Second-order Connectivity Indices Research Articles

Study on quantitative structure-biodegradability relationships of amine collectors by GFA-ANN method

In this study, the biodegradability of 17 amine collectors, categorized by fatty amine, quaternary ammonium compounds and oxygen-containing amine collectors, are tested with the Closed Bottle Test for 90 days, and the results indicate most amine collectors are not readily biodegradable. The oxygen-containing amine collectors have the best biodegradability due to the introduced oxygen-containing functional groups, subsequently fatty amine collectors with branched chains, while the tested quaternary ammonium compounds all have poor biodegradation ability. Besides, we search for and calculate 35 molecular descriptors to develop the quantitative structure biodegradability relationship (QSBR) of amine collectors. With the Genetic Function Approximation (GFA) algorithm, two sets of important molecular descriptors related to biodegradability (q) of amine collectors are selected from 35 molecular descriptors. Based on internal and external validations, the robust and reliable non-linear QSBR model with the squared correlation coefficient above 0.99 is determined via Artificial Neural Network (ANN) method, where the descriptors are respectively CL, N, ELUMO, δv2, indicating the biodegradable ability of amine collectors is correlated with the alkyl chain lengths (CL), the number of nitrogen atom-containing compounds (N), energy of the lowest unoccupied molecular orbital (ELUMO) and valence second-order connectivity index (δv2).

Environmentally-benign transition metal catalyst design using optimization techniques

Transition metal catalysts play a crucial role in many industrial applications, including the manufacture of lubricants, smoke suppressants, corrosion inhibitors and pigments. The development of novel catalysts is commonly performed using a trial-and-error approach which is costly and time-consuming. The application of computer-aided molecular design (CAMD) to this problem has the potential to greatly decrease the time and effort required to improve current catalytic materials in terms of their efficacy and biological effects. This work applies an optimization approach to redesign environmentally-benign homogeneous catalysts, specifically those which contain transition metal centers, to improve certain physical properties. Two main tasks must be achieved in order to perform the molecular design of a novel catalyst: biological and chemical properties must be estimated directly from the molecular structure, and the resulting optimization problem must be solved in a reasonable time. In this work, connectivity indices are used for the first time to predict the physical properties of a homogeneous catalyst. The existence of multiple oxidation states for transition metals requires a reformulation of the original equations for these indices. Once connectivity index descriptors have been defined for transition metal catalysts, structure–property correlations are then developed based on regression analysis using literature data for various properties of interest, including toxicity and electronegativity. These structure–property correlations are then used within an optimization framework to design novel homogeneous catalyst structures for use in a given application. The use of connectivity indices which define the topology of the molecule within the formulation guarantees that a complete molecular structure is obtained when the global optimum is found. In this work, second-order connectivity indices are used to obtain more information about steric features of the catalyst molecules, and non-linear correlations are employed to improve the accuracy of the property prediction equations. The structure–property correlations are then combined with linear structural feasibility constraints to form a mixed-integer non-linear program (MINLP), which when solved to optimality results in a catalyst molecule which most closely matches given property targets. To solve the resulting optimization problem, two methods are applied: Tabu search (a stochastic method), and outer approximation, a deterministic approach. For the outer approximation solution, a data structure is used which permits all equations except for the property prediction expressions to be written in linear forms. The computational efficiency of Tabu search is not strongly dependent on the existence of non-linear constraints, so for solution using this method, a non-linear form for the second-order connectivity index was chosen, which decreases the number of binary variables required. The solution methods are compared using three examples involving the design of environmentally-benign homogeneous catalysts containing molybdenum centers. Results show the efficacy of the formulation, and provide evidence that the Tabu search algorithm is more suitable for this type of molecular design algorithm than the commercially available deterministic approach.

Physicochemical Interpretation of Molecular Connectivity Indices

Molecular connectivity indices are identified as components of the molecular accessibility. The first- and second-order connectivity indices represent molecular accessibility areas and volumes, respectively, whereas higher order indices represent magnitudes in higher dimensional spaces. In identifying accessibility perimeters, we recognized the atom degrees as a measure of the accessibility perimeter of the corresponding atom. The Randic and connectivity indices are identified as the two components of the molecular accessibility area. The accessibility perimeter is computed here from the van der Waals and covalent radii of the atoms and the overlapping angle between the van der Waals circumferences of bonded atoms. The description of the accessibility area in terms of the first-order Randic and connectivity indices accounts for the success of these descriptors in correlating different physicochemical and biological properties because they are a measure of the extension of intermolecular interactions. A th...

Molecular topology and chromatographic retention parameters for benzodiazepines

The relationship between gas-liquid chromatographic (GLC) retention properties and R F values in thin-layer chromatography (TLC) with molecular connectivity indices, m X t, was investigated for a series of benzodiazepines using multiple correlation coefficients, standard errors of estimate, F-Snedecor function values and Student's t-test as the criteria for best equation selection. Regression analyses show that the molecular connectivity model predicts the retention properties in GLC with the polar stationary phase OV-17 at 280°C and the R F values in TLC with the stationary phase silica gel. However, zero- or second-order connectivity indices alone are not sufficient; higher-order indices are shown to be necessary. The effect of the polarity of the mobile phases in TLC was also investigated.