Novel shape descriptors for molecular graphs.

We report on novel graph theoretical indices which are sensitive to the shapes of molecular graphs. In contrast to the Kier's kappa shape indices which were based on a comparison of a molecular graph with graphs representing the extreme shapes, the linear graph and the "star" graph, the new shape indices are obtained by considering for all atoms the number of paths and the number of walks within a graph and then making the quotients of the number of paths and the number of walks the same length. The new shape indices show much higher discrimination among isomers when compared to the kappa shape indices. We report the new shape indices for smaller alkanes and several cyclic structures and illustrate their use in structure-property correlations. The new indices offer regressions of high quality for diverse physicochemical properties of octanes. They also have lead to a novel classification of physicochemical properties of alkanes.     

Quantum molecular similarity. 3. QTMS descriptors.

Building on the ideas of a previous paper [part 1, J. Phys. Chem. A 1999, 103, 2883] we present a new molecular similarity method based on the topology of the electron density. This method is directly applicable to QSARs and is called quantum topological molecular similarity (QTMS). It has been tested for five sets of carboxylic systems including para- and meta-benzoic acid, para-phenylacetic acid, 4-X-bicyclo[2.2.2]octane-1-carboxylic acids, and polysubstituted benzoic acids. In combination with the partial least squares (PLS) procedure QTMS is able to produce excellent and statistically valid regressions. It is shown that QTMS avoids certain challenges of traditional Carbó-like similarity indices. Finally, QTMS is able to suggest a molecular fragment that contains the active center or the part of the molecule that is responsible for the QSAR.     

Using molecular quantum similarity measures as descriptors in quantitative structure-toxicity relationships

In this paper molecular quantum similarity measures (MQSM) are used to describe molecular toxicity and to construct Quantitative Structure-Toxicity Relationships (QSTR) models. This study continues the recently described relationships between MQSM and log P values, which permits to use the theoretical MQSM as an alternative to the empirical hydrophobic parameter in QSPR studies. In addition a new type of MQSM is presented in this work: it is based on the expectation value of electron-electron repulsion energy. The molecular properties studied here, as application examples are aquatic toxicity, toxicology on Bacteria and inhibition of a macromolecule employing four different molecular sets.     

Natural molecular shells as open subsystems of small molecules

We compare the first few natural molecular shells of several small molecules to the corresponding “restricted Hartree‐Fock,” “second‐order Møller‐Plesset,” and “local density approximation” molecular shells. Occupation probabilities of each molecular shell are computed ab initio, especially the single‐occupation and double‐occupation probabilities, that is, the probabilities that the molecular shell is occupied by exactly one electron or by exactly two electrons. We observe that among corresponding molecular shells, the natural molecular shell has the least single‐occupation probability and the greatest double‐occupation probability. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Comparative study of GQ and QG indices as potentially favorable molecular descriptors

In chemical graph theory, several degree-based topological indices are introduced and put forward in the development of quantitative structure-property relationships (QSPR)/quantitative structure-activity relationships (QSAR) studies. However, only a few of them are considered employable in the prediction of physical and chemical properties and biological activities of molecular compounds. Here, we focus our attention on some foremost characteristics of newly defined Geometric–Quadratic $$ and Quadratic–Geometric $$ indices such as prediction power, degeneracy and structure sensitivity. Based on these attributes, we discuss their comparison with other well-established degree-based topological indices with the help of statistical analysis and computational techniques on the data sets of octane, nonane and decane isomers. Some of the graphical approaches, statistical outcomes and computational tests exhibit the dominating nature of the $$ and $$ indices over other topological indices.     

1D 13C-NMR data as molecular descriptors in spectra--structure relationship analysis of oligosaccharides

Spectra-structure relationships were investigated for estimating the anomeric configuration, residues and type of linkages of linear and branched trisaccharides using 13C-NMR chemical shifts. For this study, 119 pyranosyl trisaccharides were used that are trimers of the α or β anomers of D-glucose, D-galactose, D-mannose, L-fucose or L-rhamnose residues bonded through a or b glycosidic linkages of types 1→2, 1→3, 1→4, or 1→6, as well as methoxylated and/or N-acetylated amino trisaccharides. Machine learning experiments were performed for: (1) classification of the anomeric configuration of the first unit, second unit and reducing end; (2) classification of the type of first and second linkages; (3) classification of the three residues: reducing end, middle and first residue; and (4) classification of the chain type. Our previously model for predicting the structure of disaccharides was incorporated in this new model with an improvement of the predictive power. The best results were achieved using Random Forests with 204 di- and trisaccharides for the training set-it could correctly classify 83%, 90%, 88%, 85%, 85%, 75%, 79%, 68% and 94% of the test set (69 compounds) for the nine tasks, respectively, on the basis of unassigned chemical shifts.     

Graph theory and molecular orbitals. The loop rule

Graph theory is applied to the study of the dependence of total π-electron energy, π-electron charge distribution and free valency indices of conjugated hydrocarbons on molecular topology. It is shown that the number of loops in the molecular graph determines these quantities.