Two-dimensional coronene fractal structures: topological entropy measures, energetics, NMR and ESR spectroscopic patterns and existence of isentropic structures

On some counting polynomials and energy properties of superphenalene and supertriphenylene

In order to generate a wide range of meaningful topological indices, counting polynomials can be utilised in a number of different ways, including explicitly, after calculating derivatives. Certain polynomials, particularly Theta, Omega, Padmakar-Ivan, and Sadhana polynomials, are subservient to the equidistant and non-equidistant edges of graphs. Such polynomials have a wide range of applications, including the computation of the topological indices that correspond to them. Counting polynomials and corresponding indices in the context of super-polycyclic aromatic compounds with hexabenzocoronene as a base molecule, including superphenalene and supertriphenylene, refer to mathematical representations that encode structural information about the molecules. In addition, we have been able to acquire the spectral and energetic characteristics of these structures, which include the HOMO-LUMO gaps, bond delocalisation energies, and 13C NMR patterns.

Structure-property modeling of physicochemical properties of fractal trigonal triphenylenoids by means of novel degree-based topological indices

Trigonal triphenylenoids (TTPs) are a fascinating class of organic molecules with unique structural and electronic properties. Their diverse applications, ranging from organic electronics to nonlinear optics, have spurred significant research interest in understanding their physicochemical behavior. Topological indices, mathematical descriptors derived from the molecular graph, offer valuable insights into the structural complexity and potential properties of TTPs. This work focuses on exploring the utility of degree-based topological indices in characterizing and predicting the properties of trigonal triphenylenoids. We systematically calculate various degree-based topological indices, for a diverse set of TTPs with varying substituents and topologies. The relationships between these indices and key physicochemical properties, such as HOMO-LUMO energy gap, thermodynamic stability, and reactivity are investigated using statistical and machine learning approaches. We identify significant correlations between specific degree-based indices and different properties, allowing for potential prediction of these properties based solely on the topological information.

Guanidinium and hydrogen carbonate rosette layers: Distance and degree topological indices, Szeged-type indices, entropies, and NMR spectral patterns

Supramolecular chemistry explores non-covalent interactions between molecules, and it has facilitated the design of functional materials and understanding of molecular self-assembly processes. We investigate a captivating class of supramolecular structures, the guanidinium and hydrogen carbonate rosette layers. These rosette layers are composed of guanidinium cations and carbonate anions, exhibiting intricate hydrogen-bonding networks that lead to their unique structural properties. Topological and entropy indices unveil the connectivity and complexity of the structures, providing valuable insights for diverse applications. We have developed the cut method technique to deconstruct the guanidinium and hydrogen carbonate rosette layers into smaller components and obtain the distance, Szeged-type and entropy measures. Subsequently, we conducted a comparative analysis between topological indices and entropies which contributes to a deeper understanding of the structural complexity of these intriguing supramolecular systems. We have derived the degree based topological indices and entropies of the underlying rosette layers. Furthermore, our computations reveal several isentropic structures associated with degree and entropy indices. We have employed distance vector sequence-based graph theoretical techniques in conjunction with symmetry-based combinatorial methods to enumerate and construct the various NMR spectral patterns which are demonstrated to contrast the isomers and networks of the rosettes.

Edge valency-based entropies of tetrahedral sheets of clay minerals

Humanity has always benefited from an intercapillary study in the quantification of natural occurrences in mathematics and other pure scientific fields. Graph theory was extremely helpful to other studies, particularly in the applied sciences. Specifically, in chemistry, graph theory made a significant contribution. For this, a transformation is required to create a graph representing a chemical network or structure, where the vertices of the graph represent the atoms in the chemical compound and the edges represent the bonds between the atoms. The quantity of edges that are incident to a vertex determines its valency (or degree) in a graph. The degree of uncertainty in a system is measured by the entropy of a probability. This idea is heavily grounded in statistical reasoning. It is primarily utilized for graphs that correspond to chemical structures. The development of some novel edge-weighted based entropies that correspond to valency-based topological indices is made possible by this research. Then these compositions are applied to clay mineral tetrahedral sheets. Since they have been in use for so long, corresponding indices are thought to be the most effective methods for quantifying chemical graphs. This article develops multiple edge degree-based entropies that correlate to the indices and determines how to modify them in order to assess the significance of each type.

Entropy structural characterization of zeolites BCT and DFT with bond-wise scaled comparison

Entropy of a connected network is a quantitative measure from information theory that has triggered a plethora of research domains in molecular chemistry, biological sciences and computer programming due to its inherent capacity to explore the structural characteristics of complex molecular frameworks that have low structural symmetry as well as high diversity. The analysis of the structural order is greatly simplified through the topological indices based graph entropy metrics, which are then utilized to predict the structural features of molecular frameworks. This predictability has not only revolutionized the study of zeolitic frameworks but has also given rise to new generations of frameworks. We make a comparative study of two versatile framework topologies namely zeolites BCT and DFT, which have been widely utilized to create a new generation of frameworks known as metal organic frameworks. We discuss bond-additive topological indices and compute entropy measure descriptors for zeolites BCT and DFT using degree and degree-sum parameters. In addition, we perform bond-wise scaled comparative analysis between BCT and DFT which shows that zeolite BCT has greater entropy values compared to zeolite DFT.

Topological Entropy Characterization, NMR and ESR Spectral Patterns of Coronene-Based Transition Metal Organic Frameworks

Metal organic frameworks (MOFs) are topical crystalline materials with high porosity and inner surface areas synthesized from naturally occurring minerals. Such MOFs with transition metals have attracted considerable attention because of their fascinating morphological diversity and tunable characteristics. The coronene-based structural frameworks with transition metal atoms are synthesized by repeating a fixed coronene unit at several levels. In this study, topological indices and NMR and ESR spectral patterns are computed for these MOFs to shed light on their structures and spectral properties. We obtained mathematical expressions of topological indices based on degree and degree-sum values of MOFs for the rectangular, hexagonal, and parallelogram peripheral shapes. Furthermore, the entropy measures of these novel frameworks are evaluated with the help of index functionals and compared to a wide range of degree-based descriptors. The NMR and ESR spectral patterns have been obtained from the distance degree vector sequences and symmetries for the three MOFs.

Tetrahedral sheets of clay minerals and their edge valency-based entropy measures

Humanity has always benefited from an intercapillary study in the quantification of natural occurrences in mathematics and other pure scientific fields. Graph theory was extremely helpful to other studies, particularly in the applied sciences. Specifically, in chemistry, graph theory made a significant contribution. For this, a transformation is required to create a graph representing a chemical network or structure, where the vertices of the graph represent the atoms in the chemical compound and the edges represent the bonds between the atoms. The quantity of edges that are incident to a vertex determines its valency (or degree) in a graph. The degree of uncertainty in a system is measured by the entropy of a probability. This idea is heavily grounded in statistical reasoning. It is primarily utilized for graphs that correspond to chemical structures. The development of some novel edge-weighted based entropies that correspond to valency-based topological indices is made possible by this research. Then these compositions are applied to clay mineral tetrahedral sheets. Since they have been in use for so long, corresponding indices are thought to be the most effective methods for quantifying chemical graphs. This article develops multiple edge degree-based entropies that correlate to the indices and determines how to modify them to assess the significance of each type.

Topological and Spectral Properties of Wavy Zigzag Nanoribbons

Low-dimensional graphene-based nanomaterials are interesting due to their cutting-edge electronic and magnetic properties. Their large surface area, strong mechanical resistance, and electronic properties have enabled potential pharmaceutical and opto-electronic applications. Graphene nanoribbons (GNRs) are graphene strips of nanometer size possessing zigzag and armchair edge geometries with tunable widths. Despite the recent developments in the characterization, design and synthesis of GNRs, the study of electronic, magnetic and topological properties, GNRs continue to pose a challenge owing to their multidimensionality. In this study, we obtain the topological and electronic properties of a series of wave-like nanoribbons comprising nanographene units with zigzag-shaped edges. The edge partition techniques based on the convex components are employed to compute the mathematical formulae of molecular descriptors for the wave-like zigzag GNRs. We have also obtained the spectral and energetic properties including HOMO-LUMO gaps, bond delocalization energies, resonance energies, 13C NMR and ESR patterns for the GNRs. All of these computations reveal zero to very low HOMO-LUMO gaps that make these nanoribbons potential candidates for topological spintronics.