Topological indices derived from the G(a,b,c) matrix, useful as physicochemical property indices (original) (raw)
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Iranian journal of mathematical chemistry, 2015
Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. One of the useful indices for examination of structure- property relationship is Randic' index. In this study is represented the relationship between the Randic', Balaban and Szeged indices and Harary numbers to the enthalpies of combustion ( C H sub H ) of monocarboxylic acids (C2C20) are established, and then, some useful topological indices for examination of the structure- property relationship are presented.
2018
QSPR models are mathematical equations that attempt to correlate chemical structure with a wide variety of physical, chemical and biological properties. In this study, the relationships between the Randic' (χ), Balaban (J), Wiener polarity (Wp), Hyper Wiener (WW), Szeged (Sz), Harary (H), and Wiener (W) indices to the entropy (S) , thermal energy (Eth) and heat capacity (CV) of alcohols are presented. Physicochemical properties are determined by the quantum mechanics methodology at the Hartree-Fock (HF) level using the ab initio 6-31G basic set. Multiple linear regressions (MLR) and backward methods were employed to obtain the QSPR models. After MLR analysis, we studied the validation of linearity between the molecular descriptors in the best models for the used properties. The satisfactory results obtained show that the combination of the three descriptors (χ, J, W) is excellent to predict heat capacity and thermal energy while the three descriptors (J, W, WP) are useful to pre...
QSPR study on benzene derivatives to some physico-chemical properties by using topological indices
Iranian journal of mathematical chemistry, 2016
QSPR study on benzene derivatives have been made using recently introduced topological methodology. In this study the relationship between the Randic' (x'), Balaban (J), Szeged (Sz),Harary (H), Wiener (W), HyperWiener and Wiener Polarity (WP) to the thermal energy (Eth), heat capacity (CV) and entropy (S) of benzene derivatives is represented. Physicochemical properties are taken from the quantum mechanics methodology with HF level using the ab initio 6-31G basis sets. The multiple linear regressions (MLR) and back ward methods (with significant at the 0.05 level) were employed to give the QSPR models. The satisfactory obtained results show that combining the two descriptors (Sz, HW) are useful topological descriptors for predicted (CV) and (S) of the 45 benzene derivatives. The training set models established by MLR method have not good correlation of (Eth), which means QSPR models could not predict the thermal energy of compounds.
QSPR Analysis of Degree-Based Topological Indices with physical properties of Benzenoid Hydrocarbons
General Letters in Mathematics
Benzenoid hydrocarbons are condensed polycyclic unsaturated fully conjugated hydrocarbons composed exclusively of six membered rings. Benzenoid system may be represented by different kinds of graphs. Each hexagon of a benzenoid or coronoid system may be represented by a single vertex. In this paper, we find the values of six important degree-based topological indices of molecular graph of benzenoid hydrocarbons. Further, we show that these parameters are highly correlated with physical properties of benzenoid hydrocarbons.
Iranian journal of mathematical chemistry, 2016
Quantitative Structure-Property Relationship (QSPR) models are useful in understanding how chemical structure relates to the physicochemical properties of natural and synthetic chemicals. In the present investigation the applicability of various topological indices are tested for the QSPR study on 24 aldehydes. The topological indices used for the QSPR analysis were Randic () (the first order molecular connectivity), Balaban (J), Wiener (W) and Harary (H) indices. In this study, the relationship between the topological indices to the thermal energy (Eth), heat capacity (Cv) and entropy(S) of 24 aldehydes are established. The thermodynamic properties are taken from HF level using the ab initio 6-31 G basis sets from the program package Gussian 98. For obtaining appropriate QSPR model we have used multiple linear regression (MLR) techniques and followed Back ward regression analysis. The results have shown that combining the three descriptors (J, W, ) could be used successfully for ...
Molecules, 2003
A novel topological approach for obtaining a family of new molecular descriptors is proposed. In this connection, a vector space E (molecular vector space), whose elements are organic molecules, is defined as a "direct sum" of different ℜ i spaces. In this way we can represent molecules having a total of i atoms as elements (vectors) of the vector spaces ℜ i (i=1, 2, 3,..., n; where n is number of atoms in the molecule). In these spaces the components of the vectors are atomic properties that characterize each kind of atom in particular. The total quadratic indices are based on the calculation of mathematical quadratic forms. These forms are functions of the k-th power of the molecular pseudograph's atom adjacency matrix (M). For simplicity, canonical bases are selected as the quadratic forms' bases. These indices were generalized to "higher analogues" as number sequences. In addition, this paper also introduces a local approach (local invariant) for molecular quadratic indices. This approach is based mainly on the use of a local matrix [M k (G, F R )]. This local matrix is obtained from the k-th power (M k (G)) of the atom adjacency matrix M. M k (G, F R ) includes the elements of the fragment of interest and those that are connected with it, through paths of length k. Finally, total (and local) quadratic indices have been used in QSPR studies of four series of organic compounds. The quantitative models found are significant from a statistical Molecules 2003, 8 688 point of view and permit a clear interpretation of the studied properties in terms of the structural features of molecules. External prediction series and cross-validation procedures (leave-one-out and leave-group-out) assessed model predictability. The reported method has shown similar results, compared with other topological approaches.
QSAR & …, 2004
The primary goal of a quantitative structure-property relationship (QSPR) is to identify a set of structurally based numerical descriptors that can be mathematically linked to a property of interest. Recently, we proposed some new topological indices (Sh indices) based on the distance sum and connectivity of a molecular graph that derived directly from two-dimensional molecular topology for use in QSAR/QSPR studies. In this study, the ability of these indices to predict the liquid densities (r) of a large and diverse set of organic liquid compounds (521 compounds) has been examined. Ten different Sh indices were calculated for each molecule. Both linear and non-linear modeling methods were implemented using principal component regression (PCR) and principal component-artificial neural network (PC-ANN) with back-propagation learning algorithm, respectively. Correlation ranking procedure was used to rank the principal components and entered them into the models. PCR analysis of the data showed that the proposed Sh indices could explain about 91.82% of variations in the density data, while the variations explained by the ANN modeling were more than 97.93%. The predictive ability of the models was evaluated using external test set molecules and root mean square errors of prediction of 0.0308 g ml À1 and 0.0248 g ml À1 were obtained for liquid densities of external compounds by linear and non-linear models, respectively.
Revue Roumaine de Chimie, 2019
In this work, normal boiling points (NBPs) for a group of aliphatic esters were modeled using a combination of the modified Xu (m Xu) and the atom-type-based AI topological indice. The multiple linear regression model consisting of m Xu, AI(-CH 3) and AI(-O-) showed the squared correlation coefficient, Fisher ratio and standard error values of 0.994, 6705.7 and 4.54, respectively. Statistical validity of the model was verified by the external validation technique. Based on the results, fraction contribution of the topological indices entered the model decreased in the order of m Xu > AI(-CH 3) > AI(-O-) showing that NBPs of aliphatic esters are mainly dominated by molecular size, and degree of branching and polarity of the molecules have smaller contributions to the normal boiling points.
Canadian Journal of Chemistry, 2009
The new topological indices (Sh indices) based on the distance sum and connectivity of a molecular graph, previously developed by our team, were extended to predict the two physicochemical properties, including normal boiling point (NBP) and molar refractivity (MR), of a large set of organic compounds consisting of alkanes, alkenes, ethers, amines, alcohols, alkylbenzenes, and alkylhalides. The sets of molecular descriptors were derived directly from the two-dimensional molecular structure of the compounds based on graph theory. Both linear and nonlinear modelings were implemented by using principal component regression (PCR) and principal component -artificial neural network (PC-ANN) with back-propagation learning algorithm, respectively. Eigenvalue and correlation-ranking procedures were used to rank the principal components and entered them into the models. Principal component analysis of Sh data matrix showed that the respective six and seven PCs could explain 97.49% and 99.22% of variances in the Sh indices. PCR analysis of the NBP and MR data demonstrated that the proposed Sh indices could explain about 97.52% and 99.52% of variations, while the variations explained by the PC-ANN modeling were more than 99.00% and 99.82%, respectively. The predictive ability of the models were evaluated using an external test set for NBP and MR of the molecules with the respective root-mean -square errors lower than 9.69 K and 0.660 cm 3 mol -1 for the linear model and 6.17 K and 0.416 cm 3 mol -1 for the nonlinear model.
2017
Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and itsresults have applications in many areas of sciences.A graph is atopological conceptrather than a geometrical concept of fixed geometry, and henceEuclidean metriclengths, angles and three-dimensional spatial configurations have nomeaning. One of the useful indices for examination of structureproperty relationship is Randic' index. In this study, the relationship between the Randic'( 1 X), Balaban (J) and Szeged (Sz) indices and Harary numbers (H) to the thermal energy (Eth), heat capacity (Cv) and entropy(S) of monocarboxylic acids (C2C20) are established. The thermodynamic properties are taken from HF level using the ab initio 6-31 G basis sets from the program...