维纳指数用于寻找烷烃拓扑结构和折光率的关系的研究

H.Wiener 于1947年在考察烷烃分子拓扑结构与沸点的关系时,引入指数 W 和 p(简称维纳指数,下文同),得到了一个较准确的函数关系式,其后,人们又研究了维纳指数与分子     

关于烷烃异构体密度与拓扑指数间的定量关系问题——与王克强同志商榷

长期以来,利用图论方法根据化合物的结构特征生成的各种拓扑指数以研究定量结构活性关系(QSAR)与定量结构-性质关系(QSPR)一直是化学中十分活跃的领域。特别是对烷烃异构体,因其结构简单和各种物理化学性质数据齐全,成为各种拓扑指数产生和应用的基础。本刊在1988年第3期发表了倪才华等人(以下简称倪文)用Wiener指数W,P和碳原子总数N三个拓扑量来寻求烷烃异构体拓扑结构与密度的关系,得到计算烷烃分子的密度(D)的通式:     

酚的拓扑指数在色谱分析中的应用

图论基础上的拓扑指数在研究物质的定量结构-性质相关性(QSPR)方面发挥了重要的作用. 在众多的拓扑指数中,Wiener指数和物性相关性好,容易计算,应用范围较广[1].在色谱分析中,色谱保留指数作为定性指标的保留值是一种较为可靠的参数.本文选择了酚中具有代表性的15种酚及色谱保留指数,通过对Wiener指数(W),官能团位置指数(Sox)和酚上的甲基数(X-CH3)与色谱保留指数的多元线性回归分析,得到了良好的相关性 .可以说,当测得某一色谱保留指数时可估计其结构特性,进而为酚类化合物的定性分析提供有利的信息.     

甲基烷烃结构与色谱保留指数相关性的拓扑指数法研究

计算了207个甲基烷烃的127个拓扑指数变量,把变量选择方法GAPLS方法引入到定量结构与气相色谱保留关系研究中,对127个拓扑指数变量进行选择,得到了含7个变量的化合物的定量结构与色谱保留指数关系(QSRR)模型,其复相关系数的平方为0.99998,标准偏差为2.88。交互验证的复相关系数为0.99997,交互验证的预测标准偏差为2.95,表明该模型具有良好的稳定性和可靠性。对获得的7个变量进行了合理的结构解释,表明甲基烷烃色谱保留指数完全能用拓扑指数来精确表征。     

链烷烃标准熵的拓扑研究

根据核磁共振的峰数及Randic的碳原子支化度,提出了碳原子特征值.基于连接矩阵和碳原子特征值,建立新的连接指数 mY.其中的0阶连接性指数 0Y很容易计算,且对烷烃异构体有很强的区分能力.将157种气态链烷烃的标准熵与其 0Y相关联, R=0.9985, 属于优级模型.与Randic指数的 0χ及倪才华等提出的信息拓扑指数Ix、 IW比较, 0Y具有良好的性质相关性与结构选择性.     

烷基衍生物标准生成焓的QSPR研究

根据分子拓扑理论,建立了一个新的拓扑指数Y~X,并用Y~X对不同系列烷基衍生物M~nL(n=1,2,3;L=F,OH,Cl,NH~2,Br,SH,I;M=Me,Et;i-Pt,t-Bu,n-Pr,n-Bu,Amyl)的标准生成焓-△~fH~m^θ进行拟合,其相关系数均在0.999以上。计算结果表明,新的拓扑指数易于计算,物量意义明确,具有良好的结构选择性和性质相关性。该法可进一步用于估算其它烷基衍生物的标准生成焓。     

直链饱和烃取代衍生物的标准汽化热的拓扑指数

直链饱和烃取代衍生物的标准汽化热的拓扑指数张秀利（河北轻化工学院基础部石家庄０５００１８）关键词汽化热拓扑指数ＺＧ中图分类号６２４．１１汽化热是反映液体分子间相互作用力大小的重要热力学参数。前人对其估算做了大量的工作［１－３］。这些方法大都未能很好地...     

Wiener指数的新定义及其对气相色谱保留指数的相关性研究

1引言 Wiener于1947年提出的距离矩阵指数W，是世界上第一个分子拓扑指数，但由于Ⅳ所含信息较少，限制了Wiener指数在更广泛领域的应用。许多学者对此进行了改进并提出了许多距离矩阵指数，如Hosoya指数、Detour指数、Harary指数等。但是这些指数缺少分子结构中杂原子、多重键等信息，其应用仍然仅限于碳氢化合物。本研究采用原子的拓扑能量重新定义Wiener矩阵的矩阵元，将杂原子的信息引入Wiener指数中，重新定义Wiener指数为形^＋，并利用W^＋指数研究含杂原子胺、硫醚、卤代烷类化合物的气相色谱保留指数砌，将距离矩阵指数的应用扩展到含杂原子的体系。     

直链单炔烃保留指数与分子结构关系研究

根据同系直链单炔烃保留指数与同碳数正构烷烃保留指数差值与分子碳数间关系曲线拟合，提出预测同系直链单炔烃保留指数的较准确公式。研究并发现同碳数直链单炔烃各异构体分子中三键位置与化合物保留指数具有指数关系，首次提出了据分子中三键位置预测其保留指数的较准确公式。解决了从低碳数直链单炔烃保留指数预测高碳数直链单炔烃保留指数问题。     

一种新的分子拓扑指数

本文同时以分子图的距离矩阵和邻接矩阵为基础，提出了一种新的表征有机化合物结构特征的拓扑提数Ｘｚｏ对２－９个碳原子饱和烷烃共７４个分子的计算结果表明，与现有的一些拓扑指数相比较，该指数具有较好的结构选择和性质相关性。     

Topological estimation of proton-ligand formation constants of potential antitumour agents: Salicylhydroxamic acids

Proton-ligand formation constants of salicylhydroxamic acids (SHA) and their nuclear substituted derivatives have been estimated topologically using the normalized Wiener index, referred to as mean square Wiener index (Wms). Regression analysis of the data indicates that Wms can be used successfully for estimating and monitoring proton-ligand formation constants.     

环烷烃及烷烃的折光指数与结构的关系研究

A new structure information autocorrelation topological index tX is designed and developed based on the vertex degree of molecular topology and autocorrelation function of mathematics. Quantitative structure property the relationships for estimating the refractive index of cycloalkane and alkane are set up based on multiple linear regression. The vertex degree is defined as βi .The structure information autocorrelation topological index tX is set up with the βi. The refractive index （nD）, for the 64 cycloalkanes, are correlated with this topological indices. The index, for the 27 alkanes, are also correlated with this topological indices. The calculated results showed that the calculated refractive index of cycloalkanes and alkanes are in good agreement with the experimental data, with the mean velative deviation 0.25%. With the established model, the refractive index of the other 5 alkanes are predicted.     

Generalized Hosoya polynomials of hexagonal chains

Similar to the well-known Wiener index, Eu et al. [Int. J. Quantum Chem. 106 (2006) 423–435] introduced three families of topological indices including Schultz index and modified Schultz index, called generalized Wiener indices, and gave the similar formulae of generalized Wiener indices of hexagonal chains. They also mentioned three families of graph polynomials in x, called generalized Hosoya polynomials in contrast to the (standard) Hosoya polynomial, such that their first derivatives at x = 1 are equal to generalized Wiener indices. In this note we gave explicit analytical expressions for generalized Hosoya polynomials of hexagonal chains.     

How to compute the Wiener index of a graph

The Wiener index of a graphG is equal to the sum of distances between all pairs of vertices ofG. It is known that the Wiener index of a molecular graph correlates with certain physical and chemical properties of a molecule. In the mathematical literature, many good algorithms can be found to compute the distances in a graph, and these can easily be adapted for the calculation of the Wiener index. An algorithm that calculates the Wiener index of a tree in linear time is given. It improves an algorithm of Canfield, Robinson and Rouvray. The question remains: is there an algorithm for general graphs that would calculate the Wiener index without calculating the distance matrix? Another algorithm that calculates this index for an arbitrary graph is given.     

Modification of the Wiener index 4

A novel topological index W(F) is defined by the matrices X, W, and L as W(F) = XWL. Where L is a column vector expressing the characteristic of vertices in the molecule; X is a row vector expressing the bonding characteristics between adjacent atoms; W is a reciprocal distance matrix. The topological index W(F), based on the distance-related matrix of a molecular graph, is used to code the structural environment of each atom type in a molecular graph. The good QSPR/QSAR models have been obtained for the properties such as standard formation enthalpy of inorganic compounds and methyl halides, retention indices of gas chromatography of multiple bond-containing hydrocarbons, aqueous solubility, and octanol/water partition of benzene halides. These models indicate that the idea of using multiple matrices to define the modified Wiener index is valid and successful.     

Relation between distance-based topological indices

The pi-index of the line graph of the molecular graph of an alkane is shown to be related to the pi, Harary, and reciprocal Wiener indices of that alkane. Thus a mathematical relation between several distance-based topological indices is obtained.