GTI-space: the space of generalized topological indices

A new extension of the generalized topological indices (GTI) approach is carried out to represent “simple” and “composite” topological indices (TIs) in an unified way. This approach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randić connectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index and reverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI-space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given.     

Relationship between GLC retention data and topological indices for a wide variety of solutes on five stationary phases of different polarity

Summary Numerical correlations between the specific retention volumes of several dozen solutes (hydrocarbons and derivatives containing oxygen, nitrogen and halogens) and between the retention indices, from the literature, of 26 chemical derivatives of benzene on several stationary phases have been studied. Although significant linear correlations were usually obtained between logV _g and the valence connectivity indices,¹ X ^v , for hydrocarbons and non-hydrocarbons with the same chemical function, the relationship between logV _g and the Wiener,W, and Balaban,J, indices for hydrocarbons was found to be non-linear. Correlations between retention index increments and valence connectivity index increments for the 26 chemical derivatives of benzene were linear for alkyl substituents only.     

Molecular modeling of wine polyphenols

Due to wide range of health effects of wine polyphenols, it is important to investigate the relationship between their structure and physical properties (quantitative structure–property relationship, QSPR). We have investigated linear, nonlinear (polynomial), and multiple linear relationships between given topological indices and molecular properties of main pharmacological active components of wine, such as molecular weight (MW), van der Waals volume (Vw), molar refractivity (MR), polar molecular surface area (PSA) and lipophilicity (log P). Partition coefficient (log P) was calculated using three different computer program (CLOGP, ALOGPS and MLOGP). The best models were achieved using the MLOGP program. Topological indices used for correlation analysis include: the Wiener index, W(G); connectivity indices, χ(G); the Balaban index, J(G); information-theoretic index, I(G); and the Schultz index, MTI(G). QSPR was performed on the set of 19 polyphenols and, particularly, on the group of phenolic acids, and on the group of flavonoids with resveratrol. The connectivity index has been successfully used for describing almost all parameters. Significant correlations were achieved between the Wiener index and van der Waals volume, as well as molecular weight.     

修正的分子连接性指数mL用于氯代苯、醇、酯的QSAR/QSRR研究

在分子拓扑理论的基础上，提出了1个改进的连接性指数气^mL并用气研究了氯代苯、醇、酯的正辛醇-水分配系数及气相色谱保留指数，^mL不仅对这些有机化合物有良好的结构选择性，而且与其正辛醇-水分配系数、气相色谱保留指数有良好的相关性；由方程得出的预测值与实验测定值之间能较好地吻合。     

Analytical expressions for topological properties of polycyclic benzenoid networks

Quantitative structure‐activity and structure‐property relationships of complex polycyclic benzenoid networks require expressions for the topological properties of these networks. Structure‐based topological indices of these networks enable prediction of chemical properties and the bioactivities of these compounds through quantitative structure‐activity and structure‐property relationships methods. We consider a number of infinite convex benzenoid networks that include polyacene, parallelogram, trapezium, triangular, bitrapezium, and circumcorone series benzenoid networks. For all such networks, we compute analytical expressions for both vertex‐degree and edge‐based topological indices such as edge‐Wiener, vertex‐edge Wiener, vertex‐Szeged, edge‐Szeged, edge‐vertex Szeged, total‐Szeged, Padmakar‐Ivan, Schultz, Gutman, Randić, generalized Randić, reciprocal Randić, reduced reciprocal Randić, first Zagreb, second Zagreb, reduced second Zagreb, hyper Zagreb, augmented Zagreb, atom‐bond connectivity, harmonic, sum‐connectivity, and geometric‐arithmetic indices. In addition we have obtained expressions for these topological indices for 3 types of parallelogram‐like polycyclic benzenoid networks.     

The study of the relationship between the new topological index A(m) and the gas chromatographic retention indices of hydrocarbons by artificial neural networks

The newly developed topological indices A_m1-A_m3 and the molecular connectivity indices ^mX were applied to multivariate analysis in structure-property correlation studies. The topological indices calculated from the chemical structures of some hydrocarbons were used to represent the molecular structures. The prediction of the retention indices of the hydrocarbons on three different kinds of stationary phase in gas chromatography can be achieved applying artificial neural networks and multiple linear regression models. The results from the artificial neural networks approach were compared with those of multiple linear regression models. It is shown that the predictive ability of artificial neural networks is superior to that of multiple linear regression method under the experimental conditions in this paper. Both the topological indices ²X and A_m1 can improve the predicted results of the retention indices of the hydrocarbons on the stationary phase studied.     

Discrimination between linear and non-linear models describing retention data of alkylbenzenes in gas-chromatography

Summary Detailed statistical analysis is presented to describe the retention indices of alkylbenzenes as a function of their physical (boiling point, modrefraction) and topological (connectivity and complexity indices) properties. With the help of several statistical characteristics (examination of residuals, F test, partial F test, termination criteria, correlation indices) a discrimination is made among different models. A nonlinear equation was chosen which describes the retention data on slightly polar phases with the practically attainable precision. A comparison with literature sources shows that this equation provides the smallest residual error and, hence, it can be applied for prediction purposes. A correlation was found between the preexponential factor in the simple exponential model and the polarity of stationary phases on the Tarján scale.     

广义α~N指数及其应用 IV: 广义α~N指数在碳氢化合物中的应用

本文计算了七对顺、反异构体的广义α~N指数, 结果表明, 广义α~N指数不仅能很好地区分碳氢化合物的顺、反异构体, 而且与其物理性质(沸点、密度、折光率、分子折射度等)有良好的单变量线性相关关系, 解决了拓扑指数不能区分顺、反异构体的困难。本文还计算了庚烷、辛烷系列的广义α~N指数, 并比较了多种拓扑指数与辛烷值的相关分析结果。     

Relationship between the structure and physicochemical characteristics of 1,2,3,4-tetrahydroquinoline derivatives

A number of physicochemical characteristics of ten 1,2,3,4-tetrahydroquinoline derivatives synthesized for the first time, along with their third order Wiener and Randi? indices are calculated by quantum chemical methods. Correlations between the topological indices, physicochemical parameters, and retention factors of the mentioned compounds are obtained for conditions of reversed-phase high performance liquid chromatography on porous graphitized carbon.     

烷基苯类化合物结构-热力学性质定量构效关系研究

计算并研究了烷基苯类化合物拓扑指数N、J、Ij与其热力学性质ΔHc^θ(g)、ΔHf^θ(g)、S^θ(g)、ΔG1^θ(g)、logKp之间的相关性和选择性,结果显示,本文所构建经验公式其相关性和选择性均优于文献[13]、[15]。