QSPR Models Research Articles

Extremal hyper-Zagreb index of trees of given segments with applications to regression modeling in QSPR studies

Introduced by Gutman & Trinajstić in 1972, the two well-known Zagreb indices efficiently determine the total π-electron energy of alternant hydrocarbons. The hyper-Zagreb index is a variant of the classical first Zagreb index. A tree is an acyclic graphical structure. A segment in a tree is equivalent to a vertex of degree two. This paper derives sharp upper and lower bounds on the hyper-Zagreb index of trees with given number of segments. We also characterize the corresponding trees achieving those bounds. The second part of the paper studies the predictive potential of the hyper-Zagreb index for determining physicochemical properties such as the enthalpies of combustion, formation, sublimation, and vaporization of monocarboxylic acids. Our statistical analysis asserts that the hyper-Zagreb index correlates these physicochemical properties of monocarboxylic acids with correlation coefficient ρ>0.99. The strongest correlation by the hyper-Zagreb index was obtained with the enthalpy of combustion having correlation coefficient ρ=0.999991. This warrants the further employability of the hyper-Zagreb index in QSPR modeling. This potential applicability justifies the construction of the hyper-Zagreb graphical index whose motivation of defining was purely mathematical.

QSPR-based prediction of air-water interfacial adsorption coefficients for nonionic PFAS with large headgroups

Air-water interfacial adsorption has been demonstrated to be an important process affecting the retention and distribution of PFAS in soil, surface waters, and the atmosphere, as well as being central to certain remediation methods. Measured or estimated air-water interfacial adsorption coefficients are needed for quantifying and modeling the interfacial adsorption of PFAS. A single-descriptor QSPR model developed in prior work for predicting air-water interfacial adsorption coefficients of PFAS was demonstrated to successfully represent more than 60 different PFAS, comprising all headgroup types and a wide variety of tail structures. However, the model overpredicted values for nonionic PFAS with very large headgroups. A revised QSPR model was developed in the present study to predict air-water interfacial adsorption coefficients for nonionic PFAS with large headgroups. A two-descriptor QSPR model employing molar volume and headgroup-to-tail molar-volume ratio successfully represented measured data for both nonionic PFAS and nonionic hydrocarbon surfactants. This new model provides a means to produce estimates of air-water interfacial adsorption coefficients for nonionic PFAS for which measured values are typically not available.

QSPR Analysis of Some Phenolic Compounds Present in Moringa Oleifera

QSPR analysis can be used in a variety of applications, such as drug discovery, materials science, and environmental chemistry. For example, QSPR models can be used to predict the toxicity of new chemicals, to design more effective drugs, or to optimize the properties of materials for specific applications. Phenolic compounds act as anti-oxidants, anti-carcinogenic, and anti-bacterial agents present in Moringa oleifera. These Phenolic compounds have significant antioxidant properties as they can scavenge free radicals, slow the aging process, and improve glucose uptake in muscles. They are also used to prevent the accumulation of lipids in the liver and subsequently prevent fatty liver disease, protect kidneys, prevent cancer, prevent whitening skin, chemopreventive for cancer, induce apoptosis in ovarian cancer, protect kidneys, decrease pro-inflammatory enzymes, and increase antioxidants enzymes. Furthermore, phenolic compounds inhibit enzymes linked to diabetes type-2 and they can be used to cure diabetes. Owing to the significance of these phenolic compounds, we carried out QSPR analysis using degree-based indices to know the physical characteristics affiliated with them. The outcomes indicate that these phenolic compounds could be investigated further by pharmacists and chemists when designing drugs using these topological indices values. Since the correlation for the topological indices has been discovered, positively correlated compounds may be considered for the combination of novel drug designs. Also, the computed results are useful to predict the physical properties of the phenolic compounds.

Conjugated quantitative structure-property relationship models: Prediction of kinetic characteristics linked by the Arrhenius equation.

Conjugated QSPR models for reactions integrate fundamental chemical laws expressed by mathematical equations with machine learning algorithms. Herein we present a methodology for building conjugated QSPR models integrated with the Arrhenius equation. Conjugated QSPR models were used to predict kinetic characteristics of cycloaddition reactions related by the Arrhenius equation: rate constant , pre-exponential factor , and activation energy . They were benchmarked against single-task (individual and equation-based models) and multi-task models. In individual models, all characteristics were modeled separately, while in multi-task models , and were treated cooperatively. An equation-based model assessed using the Arrhenius equation and and values predicted by individual models. It has been demonstrated that the conjugated QSPR models can accurately predict the reaction rate constants at extreme temperatures, at which reaction rate constants hardly can be measured experimentally. Also, in the case of small training sets conjugated models are more robust than related single-task approaches.

Molecular Structure-Based Prediction of Absorption Maxima of Dyes Using ANN Model

The exponentially growing energy requirements and, in turn, extensive depletion of non-restorable sources of energy are a major cause of concern. Restorable energy sources such as solar cells can be used as an alternative. However, their low efficiency is a barrier to their practical use. This provokes the research community to design efficient solar cells. Based on the study of efficacy, design feasibility, and cost of fabrication, DSSC shows supremacy over other photovoltaic solar cells. However, fabricating DSSC in a laboratory and then assessing their characteristics is a costly affair. The researchers applied techniques of computational chemistry such as Time-Dependent Density Functional Theory, and an ab initio method for defining the structure and electronic properties of dyes without synthesizing them. However, the inability of descriptors to provide an intuitive physical depiction of the effect of all parameters is a limitation of the proposed approaches. The proven potential of neural network models in data analysis, pattern recognition, and object detection motivated researchers to extend their applicability for predicting the absorption maxima (λmax) of dye. The objective of this research is to develop an ANN-based QSPR model for correctly predicting the value of λmax for inorganic ruthenium complex dyes used in DSSC. Furthermore, it demonstrates the impact of different activation functions, optimizers, and loss functions on the prediction accuracy of λmax. Moreover, this research showcases the impact of atomic weight, types of bonds between constituents of the dye molecule, and the molecular weight of the dye molecule on the value of λmax. The experimental results proved that the value of λmax varies with changes in constituent atoms and types of bonds in a dye molecule. In addition, the model minimizes the difference in the experimental and calculated values of absorption maxima. The comparison with the existing models proved the dominance of the proposed model.

Development of QSPR models for furan derivatives as corrosion inhibitors for mild steel

The quantitative structure-property relationship QSPR method has been used to analyze the corrosion inhibition properties of furan derivative inhibitors against mild steel. This modeling is based on the correlation between corrosion inhibition efficiency (IE%) and several electronic properties of compounds such as EHOMO (highest occupied molecular orbital energy), ELUMO (lowest unoccupied molecular orbital energy), EL-H (gap energy), μ (dipole moment), IP (ionization potential), EA (electron affinity), ƞ (hardness), σ (softness), χ (electronegativity), ∆N (fraction of electron transfer), ω (electrophilicity index), ∆EB-D (back-donation energy), Log P, Vm (critical volume), and Mr (relative molecular mass). These properties were calculated using DFT at B3LYP/6–31 G(d). Statistically, they analyzed using four methods: partial least squares regression PLS, principal component regression PCR, multiple linear regression MLR, and principal component analysis PCA. The best QSPR modeling results are by PCR statistical analysis. It is proven by the validation results (R2 = 0.976; R2adj = 0.90) and analysis of collinearity in the data. The predictions of the four furan-derived compounds from PCR modeling gave promising results.

Sharp Bounds on the Generalized Multiplicative First Zagreb Index of Graphs with Application to QSPR Modeling

Degree sequence measurements on graphs have attracted a lot of research interest in recent decades. Multiplying the degrees of adjacent vertices in graph Ω provides the multiplicative first Zagreb index of a graph. In the context of graph theory, the generalized multiplicative first Zagreb index of a graph Ω is defined as the product of the sum of the αth powers of the vertex degrees of Ω, where α is a real number such that α≠0 and α≠1. The focus of this work is on the extremal graphs for several classes of graphs including trees, unicyclic, and bicyclic graphs, with respect to the generalized multiplicative first Zagreb index. In the initial step, we identify a set of operations that either increases or decreases the generalized multiplicative first Zagreb index for graphs. We then involve analysis of the generalized multiplicative first Zagreb index achieving sharp bounds by characterizing the maximum or minimum graphs for those classes. We present applications of the generalized multiplicative first Zagreb index Π1α for predicting the π-electronic energy Eπ(β) of benzenoid hydrocarbons. In particular, we answer the question concerning the value of α for which the predictive potential of Π1α with Eπ for lower benzenoid hydrocarbons is the strongest. In fact, our statistical analysis delivers that Π1α correlates with Eπ of lower benzenoid hydrocarbons with correlation coefficient ρ=−0.998, if α=−0.00496. In QSPR modeling, the value ρ=−0.998 is considered to be considerably significant.

Investigation for metallic crystals through chemical invariants, QSPR and fuzzy-TOPSIS

Chemical graph theory has revolutionary impacts in the field of mathematical chemistry when complex structures are investigated through various chemical invariants (topological indices). We have performed evaluations by considering alternatives as crystal structures, namely Face-Centered Cubic (FCC), hexagonal close-packed (HCP), Hexagonal (HEX), and Body Centered Cubic (BCC) Lattice structures, through the study of two-dimensional degree-based chemical invariants, which we considered criteria. QSPR modeling has been implemented for the targeted crystal structures to investigate the ability of targeted chemical invariants to predict targeted physical properties. Furthermore, the Fuzzy-TOPSIS technique provides the optimal structure HCP ranking as first among all structures when investigated under more than one criterion, which justifies further that the structure attaining dominant countable invariant values ranks high when investigated through physical properties and fuzzy TOPSIS. Communicated by Ramaswamy H. Sarma

Gas-to-ionic liquid partition: QSPR modeling and mechanistic interpretation.

The present work was devoted to explore the quantitative structure-property relationships for gas-to-ionic liquid partition coefficients (log KILA ). A series of linear models were first established for the representative dataset (IL01). The optimal model was a four-parameter equation (1Ed) consisting of two electrostatic potential-based descriptors ( and Vs,max ), one 2D matrix-based descriptor (J_D/Dt) and dipole moment (μ). All of the four descriptors introduced in the model can find the corresponding parameters, directly or indirectly, from Abraham's linear solvation energy relationship (LSER) or its theoretical alternatives, which endows the model good interpretability. Gaussian process was utilized to build the nonlinear model. Systematical validations, including 5-fold cross-validation for the training set, the validation for test set, as well as a more rigorous Monte Carlo cross-validation were performed to verify the reliability of the constructed models. Applicability domain of the model was evaluated, and the Williams plot revealed that the model can be used to predict the log KILA values of structurally diverse solutes. The other 13 datasets were also processed in the same way, and all of the linear models with expressions similar to equation 1Ed were obtained. These models, whether linear of nonlinear, represent satisfactory statistical results, which confirms the universality of the method adopted in this study in QSPR modeling of gas-to-IL partition.

Fundamental Aspects of Skin Cancer Drugs via Degree-Based Chemical Bonding Topological Descriptors.

Due to significant advancements being made in the field of drug design, the use of topological descriptors remains the primary approach. When combined with QSPR models, descriptors illustrate a molecule's chemical properties numerically. Numbers relating to chemical composition topological indices are structures that link chemical composition to physical characteristics. This research concentrates on the analysis of curvilinear regression models and degree-based topological descriptors for thirteen skin cancer drugs. The physicochemical characteristics of the skin cancer drugs are examined while regression models are built for computed index values. An analysis is performed for several significant results based on the acquired data.

An Algebraic Approach to Calculate Some Topological Coindices and QSPR Analysis of Some Novel Drugs Used in the Treatment of Breast Cancer

Breast cancer is one of the most leading deadly diseases in the world whose ranks first among all oncological diseases in women and it is the second spearheading reason of cancer deadness after lung cancer in the United States. Researchers from all over the world are working for finding better ways for preventing, identifying, and treating breast cancer. Topological indices are the functions generating a numerical value from the molecular graph of compounds and they are also a useful tool to estimate the pyhsicochemical and biological properties of molecules in the quantitative structure-property (activity) relationship (QSPR/QSAR) studies. In this paper, some drugs are studied which are used for the treatment of breast cancer. CoM-polynomials based on degree are occurred for chemical graphs of these drugs and the values of some variable topological coindices are calculated via these polynomials. The results obtained by regression analysis show that the correlations of the chosen coindices with the physicochemical properties of the determined drugs are good even strong for some of them. The QSPR models are constructed using the curvilinear regression method with topological coindices.

Systematic Study of Solid-State Fluorescence and Molecular Packing of Methoxy-trans-Stilbene Derivatives, Exploration of Weak Intermolecular Interactions Based on Hirshfeld Surface Analysis

In recent years, fluorescent compounds that emit efficiently in the solid state have become particularly interesting, especially those that are easily prepared and inexpensive. Hence, exploring the photophysical properties of stilbene derivatives, supported by a detailed analysis of molecular packing obtained from single-crystal X-ray diffraction data, is a relevant area of research. A complete understanding of the interactions to determine the molecular packing in the crystal lattice and their effect on the material's physicochemical properties is essential to tune various properties effectively. In the present study, we examined a series of methoxy-trans-stilbene analogs with substitution pattern-dependent fluorescence lifetimes between 0.82 and 3.46 ns and a moderate-to-high fluorescence quantum yield of 0.07-0.69. The relationships between the solid-state fluorescence properties and the structure of studied compounds based on X-ray analysis were investigated. As a result, the QSPR model was developed using PLSR (Partial Least Squares Regression). Decomposition of the Hirshfeld surfaces (calculated based on the arrangement of molecules in the crystal lattice) revealed the various types of weak intermolecular interactions that occurred in the crystal lattice. The obtained data, in combination with global reactivity descriptors calculated using HOMO and LUMO energy values, were used as explanatory variables. The developed model was characterized by good validation metrics (RMSECAL = 0.017, RMSECV = 0.029, R2CAL = 0.989, and R2CV = 0.968) and indicated that the solid-state fluorescence quantum yield of methoxy-trans-stilbene derivatives was mainly dependent on weak intermolecular C…C contacts corresponding to π-π stacking and C…O/O…C interactions. To a lesser extent and inversely proportional, the fluorescence quantum yield was affected by the interactions of the type O…H/H…O and H…H and the electrophilicity of the molecule.

QSPR Modeling with Curvilinear Regression on the Reverse Entropy Indices for the Prediction of Physicochemical Properties of Benzene Derivatives

Reverse entropies are the molecular descriptors that describe the structures of chemical compounds. They are used in isomer discrimination, structure-property relationship, and structure-activity relations. In this study, the QSPR models were designed using the reverse degree-based entropies to predict the physical properties of benzene derivatives. The relationship analyses between the physicochemical properties and the reverse entropies were done by using the curvilinear regression method. A Maple software based algorithm was designed to make the computation of reverse degree-based entropies easy. Analysis was performed using SPSS software. We analyzed that physical properties such as critical pressure, critical temperature, critical volume, Gibb’s energy, LogP, molar refractivity, and Henry’s law can be estimated by the QSPR model using reverse entropies. All the results were highly positive and significant.

Quasi-SMILES as a basis for the development of QSPR models to predict the CO2 capture capacity of deep eutectic solvents using correlation intensity index and consensus modelling

The interpretation of the CO2 capture capacity of the deep eutectic solvents (DESs) as a mathematical function of (i) hydrogen bond acceptor(HBA); (ii) hydrogen bond donor (HBD); (iii) Molar ratio (HBA: HBD) (iv) temperature in kelvin and (v) p (MPa) gives quantitative models with good statistical quality. The quasi-SMILES are employed to represent the DESs (deep eutectic solvents under different conditions) for building up QSPR models. Quasi-SMILES differ from regular SMILES (simplified molecular input-line entry system) by including extra characters that indicate experimental parameters. SMILES descriptors may be used to construct quantitative structure–property/activity relationships (QSPRs/QSARs), whilst quasi-SMILES descriptors can be employed to build quantitative models of laboratory findings under diverse situations. Four random splits are prepared from the dataset of 72 DESs and each split is further divided into four sets namely active training, passive training, calibration and validation set. The percentage of the common quasi-SMILES in a set of two splits is zero. Three target functions with and without the index of ideality of correlation (IIC) and correlation intensity index (CII) are applied to build 12 QSPR models. The statistical quality of present QSPR models (mCO2) developed by the third target function is good to excellent, with determination coefficients ranging from 0.8303 to 0.9206 for the external validation set. In the last, consensus modelling using the intelligent consensus tool of DTC lab (https://dtclab.webs.com/software-tools) is also performed to predict the robustness of the developed models. The distribution of the dataset of all splits is applied to generate different consensus models and in all cases, the consensus model is found winner. The determination coefficient of all winner consensus models was in the range of 0.9751 to 0.9910 (CM0Split1R2=0.9909;CM0Split2R2=0.9883;CM2Split3R2=0.9910;andCM3Split4R2=0.9751). The statistical results of the determination coefficient and MAE (95%) of the second consensus model of split 3 (CM2Split3R2=0.9910;CM2Split3MAE95%=0.17776) was found best than the R2 and MAE (95%) of other consensus models of all splits. Therefore, it was considered as a winner consensus model from all consensus models.

QSPR Model to Predict the Speed of Sound of Ionic Liquids as a Function of Variable Temperature and Pressure

QSPR Model to Predict the Speed of Sound of Ionic Liquids as a Function of Variable Temperature and Pressure

QSPR Analysis of Some Drug Candidates Investigated for COVID-19 via New Topological Coindices

The COVID-19 outbreak has appeared as a matchless global threat against all humanity. Even the most developed countries have been shocked by the adversities of the COVID-19 pandemic affecting social life, especially human health. All over the world, researchers still have been studying to develop new medicines the combat outbreak. A topological index can be thought of as the conversion of a chemical structure to a real number. Topological indices are often used to provide information about the physicochemical properties and biological properties of molecules. Topological coindices are the numeric values, obtained by the complement graph of a molecular structure, which is used in Quantitative Structure Property/Activity Relationship (QSPR/QSAR) studies to evaluate the physicochemical and biological properties of compounds. In this study, we construct some new topological coindices and define the concept of CoNM -polynomial. Owing to these polynomials we pass the difficulty of calculating the topological coindices. The computing process is done for the molecular graph structure of fixed analogs of Lopinavir, Favipiravir and Ritonavir. Afterward, obtained values are evaluated in QSPR modeling via linear and quadratic regression analysis to examine some physicochemical properties of the analog medicines such as enthalpy of vaporization (E), flash point (FP), molar refractivity (MR), polarizability (P), surface tension (T), molar volume (MV).

QSPR Modeling with Topological Indices of Some Potential Drugs against Cancer

In Sri Lanka as well as the rest of the globe, cancer is the top cause of mortality. One of the key medicines in treating tumors is anticancer medications and delivery dendrimers. To prevent the formation of the rapid proliferation of cancer cells, several tests were carried out. Because of this, research on dendrimers and anti-cancer medications is crucial. Topological indices (TIs) are molecular descriptors numerical values corresponding to the physical characteristics of a molecule’s chemical structure. It costs money to determine a molecule’s physical characteristics in a lab since it takes a lot of materials, medications, and time. Therefore, the relevant information about molecules may be obtained by computing TIs. This study’s goals are to compute hitherto uncalculated eccentricity-based TIs for various anticancer structures and to use curvilinear regression models to forecast the physical characteristics of particular anticancer medications. These anticancer medications were given different TIs developed in this work, allowing the researchers to understand the physical, physicochemical, and chemical characteristics related to them. In addition comparative study of the novel indices with some well-known and mostly used indices in structure–property modeling and anticancer drugs in performed.

Development of QSPR-ANN models for the estimation of critical properties of pure hydrocarbons

The current work aimed to predict three critical properties: critical temperature (Tc), critical volume (Vc), and critical pressure (Pc) of pure hydrocarbons. A multi-layer perceptron artificial neural network (MLP-ANN) has been adopted as a nonlinear modeling technique and computational approach based on a few relevant molecular descriptors. A set of diverse data points was used to build three QSPR-ANN models, including 223 points for Tc, Vc, and 221 for Pc. The entire database was randomly split into two subsets: 80% for the training set and 20% for the testing set. A large number of 1666 molecular descriptors were calculated and then reduced by a statistical methodology based on several phases to retain them into a reasonable number of relevant descriptors, wherein about 99% of initial descriptors were excluded. Thus, the Quasi-Newton backpropagation (BFGS) algorithm was applied to train the ANN structure. The results of three QSPR-ANN models showed good precision, confirmed by the high values of determination coefficient (R2) ranging from 0.9990 to 0.9945, and the low values of calculated errors, such as the Mean Absolute Percentage Error (MAPE) that ranged from 2.2497 to 0.7424% for the best three models of Tc, Vc, and Pc. The weight sensitivity analysis method was applied to know the contribution of each input descriptor individually or by class on each appropriate QSPR-ANN model. Moreover, the applicability domain (AD) method was also used with a strict limit of standardized residual values (di = ±2). However, the results were promising, with nearly 88% of the data points validated within the AD range. Finally, the results of the proposed QSPR-ANN models were compared with other well-known QSPR or ANN models for each property. Consequently, our three models provided satisfactory results, outperforming most of the models mentioned in this comparison. This computational approach can be applied in petroleum engineering and other related fields to accurately determine the critical properties of pure hydrocarbons: Tc, Vc, and Pc.

Implementing QSPR modeling via multiple linear regression analysis to operations research: a study toward nanotubes.

Chemical graph theory significantly predicts multifarious physio-chemical properties of complex and multidimensional compounds when investigated through topological descriptors and QSPR modeling. The targeted compounds are widely studied nanotubes attaining exquisite nanostructures due to their distinguishable properties attaining numeric values. The studied nanotubes are carbon, naphthalene, boron nitride, V-phenylene, and titania nanotubes. In this research work, these nanotubes are characterized through their significance level by implementing highly applicable MCDM techniques. TOPSIS, COPRAS, and VIKOR are used to perform a comparative analysis between them through each optimal ranking. The criteria originated from multiple linear regression modeling established between degree-based topological descriptors and the physio-chemical properties of each nanotube.

Evaluation of Anti-wear Properties of Different Vegetable Oils Based on QSPR Model

Evaluation of Anti-wear Properties of Different Vegetable Oils Based on QSPR Model