Topological Estimation of Aromatic Stabilities of Polyacenes and Helicenes: Modeling of Resonance Energy and Benzene Character

The distance-based topological indices viz Wiener (W)-, Szeged (Sz)-, Padmakar-Ivan (PI)- and Sadhana (Sd)-indices have been used for estimating aromatic stabilities as well as % benzene character of polyacenes and helicenes. Excellent models are obtained in combined set and there was no need to split the data set into polyacenes and helicenes. The newly introduced Sd index was found the best index among all the four indices used. In bi-parametric modeling with the combination of the Sd index with the PI index yielded excellent results. The results are discussed critically on the basis of variety of statistical parameters.     

A comparative QSAR study using Wiener, Szeged, and molecular connectivity indices

In this study we have investigated the relative correlation potential of Wiener (W), Szeged (Sz), and molecular connectivity indices (0chiR, 1chiR and 2chiR) in developing quantitative structure-activity relationships, QSAR; log P values of benzoic acid and its nuclear-substituted derivatives were used for this purpose. The statistical analyses for univariate and multivariate correlations had indicated that both W and Sz are closely related to the connectivity indices (mchiR) and that the W, the Sz, and the 1chiR indices have similar modeling potentials. 1chiR gives slightly better results than both W and Sz. Other connectivity indices 0chiR and 2chiR correlate poorly with log P.     

QSAR study on binding affinity of PATs (rodenticides) to the [3H]-mepyramine-labelled H1 receptor in rat and guinea pig brain

The binding of a series of PAT analogues (rodenticides) to the [3H]-mepyramine-labelled H1 receptor in rat and guinea pig brain was investigated topologically using negentropy (N), molecular redundancy (MRI), first-order molecular connectivity (1chi(v)), Wiener (W), and Szeged (Sz) indices. Multiple regression analyses showed that MRI provided excellent results upon introduction of indicator parameters. Predictive ability of the proposed models was discussed using cross-validation parameters.     

On the geometric–arithmetic index by decompositions-CMMSE

The concept of geometric–arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. There are many papers studying different kinds of indices (as Wiener, hyper–Wiener, detour, hyper–detour, Szeged, edge–Szeged, PI, vertex–PI and eccentric connectivity indices) under particular cases of decompositions. The main aim of this paper is to show that the computation of the geometric-arithmetic index of a graph G is essentially reduced to the computation of the geometric-arithmetic indices of the so-called primary subgraphs obtained by a general decomposition of G. Furthermore, using these results, we obtain formulas for the geometric-arithmetic indices of bridge graphs and other classes of graphs, like bouquet of graphs and circle graphs. These results are applied to the computation of the geometric-arithmetic index of Spiro chain of hexagons, polyphenylenes and polyethene.     

Computing weighted Szeged and PI indices from quotient graphs

The weighted (edge-)Szeged index and the weighted (vertex-)PI index are modifications of the (edge-)Szeged index and the (vertex-)PI index, respectively, because they take into account also the vertex degrees. As the main result of this article, we prove that if G is a connected graph, then all these indices can be computed in terms of the corresponding indices of weighted quotient graphs with respect to a partition of the edge set that is coarser than the Θ^*-partition. If G is a benzenoid system or a phenylene, then it is possible to choose a partition of the edge set in such a way that the quotient graphs are trees. As a consequence, it is shown that for a benzenoid system, the mentioned indices can be computed in sublinear time with respect to the number of vertices. Moreover, closed formulas for linear phenylenes are also deduced.     

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.     

QSAR Study on Binding Affinity of PATs (Rodenticides) to the [3H]-Mepyramine-Labelled H1 Receptor In Rat and Guinea Pig Brain

Abstract

The binding of a series of PAT analogues (rodenticides) to the [³H]-mepyramine-labelled H₁ receptor in rat and guinea pig brain was investigated topologically using negentropy (N), molecular redundancy (MRI), first-order molecular connectivity (¹X _v ), Wiener (W), and Szeged (Sz) indices. Multiple regression analyses showed that MRI provided excellent results upon introduction of indicator parameters. Predictive ability of the proposed models was discussed using cross-validation parameters.     

Contribution to linearly programmed temperature gas chromatography. Further application of the Van den Dool-Kratz equation, and a new utilization of the Sadtler retention index library

Programmed temperature retention indices (PTRIs) calculated according to the equations of Van den Dool and Kratz, Golovnya and Uraletz, and Erdey et al. (also referred to as Antoine's integrated equation) are used in this work. Precalculation of isotherm retention indices from the results of a linearly programmed temperature GC is also presented. Deviations between experimental and calculated isothermal retention indices are below 2 retention index units. A relative "volatility" retention index is defined, as a function of the "volatilities"of the solute and the bracket reference n-alkanes. The comparison of the "volatility" retention indices with the PTRIs obtained with the other above equations shows absolute deviations of up to 4 retention index units. Based on an earlier "equivalent" temperature concept and on Tekler's proviso, a novel way for the utilization of Sadtler's retention index database, which takes advantage of the 3 data supplied by the library, is proposed.     

Theoretical Study on Hydrogen Bonding of Mono‐ and Dihydrated Complexes of 7‐(3′‐Pyridyl)indole in Excited States

The intermolecular hydrogen bonds of mono‐ and dihydrated complexes of 7‐(3′‐Pyridyl)indole (7‐3′PI) have been investigated using the time‐dependent density functional theory (TD‐DFT) method. The electrostatic potential analysis of monomer 7‐3′PI and 7‐(3′‐Pyridyl)indole‐water (7‐3′PI‐W) indicates that an intermolecular hydrogen bond between two waters can be formed for 7‐(3′‐Pyridyl)indole‐2water (7‐3′PI‐2W) complex. The calculated bond lengths of the intermolecular hydrogen bonds of 7‐3′PI‐W and 7‐3′PI‐2W in the S₁ state (the first excited singlet state) are all shortened compared to the ground state. By the analysis of bond length, charge population and infrared spectra, it is demonstrated that the intermolecular hydrogen bonds of 7‐3′PI‐W and 7‐3′PI‐2W are all strengthened upon electronic excitation to the S1 state. Moreover, the fluorescence of 7‐3′PI‐W and 7‐3′PI‐2W are all red‐shifted to larger wavelength compared to monomer 7‐3′PI. The red‐shift of fluorescence peak of 7‐3′PI‐W and 7‐3′PI‐2W should be attributed to the change of hydrogen bond interaction before and after photoexcitation. Therefore, it can be concluded that the intermolecular hydrogen bonding strengthening in the excited S₁ state induces the fluorescence weakening of 7‐3′PI.     

Generalized Wiener indices in hexagonal chains

The Wiener index, or the Wiener number, also known as the “sum of distances” of a connected graph, is one of the quantities associated with a molecular graph that correlates nicely to physical and chemical properties, and has been studied in depth. An index proposed by Schultz is shown to be related to the Wiener index for trees, and Ivan Gutman proposed a modification of the Schultz index with similar properties. We deduce a similar relationship between these three indices for catacondensed benzenoid hydrocarbons (graphs formed of concatenated hexagons, or hexagonal chains, or sometimes acenes). Indeed, we may define three families of generalized Wiener indices, which include the Schultz and Modified Schultz indices as special cases, such that similar explicit formulae for all generalized Wiener indices hold on hexagonal chains. We accomplish this by first giving a more refined proof of the formula for the standard Wiener index of a hexagonal chain, then extending it to the generalized Wiener indices via the notion of partial Wiener indices. Finally, we discuss possible extensions of the result. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Novel topological index F based on incidence matrix

Based on incidence matrix W, the novel topological index F is defined by the matrices L, W, X as F = LWX. The properties, the chemical environments, and the interaction of the vertexes in a molecule are taken into account in this definition. Several good QSPR models in the hetero-atom-containing organic compounds and inorganic compounds are obtained. Moreover, based on the definition of F and the values C(i) of the vertexes or the values (m)F(ij) of the chemical bonds, we have obtained serial indices, (m)F(v), (m)F(b), and F(w). They are successfully applied to QSPR models and good correlation results have been obtained as well.     

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.     

Erythema UV-B exposure near the Antarctic Peninsula and comparison with an equatorial site

Observations of UV-B radiation in the area of the Antarctic Peninsula are described, with the objective to obtain an evaluation of the UV-B enhancements observed during ozone hole episodes, and compare these with equatorial values. The enhancements observed during Southern Hemisphere spring are described in terms of a specific case of enhancement, at the Antarctic peninsula, which has shown a maximum UV-B index of 8.7, in October 1998. The average enhancement between the autumn-unperturbed and spring-perturbed periods results in an UV-B index of 5.4, but with large fluctuations in which much larger indices are produced. These values are compared to indices normally observed in the equatorial region. For measurements obtained with the same kind of instrument at Natal (5.8°S, 35.2°W), the UV-B index varies between 7 and 14, which means that enhanced UV-B indices in the Antarctic Peninsula may become of the same order of magnitude of the lower limit equatorial values.     

On structural interpretation of several distance related topological indices.

We consider the role that individual bonds play in bond-additivities in order to better understand the structural basis of various topological indices. In particular we consider indices closely related to the Wiener index (W) and the distance matrix and search for optimal weights of terminal and interior CC bonds in alkanes for a selection of physicochemical properties. It is interesting to note that different properties are associated with different relative roles of the exterior and the interior CC bonds.