Entropy is a thermodynamic function in chemistry that reflects the randomness and disorder of molecules in a particular system or process based on the number of alternative configurations accessible to them. Distance-based entropy is used to solve a variety of difficulties in biology, chemical graph theory, organic and inorganic chemistry, and other fields. In this article, the characterization of the crystal structure of niobium oxide and a metal–organic framework is investigated. We also use the information function to compute entropies by building these structures with degree-based indices including the K-Banhatti indices, the first redefined Zagreb index, the second redefined Zagreb index, the third redefined Zagreb index, and the atom-bond sum connectivity index.

The importance of the model reduction techniques cannot be denied or ignored for a number of combustion problems in chemical sciences. We examine an analysis of very well-known method by Mass and Pope by measuring the influence of physical processes on the water-gas shift reaction (WGSR). We observe that if the process of physical and chemical reactions is coupled, this will lead to a very dramatic effect. An adaptive parameterization technique is developed for the numerical implementation. Through proper algorithm and grid size variations, the approximate solution is obtained and further refined with the method of invariant grids. Consequently, it leads us to a vicious effect on CPU when we extended this idea to higher dimensions

The mathematical language provided by various topological index types may be used to identify various properties of chemical components in a molecular structure. Within the framework of valency-based topological indices, we examine eight different dendrimer architectures. This chapter proposes two novel molecular descriptors, the Mersenne index and the Fermat index, by combining the essential notions of the Mersenne number and the Fermat number. The molecules with the highest Mersenne index and Fermat index values are found in the classes of some dendrimer families, including poly or propyl ether-imine dendrimer, polyethylene amido amine dendrimer, porphyrin dendrimer, zinc porphyrin dendrimer, porphyrin-cored dendrimer-I, porphyrin-cored dendrimer-II, porphyrin-cored dendrimer-III, and porphyrin-cored dendrimer-IV. The Fermat index differs from the Mersenne index in that it grows with the value of n, as the Fermat number is always increasing by increasing the value of n. Also, we show that the Mersenne index and the Fermat index are always members of the set of integers (Z) for any graph of chemical compounds.