Two new Zn(II)/Cd(II) complexes, [Zn(L)(cba)]n (1) and [Cd(L)(Br)2]& centerdot;H2O (2) (L = 2-(4-fluoro-phenyl)-1H-imidazo[4,5-f][1,10]phenanthroline, H2cba = 4-Carboxyphenoxyacetic acid), have been synthesized hydrothermally and their structures and properties were systematically analyzed and characterized. 1 is composed of the [Zn(L)(cba)] unit, each deprotonated 4-cba2- ligand chelates a Zn(II) atom, forming a 1D chain structure. The 1D double-chain structure is further formed through the pi-pi stacking interactions between L ligands. In addition, 2 is composed of the [Cd(L)(Br)2] unit. The molecule is further extended into a 1D supramolecular chain via the interactions between nitrogen-containing ligands, and the 1D chain structure is further stabilized by hydrogen bonding interactions.
The present work explores the correlation between the values of the heat of formation (HOF) and topological indices of hydrogen boride (B2H6), which is a compound having an unique electron-deficient molecular structure. Topological indices play a significant role in mathematical chemistry by providing numerical descriptors that reflect the structural characteristics of molecular networks and their physicochemical behavior. The current study applies sophisticated curve fitting algorithms to quantitatively assess reverse degree-based topological indices and their correlation with the heat of formation HOF for the hydrogen boride network (B2H6). To find out how well they predicted thermochemical stability, a number of reverse indices were calculated, such as the reverse Zagreb indices, reverse Balaban index, and reverse forgotten index. To construct precise mathematical correlations between each topological index and the related HOF values, nonlinear curve fitting models were created. Additionally, the combination of statistical and computational methods offers a dependable and effective framework for investigating structure-property connections in boron-based nano structures. This approach can be expanded to additional molecular systems to improve materials science and chemical graph theory predictive modeling.
Topological indices serve as important molecular descriptors in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies. In this work, we present a comprehensive topological analysis of four molecular structures based on the leap versions of several Zagreb indices. The mathemat ical formulations are accompanied by numerical evalua tions and graphical illustrations, providing systematic insights into the structural properties of these chemical networks. The obtained analytical expressions provide structural descriptors that encode second neighborhood information of the considered molecular networks and may support future QSPR/QSAR modeling and comparative structural analysis of nanostructures.
Topological indices play a central role in mathematical chemistry for correlating structural features of molecular graphs with physicochemical properties. Motivated by limitations of existing degree and distance-based descriptors, we introduce a novel connectivity index that counts the d-neighbors (vertices whose distance equals their degree in a connected molecular graph). This new descriptor, called the d-connectivity index, extends classical connectivity frameworks. We establish fundamental theoretical results, including lower bounds, relationships with the first Zagreb index, and expressions for subdivision graphs and graphs of small diameter. Furthermore, we compute and compare the d-connectivity index with six widely used indices for three hexa-organic molecular structures. The findings highlight strong structural sensitivity and the potential applicability of the proposed index in QSPR/QSAR modelling. Moreover, the chemical relevance of the d-connectivity index is established through strong polynomial correlations with multiple physicochemical properties of benzenoid hydrocarbon compounds and octane isomers, confirming its effectiveness as a predictive molecular descriptor.
The use of probability distributions in engineering, environmental, actuarial, and biomedical sciences cannot be under-estimated. In recent years, the trigonometric distributions have gained significant attention due to their flexibility in modeling skewed and heavy-tailed data. This study proposes a new class of probability distributions embedding the trigonometric function within the Arctan generator, named as Arctan Uniform-G (ATU-G) family. The objective is to develop a new flexible model for skewed and heavy-tailed lifetime data, which is commonly encountered in reliability analysis. As a special case, the Arctan Uniform Fr & eacute;chet (ATUF) distribution is discussed in detail by considering the Fr & eacute;chet distribution as a baseline, keeping in view its importance as a statistical model in the area of both pure and applied sciences. Fundamental distributional characteristics of the proposed model, including reliability function, hazard rate function, and moments, are derived and discussed along with others. The parameters of the ATUF distribution are estimated using the maximum-likelihood method employing Monte Carlo simulation and a Bayesian framework with various loss functions. Bayesian posterior inference is carried out via the Metropolis-Hastings (MH) algorithm. Simulation results confirm the consistency and efficiency of the estimators. The empirical application demonstrates improved goodness-of-fit compared with existing Fr & eacute;chet-type models. These findings highlight the ATUF distribution's ability to model diverse hazard behaviors, indicating its broad utility in reliability and material research.
Two coordination polymers, {[Zn(1,3-BIP)(1,4-BDF)]& centerdot;H2O}n (1), {[Co(1,3-BIP)(1,3-BDC)]& centerdot;3H2O}n (2). (1,3-BIP is 1,3-bis(imidazole)propane, 1,3-BDC is 1,3-Benzenedicarboxylic acid and 1,4-BDF is 2,3,5,6-tetrafluoroterephthalic acid) were prepared under solvothermal conditions and characterized by IR spectra, thermogravimetric analyses, elemental analyses, powder and single-crystal X-ray diffraction analyses. The single-crystal X-ray diffraction analyses indicated that complex 1 and complex 2 show a two-dimensional sheet layer structure, which are reinforced through strong intermolecular hydrogen bonding to form a 3D supramolecular framework. Additionally, complex 1 exhibited photocatalytic property for the degradation of rhodamine B (Rh B) under UV light irradiation in solution. The photocatalytic performance was up to 75 % within 270 min without any other reagents.
Mathematical chemistry is the study of a chemical substance’s molecular structure as a graph and the use of computational methods and graph theory to mathematical problems. One important tool in this field that gives a network structure a numerical value is the topological index. It can be thought of as a mathematical process that gives a chemical compound’s physico-chemical properties a numerical number. R topological indices are the most recent indices that are based on the sum and multiplication of degrees in a neighborhood. In this work, we first investigate the prediction ability of the R indices for octane isomers in order to assess their potential usefulness. R indices of octanes were found to be highly correlated with entropy and acentric factor characteristics. Furthermore, stronger associations between R indices and the Randic, Wiener, and Zagreb indices of octanes were found. These results suggest that R indices will play a significant role in QSPR research.
Three dialkyltin 3,5-dinitrosalicylates, [3,5-(NO2)2-2-OC6H2COO]SnR2 [R = Me (1), Et (2), n-Bu (3)], have been synthesized by the reaction of dialkyltin dichloride with 3,5-dinitrosalicylic acid in the presence of sodium ethoxide and characterized by NMR spectroscopy and X-ray single crystal diffraction. 1⋅DMSO, 2⋅DMSO, and 3⋅DMSO crystallized from DMSO solvent are centrosymmetric dimers containing a four-membered Sn2O2 ring formed by μ-carboxylate O atom bridging two tin atoms (Sn–O–Sn). 1⋅C2H5OH and 2 obtained from C2H5OH solution have polymeric (one- or two-dimensional) structures generated by bidentate bridging coordination of carboxyl to tin atoms (Sn–O–C–O–Sn). In these complexes, 3,5-dinitrosalicylate as a dianionic ligand adopts chelating-bridging mode to coordinate to tin atom, and tin atom displays a distorted octahedral coordination geometry in which two alkyl groups occupy trans positions and four O atoms are almost in the same plane.
A new coordination polymer [Cd 2 (dpa) 2 (bbib) 2 ] n ·2 n H 2 O ( 1 ), (bbib = 1,4-bis(1 H -benzimidazolyl)butane, H 2 dpa = 2,2′-diphenit acid) has been successfully prepared under hydrothermal conditions. The structure of 1 belongs to a 2D network structure, which further stacks together to form a 3D supramolecular architecture through π–π and C–H⋯π interactions. Additionally, the solid-state fluorescence spectrum showed that 1 had a maximum emission wavelength of 427 nm at an excitation wavelength of 350 nm. In the fluorescence sensing experiment, 1 showed selective recognition ability to Fe 3+ with a detection limit of 0.16 μmol·L −1 . Furthermore, quantum chemical calculations were performed on the “molecular fragments” that were derived from the crystal structures of 1 . These calculations utilized the PBE0/LANL2DZ method and were executed through the Gaussian16 program. The calculated results demonstrate a substantial covalent interaction existing between the coordination atoms and the Cd( ii ) ions.
A new coordination polymer [Cd-2(dpa)(2)(bbib)(2)]( n )2nH(2)O (1), (bbib = 1,4-bis(1H-benzimidazolyl)butane, H(2)dpa = 2,2 '-diphenit acid) has been successfully prepared under hydrothermal conditions. The structure of 1 belongs to a 2D network structure, which further stacks together to form a 3D supramolecular architecture through pi-pi and C-H & ctdot;pi interactions. Additionally, the solid-state fluorescence spectrum showed that 1 had a maximum emission wavelength of 427 nm at an excitation wavelength of 350 nm. In the fluorescence sensing experiment, 1 showed selective recognition ability to Fe3+ with a detection limit of 0.16 mu molL-1. Furthermore, quantum chemical calculations were performed on the "molecular fragments" that were derived from the crystal structures of 1. These calculations utilized the PBE0/LANL2DZ method and were executed through the Gaussian16 program. The calculated results demonstrate a substantial covalent interaction existing between the coordination atoms and the Cd(ii) ions.
Silane compounds are a class of chemical compounds composed of silicon (Si) and hydrogen (H), characterized by the general formula SiH4−xRx{{\rm{SiH}}}_{4-x}{R}_{x}, where RR represents various organic groups. The simplest member of this family is silane itself, with the chemical formula SiH4{{\rm{SiH}}}_{4}. Silanes have structures similar to alkane in hydrocarbon, where the silicon atoms replace the carbon atoms. These compounds are of significant interest in various scientific and industrial applications due to their unique physical and chemical properties. In this work, we estimate the physical properties of silane compounds by utilizing linear, quadratic, and logarithmic regression models. 12 silane compounds were taken into consideration, and six degree-based topological descriptors, namely, reciprocal Randić index, sum-connectivity index, harmonic index, forgotten index, augmented Zagreb index, and inverse sum indeg index were used to estimate the following six important physical properties: density, polar surface area, molecular weight (MW), boiling point, flash point, and refractive index. The statistical parameters, including correlation coefficient, F-value, and P-value, were calculated for each property. It was observed that the MW of these silane compounds can be estimated with particularly high accuracy. This work contributes to the understanding of silane chemistry by leveraging computational modeling to predict their physical behavior, offering valuable insights into their applications in soft matter and materials science, particularly in interdisciplinary studies involving chemistry, physics, and engineering.
Topological indices (TIs), as numerical descriptors derived from molecular graphs, offer critical insights into structural properties of chemical compounds by quantifying atomic connectivity, independent of spatial configuration. These indices are pivotal in quantitative structure–activity relationship studies, enabling the prediction of physicochemical and biological behaviors of compounds prior to experimental analysis. In this study, we focus on the computational application of novel Sombor indices to key main group metal-based systems, including bismuth(iii) iodide – a prominent heavy main group metal halide – as well as structurally related TOXs and silicates, which underscore the versatility of main group elements in forming diverse architectures. Additionally, we investigate nanostar dendrimers to explore topological trends in complex, hyperbranched frameworks relevant to main group metalloid-containing polymers. To validate the broader chemical utility of these indices, we analyze their degeneracy and discriminative capacity across a series of octane isomers, establishing a comparative foundation for their efficacy in distinguishing structural nuances. Our results demonstrate that these TIs exhibit strong correlations with enthalpy of vaporization, standard enthalpy of vaporization, acentric factor, and density. All evaluated indices show identical degeneracy rates of 78.67%, underscoring their consistency in structural analysis. These findings highlight the potential of Sombor indices as robust tools for modeling structure–property relationships for designing advanced materials and catalytic systems. This work bridges computational chemistry with applied main group metal research, offering predictive strategies that could streamline the development of main group derivatives for industrial applications.
New Schiff base of 5-amino-1,3-diphenyl-1H-pyrazole with 5-bromo salicylaldehyde and its cobalt and nickel complexes have been synthesized by condensation reaction. The synthesized compounds were characterized by numerous spectral (UV–vis, IR, 1H and 13C NMR, LC–MS) studies and docking studies. A square planar geometry for Co(iii) and Ni(ii) complexes has been proposed. The infrared spectral results confirm the involvement of azomethine nitrogen and phenolic oxygen in the coordination bond formation. The synthesized compounds were evaluated for in vitro antibacterial activity against Bacillus subtilis, Escherichia coli, Staphylococcus aureus, Klebsiella pneumoniae, and anticancer properties against human breast cancer cell lines. The result showed that the zone of inhibition of C1 complex against S. aureus was 16.9 mm, which was closer to the standard drug. On the other hand, C4 complex exhibited the highest cytotoxicity with the lowest IC50 values of 73.05 μg·mL−1 against human breast cancer cell lines. In addition, molecular docking studies of ligand and complexes with 3TOT, 5MVR, 6D9T, and 6HZQ receptor proteins were conducted. S. aureus shows three hydrogen bond interactions (ASP281, VAL283, ILE36) with a binding affinity of −9.7 kcal·mol−1 for C1 complex over other complexes.
A novel zinc coordination polymer, [Zn 3 (pdc) 2 (bib) 2.5 (H 2 O) 2 ] n ·4nH 2 O·0.5 n bib (H 3 pdc = 3,5-pyrazoledicarboxylic acid, bib =1,4-bis(imidazol-1-ylmethyl)butane), has been synthesized through hydrothermal methods and characterized structurally by single-crystal X-ray diffraction. The polymer crystallizes in a triclinic space group P 1 ¯ P\bar{1} , with unit cell parameters of a = 12.5612, b = 12.8928, c = 16.5488 Å, α = 105.556°, β = 102.193°, γ = 93.817°, and Z = 2. Zinc( ii ) ions possess trigonal bipyramidal coordination, connecting different pdc 3− anions to form tri-nuclear subunits. These subunits are linked to 2D networks via bib ligands. Additionally, the fluorescence properties of 1 have been examined.
This study examines many innovative topological numbers and establishes mathematical interpretations for boron clusters and borophene coverings. The general Randic index, arithmetic index, and Albertson index are discussed in this work for the alpha sheets of boron clusters. Boron cluster sheets are two-dimensional boron atom-based formations called borophene. They are similar to the two-dimensional sheet known as graphene, which is composed of carbon atoms arranged in a hexagonal lattice. The unique electrical, mechanical, and thermal properties of borophene make it a sought-after substance for a variety of uses, such as catalysis, energy storage, and electronics. There are two ways to manufacture borophene: chemical vapour deposition and molecular beam epitaxy. Degree-based topological numbers are a great example of a molecular descriptor that provides information on the connection of atoms in a molecule. These descriptions are based on the notion of a node’s degree in a molecular network, which indicates the number of neighbouring atoms that are directly connected to that node.
Reactions of AlEt3, Al(n-Oct)3, and AlEt2(n-Oct) with thiophene-2-carbonyl chloride (TPCC) at Al/TPCC (molar ratio) <1 were respectively studied. The reaction produced ketone (ethyl thienyl ketone and/or n-octyl thienyl ketone) as the main product. The ketone yield reached the maximum after a very short reaction time and then slightly decreased. When TPCC solution was injected into AlEt3 solution, faster addition of TPCC led to higher ketone yield, and higher temperature caused lower ketone yield. Increasing the size of R in AlR3 from ethyl to n-octyl caused a marked decrease in ketone yield. The yield of the ketone produced from Al−Oct was about 1/5 of the ketone from Al-Et in the TPCC-AlEt2Oct reaction. The reaction system showed rapid color changes with time in the first few seconds. Based on the kinetic feature and reaction phenomena, a mechanistic model is proposed, in which the formation of [R′CO]+ [AlR3Cl]− (R′ = thienyl) ion pair is much faster than that of R′COCl·AlR3 donor–acceptor complex, and only the former is able to produce ketone. Though the formation of the R′COCl·AlR3 complex drags behind that of the ion pair, ketone formation is completely depressed when all AlR3 molecules are coordinated by acyl chloride or ketone.
Camptothecin is a naturally occurring alkaloid known for its significant and selective inhibition of the topoisomerase nuclear enzyme, a critical target in cancer treatment. IT-101, a polymeric drug conjugate of camptothecin, exhibits potent antiglioma activity in vitro, making it a highly promising candidate for cancer therapy. This conjugate not only slows the progression of various malignancies but also enhances the therapeutic efficacy of camptothecin. Topological indices, which are numerical values associated with the molecular structure of chemical compounds, serve as powerful tools for predicting physical properties and biological activities. Calculating these indices offers an efficient alternative to time-consuming and costly laboratory experiments. In this article, we first computed the M-polynomial and NM-polynomial of the camptothecin–polymer conjugate IT-101 structure. By applying various integration and differentiation formulas, we have computed different degree-based topological indices (TIs) for the camptothecin–polymer conjugate IT-101 structure. From an application perspective, we employed a linear regression model to estimate the physicochemical properties of 29 anticancer drugs using eccentricity-based TIs. The results demonstrate that two properties, namely, molecular weight and complexity, can be predicted with high accuracy using the first Zagreb eccentric index. The results may be useful to obtain insights into its molecular characteristics and potential applications in cancer treatment.
Two new coordination polymers, {(NH2(CH3)2)2[Zn2(bipy)(SO4)3]} n (1) and [Ni(phen)(SO4)(H2O)2] n (2) (bipy = 4,4 '-bipyridine, phen = 1,10-phenanthroline) have been synthesized by using metal sulfate, nitrogen-containing ligands, and different template agents under solvothermal conditions and structurally characterized by single-crystal X-ray diffraction. 1 exhibits binuclear units and SO4 2- connect two Zn(ii) ions' centers. It shows 2D layer structure and further extends into 3D supramolecular framework by N-H & ctdot;S hydrogen bonds. Moreover, 2 possesses a 1D double-chain structure and form 2D layer by hydrogen-bonding interactions. And we further explored the infrared (IR) of 1 and 2 and luminescent properties of 1.
Abstract Supercapacitors, owing to their high power density and rapid charge–discharge capabilities, have gained significant attention as energy storage devices in various applications. In the context of electrochemical supercapacitors, this article provides a comprehensive review of the production and electrochemical performance of binary metal oxide (BMO) and reduced graphene oxide (rGO) composite materials. The synthesis processes and synergistic benefits of BMO–rGO composites, with an emphasis on how they perform better than separate parts in terms of specific capacitance and cycle stability, are discussed. The potential of BMO–rGO composites as high-performance electrode materials for supercapacitors is highlighted in this research. In the context of electrochemical supercapacitors, this work provides a comprehensive review of the production and electrochemical performance of binary transition metal oxide (TMO) and rGO composite materials. Composite materials with enhanced electrochemical characteristics that are appropriate for supercapacitor applications are the primary novelty, which is the synergistic combination of rGO with a variety of TMOs. Compared to individual TMOs or other carbonaceous materials, these composites demonstrate enhanced specific capacitance, energy density, power density, cyclic stability, and rate capability. The synthesis processes and synergistic benefits of BMO–rGO composites are discussed, with an emphasis on their superior performance in specific capacitance and cycle stability compared to individual components. This research highlights the potential of BMO–rGO composites as high-performance electrode materials for supercapacitors, showcasing their enhanced specific capacitance, improved charge storage capacity, increased power density, excellent cycling stability, and overall durability even after numerous charge–discharge cycles.
For a graph Q=(V,E){\mathbb{Q}}=\left({\mathbb{V}},{\mathbb{E}}), the transformation graph are defined as graphs with vertex set being V(Q)∪E(Q){\mathbb{V}}\left({\mathbb{Q}})\cup {\mathbb{E}}\left({\mathbb{Q}}) and edge set is described following certain conditions. In comparison with the structural descriptor of the original graph Q{\mathbb{Q}}, the topological descriptor of its transformation graphs displays distinct characteristics related to the structure. Thus, a compound’s transformation graph descriptors can be used to model a variety of structural features of the underlying molecular structure and initiate a structural analysis. In this work, the concept of transformation graphs is extended giving rise to a novel class of graphs, the (r,s)\left(r,s)-generalised transformation graphs, whose vertex set is union of rr copies of V(Q){\mathbb{V}}\left({\mathbb{Q}}), and ss copies of E(Q){\mathbb{E}}\left({\mathbb{Q}}), where r,s∈Nr,s\in N, and the edge set are defined under certain conditions. Furthermore, this class of graphs is analysed with the help of first Zagreb index. Mainly, there are eight transformation graphs based on the criteria for edge set, but under the concept of (r,s)\left(r,s)-generalised transformation graphs, infinite number of graphs can be described and analysed.
