The variable connectivity index 1chi(f) versus the traditional molecular descriptors: a comparative study of 1chi(f) against descriptors of CODESSA.

In this study we compared the prediction abilities of the variable connectivity index 1chi(f) (not included in CODESSA) with topological indices available from CODESSA. We selected the boiling points of n = 100 alcohols as the property and examined the pool of 56 topological indices. Prediction capabilities of the developed models were evaluated by classical training/test set approach. RMS errors calculated from the prediction set for the MLR models obtained from CODESSA software with 1, 2, 3, 4, and 5 parameters were 9.06, 5.69, 5.40, 4.9, and 3.37 degrees C, respectively. Using the variable connectivity index with weights x = 0.10 and y = -0.92 for carbon and oxygen atom respectively, we obtain regression BP = 38.12 1chi(f) - 37.56 with the correlation coefficient r = 0.9915, RMS error 4.21 degrees C calculated from the test set, and Fisher ratio F = 5691. Prediction capability of the variable connectivity index was better than for MLR regression model with up to four parameters.     

External factor variable connectivity index

A new variable index, external factor variable connectivity index (EFVCI), is proposed, in which the atomic attribute is divided into two parts. The innate part is denoted as outer-shell electrons and external part or perturbation by other atoms is represented as summation, multiplied by a variable x, of squared reciprocal matrix of i row (corresponds to atom A(i)). The division of atomic attribute in EFVCI is interpreted by using topological structure. In the correlation of boiling point of 149 acyclic alkanes, the optimal values will approach to a constant at -0.29 by using the zero to higher order indices of the same series. The new index, with high regression quality (R = 0.9986, s = 2.26, and F = 7088.4), is compared favorably with variable connectivity index and molecular connectivity index.     

Overall connectivities/topological complexities: a new powerful tool for QSPR/QSAR

Earlier attempts to assess the complexity of molecules are analyzed and summarized in a number of definitions of general and topological complexity. A concept which specifies topological complexity as overall connectivity, and generalizes the idea of molecular connectivities of Randic, Kier, and Hall, is presented. Two overall connectivity indices, TC and TC1, are defined as the connectivity (the sum of the vertex degrees) of all connected subgraphs in the molecular graph. The contributions to TC and TC1, which originate from all subgraphs having the same number of edges e, form two sets of eth-order overall connectivities, eTC and eTC1. The total number of subgraphs K is also analyzed as a complexity measure, and the vector of its eth-order components, eK, is examined as well. The TC, TC1, and K indices match very well the increase in molecular complexity with the increase in the number of atoms and, at a constant number of atoms, with the increased degree of branching and cyclicity of the molecular skeleton, as well as with the multiplicity of bonds and the presence of heteroatoms. The potential of the three sets of eth-order complexities for applications to QSPR was tested by the modeling of 10 alkane properties (boiling point, critical temperature, critical pressure, critical volume, molar volume, molecular refraction, heat of formation, heat of vaporization, heat of atomization, and surface tension), in parallel with Kier and Hall's molecular connectivity indices (k)chi. The topological complexity indices were shown to outperform molecular connectivity indices in 44 out of the 50 pairs of models compared, including all models with four and five parameters.     

QSPR modeling: graph connectivity indices versus line graph connectivity indices

Five QSPR models of alkanes were reinvestigated. Properties considered were molecular surface-dependent properties (boiling points and gas chromatographic retention indices) and molecular volume-dependent properties (molar volumes and molar refractions). The vertex- and edge-connectivity indices were used as structural parameters. In each studied case we computed connectivity indices of alkane trees and alkane line graphs and searched for the optimum exponent. Models based on indices with an optimum exponent and on the standard value of the exponent were compared. Thus, for each property we generated six QSPR models (four for alkane trees and two for the corresponding line graphs). In all studied cases QSPR models based on connectivity indices with optimum exponents have better statistical characteristics than the models based on connectivity indices with the standard value of the exponent. The comparison between models based on vertex- and edge-connectivity indices gave in two cases (molar volumes and molar refractions) better models based on edge-connectivity indices and in three cases (boiling points for octanes and nonanes and gas chromatographic retention indices) better models based on vertex-connectivity indices. Thus, it appears that the edge-connectivity index is more appropriate to be used in the structure-molecular volume properties modeling and the vertex-connectivity index in the structure-molecular surface properties modeling. The use of line graphs did not improve the predictive power of the connectivity indices. Only in one case (boiling points of nonanes) a better model was obtained with the use of line graphs.     

Variable connectivity index for cycle-containing structures.

In the early applications of the connectivity index the index was empirically modified for some properties of cyclic structures by subtracting 1/2 from the computed value based solely on valence of vertices in the molecular graph. In this article we looked into the origin of this heuristic adjustment of the connectivity indices for cyclic structures. We have examined the relative role of carbon atoms in cycle-containing structures by differentiating carbon atoms making up a ring and carbon atoms in exocyclic bonds. We found in the case of the boiling points of cycloalkanes and alkylcycloalkanes that contributions of "cyclic" and "acyclic" atoms to molecular additivities differ somewhat.     

取代脂环烃物理化学性质的拓扑化学研究

为了探讨有机化合物的分子结构与理化性质的关系,作者在以前的工作基础上,基于一阶分子连通性拓扑指数构建了一个信息拓扑指数.将拓扑指数与取代脂环烃系列分子的气态标准生成热、气态标准熵、气态标准生成自由能、沸点、临界温度、临界压力、临界体积、汽化热、密度、热容及表面张力等十一种热力学性质及物理化学性质相关联,用一个通用公式对各类性质进行概括,然后用已有的实验数据与拓扑指数进行回归分析,得到一系列计算各性质的经验公式.回归结果发现,分子的理化性质与拓扑指数有较好的相关性,有5类性质的复相关系数大于0.99.用经验公式对各类性质进行重新计算,其结果与实验值比较符合,用实验值对计算值作图,发现各数据点紧靠对角线,说明误差较小.残差分布呈正态分布.     

Prediction of the Retention Indices of Benzene and Methylbenzenes Based on their Retention Data-Physico Chemical Properties Relationship

Retention indices of benzene and 12 methylbenzenes were determined on two capillary columns coated with HP-5 and ZB-WAX at 100 °C. Comparison with the retention indices published by other researchers yields a good accordance. The relationship between the retention index values and several physico-chemical properties of these solutes (freezing point, boiling point, molar volume, van der Waals volume, molar refraction, refraction index, connectivity index, dipole moment and vapor pressure) was investigated by multiple linear regression analysis (MLRA). MLRA equations of seven and eight variables predicted retention indices with mean deviations of 0.66–0.97 index-units in squalane and Carbowax 20 M, and 0.76–1.25 index-units in HP-5 and ZB-WAX. PCA was applied to the system of solutes retention data and stationary phases used, giving results consistent with those of MLR analysis. Samples are scattered or joined by curves. An arrangement of the stationary phases according to the polarity is observed. TCEP was one outlier since it is much more polar than any others.Two groups of variables can be envisaged, one of which is close to the origin of the coordinates, the physicochemical properties that depend linearly. Solute vapor pressure and molar volumes were outliers.     

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 .     

Structural interpretation of the topological index. 2. The molecular connectivity index, the Kappa index, and the atom-type E-State index

The structural interpretation is extended to the topological indices describing cyclic structures. Three representatives of the topological index, such as the molecular connectivity index, the Kappa index, and the atom-type E-State index, are interpreted by mining out, through projection pursuit combining with a number theory method generating uniformly distributed directions on unit sphere, the structural features hidden in the spaces spanned by the three series of indices individually. Some interesting results, which can hardly be found by individual index, are obtained from the multidimensional spaces by several topological indices. The results support quantitatively the former studies on the topological indices, and some new insights are obtained during the analysis. The combinations of several molecular connectivity indices describe mainly three general categories of molecular structure information, which include degree of branching, size, and degree of cyclicity. The cyclicity can also be coded by the combination of chi cluster and path/cluster indices. The Kappa shape indices encode, in combination, significant information on size, the degree of cyclicity, and the degree of centralization/separation in branching. The size, branch number, and cyclicity information has also been mined out to interpret atom-type E-State indices. The structural feature such as the number of quaternary atoms is searched out to be an important factor. The results indicate that the collinearity might be a serious problem in the applications of the topological indices.     

Prediction of the critical temperatures (liquid-vapor) of organic compounds

The ampule method was used to measure the critical temperatures (liquid-vapor) for 1,4-and 1,3-tert-butylbenzenes, 1,3,5-tri-tert-butylbenzene, and 3,5-di-tert-butyltoluene. For alkanes, alkenes, alkylbenzenes, alkylphenols, and alcohols, sets of parameters for the additive components in the Tatevskii bond method and in the method based on the Randic molecular connectivity indices were obtained. The need to create individual correlations for alcohols within the framework of any method in which the normal boiling temperature is used as the basis property was substantiated. The predictive possibilities of various methods were compared. The method based on the Randic molecular connectivity indices was demonstrated to be most effective.