Calculation of retention indices by molecular topology. Chlorinated benzenes

A comparative study was undertaken to test the ability of several different topological indices to predict the retention indices of chlorinated benzenes on polar and non-polar stationary phases using both correlation coefficients and correctly predicted elution sequences as criteria of fit. The test was performed on three topological indices: connectivity indices, Wiener numbers, and Balaban indices. The regression analyses showed that the molecular connectivity model predicted the retention indices of chlorinated benzenes more successfully than either Wiener numbers or Balaban indices. The results also demonstrated that the major structural property controlling chromatographic behavior was the size of the chlorinated benzene. In addition, the use of the new non-empirical heteroatom parameterization scheme in the calculation of Wiener numbers and Balaban indices was successfully tested for the first time.     

Integration of Graph Theory and Quantum Chemistry for Structure-Activity Relationships

Abstract

The objective of this article is to outline both graph-theoretically based and quantum chemically based structural indices of potential use in quantitative structure activity correlations. We consider graph-theoretical indices such as the connectivity index, topological index, Wiener index and molecular ID indices. Several structural and geometry-dependent indices can be derived from semiempirical and ab initio quantum calculations based on the charge densities, overlap matrices, frontier orbitals, molecular hardness, free valence, density matrices, quantum spectral difference indices, quantum spectral indices and bond matrices. Finally, the use of electrostatic potentials and charge densities for the prediction of reactive sites will be discussed.     

An algorithm for construction of the molecular distance matrix

A simple computer-oriented method is presented for constructing the (molecular) distance matrix. The distance matrix considered is the graph-theoretical (topological) distance matrix.     

A generalized graph-theoretical matrix of heterosystems and its application to the VMV procedure

The extensions of generalized (molecular) graph-theoretical matrix and vector-matrix-vector procedure are considered. The elements of the generalized matrix are redefined in order to describe molecules containing heteroatoms and multiple bonds. The adjacency, distance, detour and reciprocal distance matrices of heterosystems, and corresponding vectors are derived from newly defined generalized graph matrix. The topological indices, which are most widely used in predicting physicochemical and biological properties/activities of various compounds, can be calculated from the new generalized vector-matrix-vector invariant.     

Molecules-in-molecule estimation of the extent of localization of Kekuléan substructures in polycyclic aromatic hydrocarbons

This article first revises graph-theoretical (local aromaticity and overall molecular) indices, introduced by M. Randi? in 1975, for benzenoid hydrocarbons and somewhat improves them for computer enumeration. This goes beyond total Kekulé structure enumeration, yielding an index calculation useful for the quantitative estimation of localization of different Kekuléan substructures (including ethylene-, benzene-, annulene-, and radialene-units). This may be viewed as a "molecules-in molecule" approach to polycyclic aromatic hydrocarbons within the context of graph theoretical partitioning.     

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.     

拓扑指数与手性化合物构效关系研究

传统的拓扑指数仅考虑原子间的连接关系,不能区分手性信息．故本研究对Am指数与分子连接性指数进行了扩展,并将其用于3-苯基哌啶类手性化合物的构效关系研究．扩展后的拓扑指数构造的数学模型优于用传统的Am指数与分子连接性指数得到的模型．同时进行了变量的两两相关性测试,结果显示所选3个变量之间的相关性较小．通过交叉验证,证明手性拓扑指数所得到的数学模型是稳定的．并进一步运用人工神经网络,得到了满意的结果．     

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.     

Molecular connectivity methods for the characterization of surface energetics of liquids and polymers

In the topological approach to structure-property relationships, the molecular structure is described in terms of appropriate weighted graphs to which suitable topological parameters, usually known as molecular connectivity indices, can be associated. Molecular connectivity indices are here applied to the prediction of surface free energy and Good-van Oss-Chaudhury acid-base components of organic compounds. To this aim, some quantitative structure-property relationships (QSPRs) are determined, involving both topological indices and group indicator variables of the customary functional group theory. The semiempirical models obtained to appear satisfactory and show significant advantages with respect to the models based on the purely functional group approach.