分子连接性指数~mX~z与不饱和链烃沸点的定量关系研究

提出了一个计算分子中成键原子点价δ_i~z的新方法，以δ_i~z为基础建构的 新的分子连接性指数为~mX~z = ∑(δ_i~z·δ_j~z·δ_k~z……)~(-0.5)，其中 ~0X~z，~1X~z的定义为：~0X~z = ∑(δ_i~z)~(-0.5), ~1X~z = ∑(δ_i~z·δ _j~z)~(-0.5)，并研究了~0X~z,~1X~z与不饱和链烃沸点的相关性。结果表明，该 拓扑指数具有良好的结构-性质相关性。以~0X~z,~1X~z和碳原子数N为结构参数分 别与80个单烃烃、39个单炔烃、169个不饱和链烃（包括烷烃、炔烃及烯炔）的沸 点进行关联所得到的三元回归方程为：单烯烃，log(779.13-bp) = 2.822433-0. 0133346 ~0X~z - 0.0638379 ~1X~2 + 0.0111229N (R = 0.99895, F = 202783. 65, s = 3.36)；单炔烃，log(797.47-bp) = 2.809912-0.0108374~0X~z - 0. 0864540 ~1X~z + 0.0233028N (R = 0.99935, F = 98657.36, s = 3.65);不饱和 链烃，log(741.26-bp) = 2.779526 + 0.0194388~0X~z - 0.0519158~1X~z - 0. 0211047N (R = 0.99467, F = 82387.26, s = 7.74)。应用这些经验公式可以预测 不饱和链烃的沸点。     

主量子数拓扑指数研究烷基苯的定量构效关系

由主量子数(ni)定义成键原子化学特征的点价为ti=mi(ni-1) hi,在此基础上建构一个主量子数拓扑指数nQ=∑(ti·tj·tk…)0.5,其中,0Q=∑(ti)0.5, 1Q=∑(ti·tj)0.5,并以此为参数研究了烷基苯的燃烧热、等张比容、沸点、汽化热、标准生成自由能、标准熵、摩尔体积、溶解度、辛醇/水分配系数等10种物理化学性质,提出了一个通用的关系式:p=a b 0Q c 1Q.结果表明,0Q, 1Q与烷基苯的许多物理化学性质具有广泛良好的相关性,相关系数均大于0.99.     

用原子特性自相关拓扑指数预测链烷烃的热力学性质

原子特征值 ( Si)被定义为 :Si=ni- 1ki mi( ∑Eij+ hi Ei)。由 Si建构原子特征自相关拓扑指数 ( F )及原子特征连接性指数 ( Y)的公式为 :F =∑( Si· Sj) 0 .5、Y=∑ ( Si·Sj) - 0 .5。它们与 85种链烷烃热力学性质 ( P)的二元线性回归方程为 :P =a + b F +c Y(或 P3) 。 P为标准生成焓、标准熵、标准生成自由能的二元相关指数依次为 0 .9953、0 .9992、0 .9941 ,优于文献方法     

多阶F指数对碳氢化合物的QSPR研究

根据分子中原子与原子的不同邻接情况,重新定义了关联矩阵的矩阵元,并在此基础上定义了矩阵形式的多阶F指数 pF.多阶F指数 pF考虑了分子中每一顶点原子的特性及顶点原子与其它原子的多种相互作用.采用系列指数 pF中的F, 0F′, 1F′和 2F′对烷烃、烯烃、烷基苯共144个碳氢化合物的标准生成焓进行相关研究,相关系数均大于0.98,与卤化钛化合物TiXn (n=1～4, X=F, Cl, Br, I)的标准生成焓的相关系数也在0.99以上.     

用原子特征自相关拓扑指数预测链烷烃的热力学性质

原子特征值(Si)被定义为:.由Si（ ）建构原子特征自相关拓扑指数(F)及原子特征连接性指数(Y)的公式为:F＝∑(Si.Sj)0.5、Y＝∑(Si.Sj)-0.5.它们与85种链烷烃热力学性质(P) 的二元线性回归方程为:P＝a+bF+cY(或P3).P为标准生成焓、标准熵、标准生成自由能的二元相关指数依次为0.9953、0.9992、0.9941,优于文献方法.     

不饱和链烃沸点的拓扑研究

基于邻接矩阵与边价 (fi)定义边价连接性指数 ( mF) ,其中的0 F ,1 F与 2 94种不饱和链烃 (包括烯烃、炔烃及烯炔烃 )的沸点 (Tb)关联 ,得到良好的数学模型 :ln( 70 0 -Tb) =6 5 2 3 3 1-0 0 0 4880 F2 -0 3 46771 F0 5(n =2 94,R =0 9979,R2 =0 995 8,F =3 490 4,S =5 12 ) ,该回归模型经Jackknife法检验具有总体稳健性 .可以预示 ,该指数将在定量构效关系研究中成为重要参数 .     

胺、醇、醚类化合物电离能的自相关拓扑研究

原子的染色序数 fi 定义为 :fi=gi·xi,式中 gi 为原子i在分子中的序数 ,xi 为其染色系数 .基于fi 建立改进的原子序数自相关拓扑指数mF ,其中的1F对烷烃及其衍生物具有良好的结构选择性 .使用第一电离能 (Ip)与0 F ,1F的数量关系模型对 32种脂肪族胺、醇、醚进行估算、预测 ,结果令人满意     

不饱和烃的理化性质与分子拓扑指数的关系研究

定义并分别求算了不饱和烃(烯烃、炔烃、烷基苯)的价键连通性指数和价键信息拓扑指数, 将拓扑指数分别与这些物质的标准生成热、标准熵、标准生成自由能等一系列理化性质相关联, 用计算机回归方法确定了不同性质的最佳函数形式。回归的复相关系数和重新计算的误差结果显示拓扑指数与理化性质具有优良的相关性。     

改进的连接性指数用于链烷烃热力学性质与沸点研究

基于邻接矩阵和原子特征值qi，建立邻接指数^mQ,用^0Qr,^1Q与85种链烷烃的标准生成焓、标准生成自由能、标准熵和沸点关联，相关系数均在0.99以上，属于良好模型，与Randic指数的^mX比较，^mQ具有良好的性质相关性。     

键连接性指数的建构及其在有机体系中的应用研究

以化学键为基础建构了键连接性指数及分子键连接性指数，该指数同时考虑顶 点原子的化学特征及键的性质．对于任意化学键，键连接性指数Si＝1+△I/R·[（ Z1-h1)m2/n1+(Z2-h2)m1/n2]，分子键连接性指数S为∑i=1^m√Si或∑i=1^m1/√ Si，其中，Z1，Z2为化学键键连原子的价电子数；n1，n2成键原子的价层最高主量 子数；m1，m2为成键原子的氧化数；h1，h2为与成键原子相连的氢原子个数；△I 为成键原子的电负性差(△I≥0)；R为化学键的相对键长．与以顶点为基础的价连 接性指数不同，该指数不仅能方便而有效地应用于饱和碳氢体系亦能有效地应用于 含多重键的不饱和体系及含杂原子的有机体系．研究了饱和碳氢体系标准生成焓， 不饱和碳氢体系和酮、醚、酯体系在水中的溶解度和辛醇/水分配系数，卤代甲烷 体系的标准生成焓，卤代苯体系辛醇/水分配系数，均取得比较满意的结果。     

On the connectivity index of trees

The connectivity index χ₁(G) of a graph G is the sum of the weights d(u)d(v) of all edges uv of G, where d(u) denotes the degree of the vertex u. Let T(n, r) be the set of trees on n vertices with diameter r. In this paper, we determine all trees in T(n, r) with the largest and the second largest connectivity index. Also, the trees in T(n, r) with the largest and the second largest connectivity index are characterized. Mei Lu is partially supported by NNSFC (No. 10571105).     

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.     

On Harary index

We report lower and upper bounds for the Harary index of a connected (molecular) graph, and, in particular, upper bounds of triangle- and quadrangle-free graphs. We also give the Nordhaus–Gaddum-type result for the Harary index. Dedicated to the memory of Professor Frank Harary (1921–2005), the late grandmaster of both graph theory and chemical graph theory.     

Double hexagonal chains with maximal Hosoya index and minimal Merrifield–Simmons index

It is well known that the two graph invariants, “the Hosoya index” and “the Merrifield–Simmons index” are important ones in structural chemistry. The extremal hexagonal chains with respect to the Hosoya index and Merrifield–Simmons index are determined by Gutman and Zhang (J. Math. Chem., 12 (1993) 197–210, 27 (2000) 319–329 and J. Sys. Sci. Math. Sci., 18 (4) (1998) 460–465). In this paper, we will consider a type of the pericondensed hexagonal system. The double hexagonal chains with maximal Hosoya index and minimal Merrifield Simmons index are determined.     

Another look at the degree‐Kirchhoff index

Let G be an arbitrary graph with vertex set {1,2, …,N} and degrees d_i ≤ D, for fixed D and all i, then for the index R′(G) = ∑_{i < j}d_id_jR_ij we show that We also show that the minimum of R′(G) over all N‐vertex graphs is attained for the star graph and its value is 2N² ? 5N + 3. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

烷基的憎水指数

本文提出憎水指数HBI来定量烷基的憎水能力, 结果表明: 烷基的憎水指数能较好地预报有机物在水中的溶解度、在正辛醇/水两相中的分配系数。     

Retention index,connectivity index and Van der Waals' volume of alkanes (GLC)

Summary The relationships between retention index and Van der Waals' volume and between retention index and connectivity index have been studied for 58 different alkanes (C₁–C₉) on squalane. The correlation coefficient for the former is higher than for the latter. From these equations a linear relationship between Van der Waals' volume and connectivity index is obtained which indicates that the two parameters are equivalent. A simple method for calculating the Van der Waals' volume of alkanes is proposed.     

Terminal Wiener index

Motivated by some recent research on the terminal (reduced) distance matrix, we consider the terminal Wiener index (TW) of trees, equal to the sum of distances between all pairs of pendent vertices. A simple formula for computing TW is obtained and the trees with minimum and maximum TW are characterized.     

Kirchhoff index of linear hexagonal chains

The resistance distance r_ij between vertices i and j of a connected (molecular) graph G is computed as the effective resistance between nodes i and j in the corresponding network constructed from G by replacing each edge of G with a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all pairs of vertices. In this work, according to the decomposition theorem of Laplacian polynomial, we obtain that the Laplacian spectrum of linear hexagonal chain L_n consists of the Laplacian spectrum of path P_2n+1 and eigenvalues of a symmetric tridiagonal matrix of order 2n + 1. By applying the relationship between roots and coefficients of the characteristic polynomial of the above matrix, explicit closed‐form formula for Kirchhoff index of L_n is derived in terms of Laplacian spectrum. To our surprise, the Krichhoff index of L_n is approximately to one half of its Wiener index. Finally, we show that holds for all graphs G in a class of graphs including L_n. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008