Eigenvectors obtained from the adjacency or distance matrix of graphs, corresponding to the largest negative eigenvalue, are useful real number vertex invariants for intramolecular ordering of vertices. From them or from eigenvalues, several new topological indices have been tested on the basis of intermolecular ordering of isomeric alkanes and of correlating ability with properties such as the boiling temperature.

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Molecular modeling and MTD methods are useful tools to assess both qualitative (SAR) and quantitative (QSAR) chemical structure-biological activity relationships. The 1-[(2-hydroxiethoxi)-methyl]-6-(phenylthio)thymine congeners (HEPT ligands) show in vitro anti-viral activity against the type-1 human immunodeficiency virus (HIV-1), which is the etiologic agent of AIDS. This work shows an extensive QSAR study performed upon a large series of 79 HEPT ligands using the MTD and HyperChem molecular modeling methods. The studied HEPT ligands are HIV reverse-transcriptase inhibitors. Their geometries were optimized and conformational analysis was carried out to build the hypermolecule, which allowed applying the MTD method. The hypermolecule was used for space mapping of the receptor's interaction site. The obtained results show that there are three 3D molecular zones important for the anti-HIV biological activity of the HEPT ligands under study.Int. J. Mol. Sci. 2006, 7 538

A comparative study of 36 molecular descriptors derived from the topological distance matrix and van der Waals space is carried out within this paper. They are partitioned into 16 generalized topological distance matrix indices, 11 topological distance indices known in the literature (seven obtained from eigenvalues/eigenvectors of distance matrix), and 9 van der Waals molecular descriptors. The generalized topological distance indices, k δ λ (λ = 1 -3, k = 1 -4), are introduced in this work on the basis of reciprocical distance matrix. Intercorrelation analysis reveals that topological distance indices mostly contain the same type of information, while van der Waals indices can be bound to the shape or the size of molecules. Furthermore, we found that topological distance indices are good for describing molecular size, and they may be viewed as bulk parameters. The most accurate QSPR models for predicting boiling point of alkanes are based on some of the generalized, eigenvalues/eigenvectors topological distance indices and the van der Waals descriptors of molecular size.

A theoretical study regarding the evaluation of the antioxidant character of three of the most wide-spread anthocyanidins (cyanidin, delphinidin and malvidin) was carried out at ab initio level. Different parameters (bond dissociation enthalpy, ionization potential, proton affinity, and electron transfer enthalpy) were computed for each OH group of the compounds in order to predict their antioxidant capacity. Several molecular descriptors based on frontier molecular orbital theory (hardness, electrophilicity, frontier charge density) were also calculated, as well as the atomic charges corresponding to the O atoms of the hydroxyl groups.