分子连接性指标对羧酸类疏水常数的研究

采用分子连接性指标研究了105个含有丰富取代基的羟酸分子,指标中考虑了非价、羧酸、不饱和键和杂原子对分子疏水常数的影响。通过多元逐步回归关联得一含有六个指标的方程,发现该类分子的疏水常数与非价的0χP,羧基的ΔχC,以键的Δ2χP和杂原子的1χP、5χC、6χP具有良好的相关性(N=105,S=0.25,F=127.73,R=0.94),并用此模型预测了五个羧酸分子的疏水常数,得到了满意的结果。最后对影响羧酸类分子疏水常数的原因进行了分析。     

最大重迭分子轨道和核自旋偶合常数的计算

利用前文中建立的AM1级别上最大重迭对称性分子轨道计算方案,并结合最大键级杂化轨道方法,在对分子几何优化的基础上,计算系列化合物分子中各原子的电荷分布和杂化轨道组成系数,拟合出计算C-H及C-C偶合常数的简单关系式,计算各种分子中不同C-H键和C-C键偶合常数,所得计算值和实验数据较为吻合,两者相关系数和标准偏差:.1JCH为0.982 0和6.020 5,1JCC为0.988 8和7.346 2,为计算1JCH和1JCC提供简便而直观的方法.建立的公式可预测新化合物中的C-H及C-C偶合常数,对新化合物的性质和结构及成键情况也能起到辅助推断作用,且在大分子体系的研究中极易推广.计算结果进一步表明所建AM1级别上最大重迭对称性分子轨道计算方法是可行的.     

CO在Ag(100)表面吸附行为的理论研究

应用离散变分Xα方法,对CO分子在Ag(100)表面的吸附过程进行了理论研究,计算了CO分子以垂直方式在三种不同吸附位置吸附时CO分子和Ag(100)表面原子间的键级和电荷分布。结果表明:在吸附过程中,CO分子以顶位吸附为优, 有效吸附距离为170±3 pm,在吸附过程中CO分子只与最近邻的一个表面银原子有相互作用,而其它表面原子及体相原子的电子结构没有变化。Mulliken集居数及局域态密度分析表明,吸附过程中银原子与CO之间的相互作用是表面Ag原子的杂化轨道电子进入CO中空的反键轨道(M→C)和CO上面(主要是C上)未成键电子进入到表面Ag原子空的杂化轨道(C→M) 的共同结果。     

杂化轨道理论与分子的空间构型——多媒体教学软件的设计与制作

教学软件采用计算机多媒体技术和三维动画生动地描述了化学键理论（如价键理论、杂化轨道理论、分子轨道理论，包括范德华力等）的基本知识和基本概念以及一些典型的无机和有机分子的空间构型，并重点展示了杂化轨道理论与分子空间构型之间的关系。文中介绍了软件的主要内容、设计思想及使用效果。     

L—B膜修饰电极循环伏安行为模拟：（I）电荷转移速度常数对循环…

本文用计算机数字模拟方法研究了电活性分子多层Ｚ型Ｌ－Ｂ膜修饰电极的循环伏安行为。计算了电极与修饰Ｌ－Ｂ膜分子第一层之间的电荷转速度常数ｋ０，Ｌ－Ｂ膜分子层间的电荷转移速率常数Ｋ１，对峰电位差△Ｅｐ及阳极峰面积Ｑ的影响，以及在不同条件下各层分子的氧化态分数随扫描时间的变化。为研究和设计电活性分子修饰电极的实际体系提供了大量数据的信息。     

L－B膜修饰电极循环伏安行为模拟──（Ⅰ）电荷转移速度常数对循环伏安性能的影响

本文用计算机数字模拟方法研究了电活性分子多层Ｚ型Ｌ－Ｂ膜修饰电极的循环伏安行为。计算了电极与修饰Ｌ－Ｂ膜分子第一层之间的电荷转移速度常数Ｋ_ｏ，Ｌ－Ｂ膜分子层间的电荷转移速度常数ｋ_ｉ；对峰电位差△Ｅ_ｐ及阳极峰面积Ｑ的影响，以及在不同条件下各层分子的氧化态分数随扫描时间的变化。为研究和设计电活性分子修饰电极的实际体系提供了大量数据和信息。     

部分有机污染物气相色谱保留指数的QSRR研究

用相对键长代替拓扑距离,结合距离矩阵,提出了一个可以表征含多重键、杂原子的距离调和指数Te=(N/∑Si -1)0.5。研究了该指数与烃、醇、醛酮、酯、胺等多种有机污染物气相色谱保留指数的构效关系。结果表明,Te指数与保留指数RI具有良好的相关性,相关系数均在0.99以上,且该指数计算简单,预测值与实验值较好吻合,是预测不同有机污染物分子保留指数的理想参数。     

基于电负性均衡方法准确计算杂环分子中的原子电荷

基于电负性均衡方法(EEM),依据原子类型和成键对原子进行细致划分,以准确计算分子中的原子电荷.为准确计算分子中原子的电荷,构建了包含214个分子、含各类不同基团的训练集,采用B3LYP/6-31g*基组对分子进行优化并得到各个分子中的原子Mulliken电荷.与其他校正方法将同一类原子视为拥有相同的有效电负性和有效硬度值不同,本文在EEM方程中,依据成键类型和化学环境变化,将C、N、O分别分为为4种、3种和2种不同类型,相应采用不同的电负性和硬度价态标度值,并采用全局优化算法对训练集进行优化以得到各类原子的EEM参数值.本文讨论了这些参数与其他方法所得到的参数的差异,并讨论了本方法与其他校正方法的区别.利用本文校正所得EEM方程参数,对不在训练集中的几个杂环分子的EEM电荷进行了计算,取得了较为满意的结果.     

应用量化参数研究羧酸的结构和pKa值的关系

应用密度泛函B3LYP/6.311 G**法得30种羧酸分子的优势构象,再计算羧酸-水构成的氢键复合物,获得优势构象和复合物的结构参数,并将这些参数与羧酸pKa值相比.羧基C-O键长、羧基氢自然键轨道电荷以及复合物的氢键键长和结合能等参数,与羧酸pKa实验值具有良好的线性关系.以水为探针分子获得氢键复合物结构参数的方法,可预期在预测其它含有酸性基团化合物酸性的强弱方面推广应用.     

多溴代芴的分子结构和热力学性质

多溴代芴化合物是一类潜在的化学污染物,其热力学性质数据对于进一步研究这些化合物的其它物理、化学性质以及它们在环境中的形成、分布及迁移转化机制有重要价值,但这些热力学性质数据极其缺乏.本文采用密度泛函理论在B3LYP/6-311G**水平上优化135个多溴代芴分子的几何结构,并获得它们在理想气态的一些热力学性质的数值,研究这些性质与取代的溴原子数目和位置的关系,根据各异构体的相对标准生成Gibbs自由能的大小,得它们热力学稳定性的顺序.结果表明:多溴代芴分子的几何构型,取决于溴原子的取代位置.多溴代芴最稳定及最不稳定异构体的△fHθ及ΔfGθ,都随Br原子数目增加而逐渐增加.溴原子数目相同的多溴代芴异构体的△fHθ和△fGθ与溴原子的取代位置有很大的关系,其相对稳定性看离域π键和Br…Br核排斥作用的强弱而决定.     

Some orbital test problems

Problems with periodic solutions are convenient as test problems for differential equation software because of the ease with which the accuracy of computed results can be assessed. Even the motion of a single planet around a heavy sun is useful as a test problem because orbits of varying eccentricity make varying demands on numerical software. The orbits discussed here are based on this same simple problem but with the essential difference that the distance from the planet to the sun is based on the norm ‖ . ‖_∞ rather than the usual Euclidean norm ‖ . ‖₂. Specifically, we explore orbits based on each of the differential equation systems $$X = \nabla \left( {\frac{1}{{\left\| X \right\|}}} \right)$$ and $$X = - \frac{1}{{\left\| X \right\|^3 }}.$$ A feature of both these systems, when the ‖ . ‖_∞ norm is used, is the occurrence of discontinuities in the higher derivatives of the solution. This is why they have a potential value as difficult test problems. With this application in mind, some periodic solutions are identified. For an arbitrary choice of norm, the second of the two differential equation systems considered in this paper is shown to possess periodic orbits.     

灿烂甲酚兰衍生物的结构—式电位关系及式电位预测

以半经验分子轨道方法计算灿烂甲酚兰衍生物的分子结构参数,以主因子分析和多元线性回归等方法研究了吲酚衍生物的式电位与其分子结构间的关系,在所选择的19个分子结构参数中,与氨基相连的苯环上C4上的净电荷,e(C4）;分子的电离势,Ip;联苯胺中C1－N键的交换能,Eex(C1-N)和双中心共振能,Er(2);与其式电位有较好的相关性。回归方程为：E^0‘＝20.2165 2.406e(C4)-1.78865Ip 0.1809Eex(C1-N) 0.00809Er (2)(RC=0.9988,SD=0.007),预测2－氟－,2－氯－和2－溴取代灿烂甲酚兰的式电位分别为：0.603V,0.845V和0.847V。     

链烷烃分子结构设计(I)分子构成基团的确定

以链烃一阶分子连接性指数及其与状态方程参数的关系为基础，利用神经元网络预测与之对应的。然后根据、确定分子结构的路径指数并将其转换为与分子结构，构成基团相关的顶点度数，从而确定构成基团的种类与个数。     

A transformation of series

The transformation (*) $$\sum\limits_{\nu = 0}^\infty {t_\nu z^\nu \to } \sum\limits_{\nu = 0}^\infty {\left\{ {\sum\limits_{\tau = 0}^{h - 1} {z^\tau } \Delta ^\nu t_{h\nu + \tau } + \frac{{z^h }}{{1 - z}}\Delta ^\nu t_{h(\nu + 1)} } \right\}} \left( {\frac{{z^{h + 1} }}{{1 - z}}} \right)^\nu$$ whereh≥0 is an integer and Δ operates upon the coefficients {t _v } of the series being transformed, is derived. Whenh=0, the above transformation is the generalised Euler transformation, of which (*) is itself a generalisation. Based upon the assumption that \(t_\nu = \int\limits_0^1 {\varrho ^\nu d\sigma (\varrho ) } (\nu = 0, 1,...)\) , where σ(?) is bounded and non-decreasing for 0≤?≤1 and subject to further restrictions, a convergence theory of (*) is given. Furthermore, the question as to when (*) functions as a convergence acceleration transformation is investigated. Also the optimal valne ofh to be taken is derived. A simple algorithm for constructing the partial sums of (*) is devised. Numerical illustrations relating to the case in whicht _v =(v+1) ^?1 (v=0,1,...) are given.     

Convergence,stability and truncation error estimation of a method for the numerical integration of the initial value problemY″=F(X,Y)

In this paper a detailed study of the convergence and stability of a numerical method for the differential problem $$\left\{ \begin{gathered} y'' = f(x,y) \hfill \\ y(x_0 ) = y_0 \hfill \\ y'(x_0 ) = y_0 ^\prime \hfill \\ \end{gathered} \right.$$ has carried out and its truncation error estimated. Some numerical experiments are described.     

On the complexity of computing determinants

We present new baby steps/giant steps algorithms of asymptotically fast running time for dense matrix problems. Our algorithms compute the determinant, characteristic polynomial, Frobenius normal form and Smith normal form of a dense n × n matrix A with integer entries in and bit operations; here denotes the largest entry in absolute value and the exponent adjustment by +o(1) captures additional factors for positive real constants C₁, C₂, C₃. The bit complexity results from using the classical cubic matrix multiplication algorithm. Our algorithms are randomized, and we can certify that the output is the determinant of A in a Las Vegas fashion. The second category of problems deals with the setting where the matrix A has elements from an abstract commutative ring, that is, when no divisions in the domain of entries are possible. We present algorithms that deterministically compute the determinant, characteristic polynomial and adjoint of A with n^3.2+o(1) and O(n^2.697263) ring additions, subtractions and multiplications.To B. David Saunders on the occasion of his 60th birthday     

Integration of a linear many-valued mapping of a special type

We consider the solvability of the integral equation for the unknown set W. A. bound of the integral is given for some class of sets M. The results are applied in differential games.Translated from Kibernetika, No. 3, pp. 90–95, May–June 1990.     

Numerical evaluation of a solution of a special mixed-type differential-difference equation

The function * $$f(t) = \frac{{e^{ - \alpha \gamma } }}{\pi }\int\limits_0^\infty {\cos t \xi e^{\alpha Ci(\xi )} \frac{{d\xi }}{{\xi ^\alpha }},t \in R,\alpha > 0} $$ [Ci(x)=cosine integral, γ=Euler's constant] is studied and numerically evaluated;f is a solution to the following mixed type differential-difference equation arising in applied probability: ** $$tf'(t) = (\alpha - 1)f(t) - \frac{\alpha }{2}[f(t - 1) + f(t + 1)]$$ satisfying the conditions: i) $$f(t) \geqslant 0,t \in R$$ , ii) $$f(t) = f( - t),t \in R$$ , iii) $$\int\limits_{ - \infty }^{ + \infty } {f(\xi )d\xi = 1} $$ . Besides the direct numerical evaluation of (*) and the derivation of the asymptotic behaviour off(t) fort→0 andt→∞, two different iterative procedures for the solution of (**) under the conditions (i) to (iii) are considered and their results are compared with the corresponding values in (*). Finally a Monte Carlo method to evaluatef(t) is considered.     

The construction of cubature formulae for a family of integrals: A bifurcation problem

Cubature formulae of degree 11 with minimal numbers of knots for the integral $$\int\limits_{ - 1}^1 { \int\limits_{ - 1}^1 {(1 - x^2 )^\alpha } } (1 - y^2 )^\alpha f(x,y) dxdy \alpha > - 1$$ which are invariant under rotation over an angle π/2 are determined by a system of 18 nonlinear equations in 18 unknowns. We start with a known solution for this system for α=0. By varying α smoothly, the knots and weights of the cubature formula vary smoothly except in the singular solutions such as turning points and bifurcation points where new solutions branches arise. We use for this purpose the program AUTO. We obtain surprisingly many branches of cubature formulae.