法解矛盾方程组,无须形成法方程,从而提高了运算精度     

用迭代法计算难溶电解质的溶解度

借鉴数学中求方程根的二分迭代法精确计算难溶电解质在水解、酸化、络合后的溶解度,在估计出[H+]的大致范围后,再选定迭代精度。当正电荷总浓度与负电荷总浓度之相对偏差小于迭代精度时,即可认为正电荷总浓度与负电荷总浓度相等,计算结束,得到结果。本方法能计算出传统方法无法计算的化合物的溶解度、pH及水解产物的浓度。     

A simple comparative test of multiple versus single-centered spherical gaussians

HeH⁺⁺ was selected as a simple model for the comparison of relative efficiencies of single and multi-centered Gaussian functions in computing molecular orbitals and their corresponding energies. One-, two-, and three-center linear combinations of twelve basis functions were applied to the calculation of potential curves for the ground state and lowest two excited sigma states of HeH⁺⁺. A point-by-point comparison was made with the same states generated by an exact solution calculation. This comparison demonstrated that the multi-centered functions were capable of reproducing energy minima, potential curve crossings and dissociation modes in agreement with the exact calculation. The single center functions were not capable of duplicating this behavior.     

On the calculation of single-particle time correlation functions from Bose-Einstein centroid dynamics

The calculation of single-particle time correlation functions using the Bose-Einstein centroid dynamics formalism is discussed. A new definition of the quasidensity operator is used to calculate the centroid force on a given particle for an anharmonic system. The force includes correlation effects due to quantum statistics and is used for the calculation of the classical-like dynamics of phase-space centroid variables within the centroid molecular dynamics approximation. Time correlation functions are then obtained for single-particle quantities. These correspond to the double-Kubo transform of exact quantum-mechanical correlation functions. The centroid dynamics results are compared to those of exact basis-set calculations and a good agreement is found. The level of accuracy is in fact the same as what was observed earlier for the calculation of center-of-mass correlation functions for Fermi-Dirac and Bose-Einstein statistics, and for any correlation function for Boltzmann statistics. These results show that it is now possible to use Bose-Einstein centroid molecular dynamics to calculate single-particle correlation functions for systems where quantum exchange effects are present.     

On bound states in two-body systems

The application of the Σ-separation method to the calculation of multicenter two-electron molecular integrals with Slater-type basis functions is reported. The approach is based on the approximation of a scalar component of the two-center atomic density by a two-center expansion over Slater-type functions. A least-squares fit was used to determine the coefficients of the expansion. The angular multipliers of the atomic density were treated exactly. It is shown that this approach can serve as a sufficiently accurate and fast algorithm for the calculation of multicenter two-electron molecular integrals with Slater-type basis functions. © 1995 John Wiley & Sons, Inc.     

An application of perturbation theory ideas in configuration interaction calculations

Configuration interaction calculations of electronic wave functions for atoms and molecules have generally been limited to relatively small basis sets because of the exponential increase in the number of configurations as basis functions are added. While higher than quadruply excited configurations are of negligible importance in CI wave functions, it is shown that the effect of triple and quadruple excitation configurations can be substantially included even when the matrix elements between such configurations are neglected, leaving only their diagonal elements and the elements connecting them with the single and double excitations. This approximation is seen to be formally practically equivalent to a first-order perturbation expression for the wave function (second-order for the energy) based on an optimum linear combination of the zero, single, and double excitation configurations as the zero-order function. If suitable procedures are used, the amount of computational effort involved in such a calculation is roughly proportional to the fourth power of the number of basis functions employed, thus preventing the CI stage of the calculation from increasing in magnitude much faster than the stages involving the calculation and manipulation of the elementary integrals.     

Explaining the “large numbers” via a unified (classical) theory of strong and gravitational interactions

An advantage of modified virtual orbitals of Hartree–Fock method is discussed in the calculation of the second-order perturbation energy. All the modified virtual orbitals can be fitted for the intermediate virtual states in the perturbation expansion, only if the molecular orbitals are expanded in terms of infinite basis functions and the set of molecular orbitals is infinite and complete. If the molecular orbitals are expanded in terms of finite basis functions, only the modified virtual orbitals with lower energies are appropriate to describe the intermediate virtual states, but the modified virtual orbitals with higher energies become inadequate. To explain the usefulness of the modified virtual orbitals, the calculation by the modified Hartree–Fock method without CI are compared with the calculation by the traditional Hartree–Fock method with complete CI .     

原子结构参数的改进Xa法计算

六十年代后期,在Hartree－Fock-Slater法的基础上,提出了Xα法［1］．用于原子结构计算的Xα法与HF（Hartree－Fock）法的主要区别在于：用简单的统计平均交换势替代了HF法中计算最为困难的电子交换势,从而在保持较高理论严谨性和计算精确度的同时,大大减少了计算工作量,近年来获得了广泛的应用．我们尝试用经过适当修改的Xα方法,计算原子参数,解决分子结构中的某些问题．用原子参数解决分子问题,历来是化学和物理工作者常用的方法．本工作的意图是引入一个比HF法简单的容易在微机上实现的某种表现原子参数的计算方法,提供…     

Perturbation theories and wave functions for calculation of electronic polarizabilities application to DNA bases

Three different forms of perturbation theories, variational perturbation, finite perturbation and second-order, are evaluated regarding their value for calculation of electronic polarizabilities of small and intermediate size molecules. It is concluded that with the practical constraint of a small basis set the variational perturbation method is the most promising alternative for calculation of polarizabilities. For several small molecules, our calculated polarizabilities indicate that both IEHT and ab initio wave functions give values in close agreement with each other. Variational perturbation calculations of polarizabilities with IEHT wave functions also include the DNA bases.     

Electronic Structure Calculation of Copper and Platinum Crystals in a Basis of Trimmed Functions

Energy band position and formation energy of copper and platinum crystals were calculated using a conventional basis set of atomic functions and a basis of trimmed functions with polynomial tails. A comparison between the results shows that the accuracy of calculation in the basis of trimmed functions is not worse than the accuracy of calculations in the standard basis, while the computing time is 2 times smaller.     

On the calculation of diffusion coefficients and aggregation numbers of nonionic surfactants in micellar solutions

The calculation of the diffusion coefficients of nonionic surfactants as functions of their concentrations in micellar solutions has been analyzed within the framework of the quasi-chemical version of the law of mass action. The methods of the introduction of initial calculation parameters, calculation scheme for an ideal mixture of monomeric molecules and micelles, and corrections for varying solution viscosity have been considered. Numerical estimations have been performed using aqueous tetraoxyethylene octyl ether, pentaoxyethylene hexyl ether, and octyl-β-D-glucopyranoside solutions as examples.     

Time-dependent electron localization functions for coupled nuclear-electronic motion

We study the quantum dynamics in a model system consisting of two electrons and a nucleus which move between two fixed ions in one dimension. The numerically determined wave functions allow for the calculation of time-dependent electron localization functions in the case of parallel spin and of the time-dependent antiparallel spin electron localization functions for antiparallel spin. With the help of these functions, it becomes possible to illustrate how electronic localization is modified through the vibrational wave-packet motion of the nucleus.