The Overall Hyper-Wiener Index

The concept of overall connectivity of a graph G was extended here to the definition of the overall hyper-Wiener index OWW(G) of a graph G, defined as the sum of the hyper-Wiener indexes in all subgraphs of G, as well as the sum of eth-order terms, ^e OWW(G), with e being the number of edges in the subgraph. The potential usefulness of the overall hyper-Wiener index in QSAR/QSPR is evaluated by its correlation with a number of properties of C3-C8 alkanes and cycloalkanes.     

Novel Indices for the Topological Complexity of Molecules

Abstract

The development of molecular complexity measures is reviewed. Two novel sets of indices termed topological complexities are introduced proceeding from the idea that topological complexity increases with the overall connectivity of the molecular graph. The latter is assessed as the connectivity of all connected subgraphs in the molecular graph, including the graph itself. First-order, second-order, third-order, etc., topological complexities ⁱ TC are defined as the sum of the vertex degrees in the connected subgraphs with one, two, three, etc., edges, respectively. Zero-order complexity is also specified for the simplest subgraphs–the graph vertices. The overall topological complexity TC is then defined as the sum of the complexities of all orders. These new indices mirror the increase in complexity with the increase in the number of atoms and, at a constant number of atoms, with the increase in molecular branching and cyclicity. Topological complexities compare favorably to molecular connectivities of Kier and Hall, as demonstrated in detail for the classical QSPR test-the boiling points of alkanes. Related to the wide application of molecular connectivities to QSAR studies, a similar importance of the new indices is anticipated.     

Analysis of Complex Mixtures of Aromatic Hydrocarbons. Relations between Retention Index and Molecular Structure

Abstract

Relationships between Kovats indices on nonpolar stationary phases and the structure of alkyl- and alkenylbenzenes, defined by the molecular connectivity or connectivity index, have been established.

Almost all components of aromatic naphthas are included in the different linear equations which relate both empirical indices. The constant terms of the straight lines depend on the nature and position of the substituents in the benzene ring. Substituents in para position do not influence each other, allowing the study of the effect of its nature on the ratio δI/Δχ

Equations for different series of compounds, including n-alkyl- and 1,4-di-n-alkylbenzene homologous series, are calculated in order to support its identification in aromatic naphthas.     

The overall Wiener index--a new tool for characterization of molecular topology.

Recently, the concept of overall connectivity of a graph G, TC(G), was introduced as the sum of vertex degrees of all subgraphs of G. The approach of more detailed characterization of molecular topology by accounting for all substructures is extended here to the concept of overall distance OW(G) of a graph G, defined as the sum of distances in all subgraphs of G, as well as the sum of eth-order terms, (e)OW(G), with e being the number of edges in the subgraph. Analytical expressions are presented for OW(G) of several basic classes of graphs. The overall distance is analyzed as a measure of topological complexity in acyclic and cyclic structures. The potential usefulness of the components of this generalized Wiener index in QSPR/QSAR is evaluated by its correlation with a number of properties of C3-C8 alkanes and by a favorable comparison with models based on molecular connectivity indices.     

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.     

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.     

Correlation between topological features and surface tension of binary liquid mixtures

Summary The excess surface tension of a large number of binary liquid mixtures has been correlated with their topological features quantified in terms of the molecular connectivity indices. The agreement between the calculated and experimental ^E values is reasonably well for all the mixtures. A simple correlation has also been proposed between ^E and molar excess volume (V ^E ) of a binary mixture. The correlation is quite useful in correlating ^E data even for the mixtures where either one or both the components are associated in the pure state and/or there is interaction between them.

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Korrelation zwischen topologischen Gegebenheiten und Oberflächenspannung von binären flüssigen Mischungen

Zusammenfassung Die Exzeß-Oberflächenspannungen einer großen Anzahl von binären flüssigen Mischungen wurden mit der Topologie ihrer Komponenten in Form der molekularen Konnektivitätsindices korreliert. Die Übereinstimmung zwischen den ^E -Werten ist für alle Mischungen relativ gut. Es wurde ebenfalls eine einfache Korrelation zwischen ^E und den molaren Exzeß-Volumina (V ^E ) der binären Mischungen vorgeschlagen. Diese Korrelierung ist nützlich, um die ^E -Werte sogar dann für die Korrelation von Mischungen verwenden zu können, wenn entweder eine oder beide Komponenten im Reinzustand assoziiert sind und/oder eine Wechselwirkung zwischen ihnen besteht.

     

Molecular Search of New Active Drugs Against Toxoplasma Gondii

Abstract

Molecular connectivity has been applied to the search of new compounds with activity against the protozoan Toxoplasma gondii, using a stepwise linear discriminant analysis (SLDA) which is able to classify a compound according its activity either as active or as inactive. Among the selected compounds, andrographolide and dibenzotiophene sulfone stand out, both with IC₅₀ values lower than 1 μg/m1, which are comparable to these of drugs such as sulfamethoxazole, pyrimethamine and trimethoprim, with IC₅₀ values equal to 1.1, 0.04 and 2.31 μg/ml, respectively. These results confirm the usefulness of our topological approach for the selection and design of new-lead drugs active against Toxoplasma gondii.     

Hazard Evaluation of Ten Organophosphorus Insecticides Against the Midge,Chironomus riparius via QSAR

Abstract

Toxicities of ten organophosphorus (OP) insecticides were measured against midge larvae (Chironomus riparius) under varying temperature (11, 18, and 25°C) and pH (6, 7, and 8) conditions and with and without sediment. Toxicity usually increased with increasing temperature and was greater in the absence of sediment. No trend was found with varying pH. A series of unidimensional parameters and multidimensional models were used to describe the changes in toxicity. Log K _ow was able to explain about 40–60% of the variability in response data for aqueous exposures while molecular volume and aqueous solubility were less predictive. Likewise, the linear solvation energy relationship (LSER) model only explained 40–70% of the response variability, suggesting that factors other than solubility were most important for producing the observed response. Molecular connectivity was the most useful for describing the variability in the response. In the absence of sediment, ¹χ ^v and ³κ were best able to describe the variation in response among all compounds at each pH (70–90%). In the presence of sediment, even molecular connectivity could not describe the variability until the partitioning potential to sediment was accounted for by assuming equilibrium partitioning. After correcting for partitioning, the same molecular connectivity terms as in the aqueous exposures described most of the variability, 61–87%, except for the 11°C data where correlations were not significant. Molecular connectivity was a better tool than LSER or the unidimensional variables to explain the steric fitness of OP insecticides which was crucial to the toxicity.     

Use of molecular connectivity indices to predict LC retention of dansylamides in six different eluent systems

Summary Molecular connectivity indices (x) through the sixth order were calculated and compared with measured reversed-phase liquid chromatographic retention data of sixteen dansyl derivatives of amines (dansylamides). Retention measurements were performed in the capacity factor, k′, range 1–30 with organic solvent-water eluents using acetone, acetonitrile, ethanol, methanol, 1-propanol and 2-propanol. Mainly valence level indices were selected to describe retention. Indices of different order were selected in the different eluents, suggesting that there are differences in the retention mechanism in these eluents. Retention can be predicted with great accuracy by the molecular connectivity indices, as the high correlations between the calculated and observed retention indicate. Presented at the 15th International Symposium on Chromatography, Nürnberg, October 1984     

Correlations between topological features and physicochemical properties of molecules

The article reviews in brief, thede novo group additivity approach and, at length, the different topological approaches to obtain predictive and internally consistent correlations between various properties and structural features of molecules. The stress has mainly been on the molecular connectivity method. A new rational scheme for nomenclature of connectivity indices of different orders and types is introduced. The concept of the perturbation connectivity parameter developed by us recently has been applied to obtain correlations for molar refraction, boiling point, molar volume, heat of atomisation, heat of combustion, heat of vaporisation, magnetic susceptibility and critical constants of alkanes, alcohols and alkylbenzenes. A comparative study of various approaches reveals that the present perturbation topological approach has an edge over other similar methods.     

链烷烃的内压与分子连通指数

测定T2-甲基戊烷、3-甲基戊烷和正乙烷在293．15－318．15K温度范围的热压力系数．一个根据对应状态原理建立的模型被用来描述链烷烃的内压，它们的模型参数能很好地用分子连通指数关联．用这种方法能预测各种链烷烃从三相点到临界点广阔温度范围的内压．     

Modeling of the θ(lower critical solution temperature) in polymer solutions using molecular connectivity indices

In this work, correlations for the estimation of the θ(lower critical solution temperature, LCST) for Polystyrene, Polyethylene, Polypropylene, Polybutene-1, Polypentene-1, Poly(4-methylpentene-1), Polydimethylsiloxane and Polyisobutylene solutions were proposed based on the molecular connectivity index. The correlations give satisfactory estimation of the θ(LCST), with the absolute error smaller than 20 K for most systems studied. Since the new correlations require only molecular connectivity indices of the solvent in the calculations, and the molecular connectivity indices can be calculated easily once the molecular structure of the substance concerned is known, they have better predictive capability and are easier to apply comparing with the existing methods and models.