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One of the fundamental challenges in reticular chemistry is the characterization of the complexity of the underlying molecular network, in which high complexity signifies low symmetry and high diversity. The entropy of a network is one such topological descriptor that serves to characterize the order/disorder structural complexity. In this paper, we obtain the entropy measures by computing systematic expressions of the self-powered degree-based topological indices for three isoreticular metal organic frameworks with a zinc based central unit and stringed binding linkers with varying benzene molecule counts. We have also enumerated the self-returning and nonreturning walks for these isoreticular structures in order to provide potential pathways for charge and ion transport. We have considered other properties such as eccentricities, radius, diameter, vertex and edge equivalence classes that facilitate rapid computations of thermochemistry and hence relative stabilities of isoreticular networks. [ABSTRACT FROM AUTHOR]

Cycloarenes are polycyclic aromatic hydrocarbons formed by circularly fused benzene rings, which provide a potential cavity trap for metal ions. These polycyclic aromatics have been the focus of several studies due to their superaromaticity, magnetic and other electronic and geometric properties. The first representative of these macrocyclic conjugated compounds is kekulene, a doughnut-shaped structure consisting of cyclically arranged benzene rings with intriguing structural features that are suitable for theoretical studies including the study of conjugation circuits of π electrons. Topological characterization of such structures is thus essential for the prediction of their properties. In this study, we present two novel series of giant polycyclic compounds that are generated through tessellations of several kekulene doughnuts providing a potential molecular belt with multiple cavities. We have computed a number of topological quantity indices for such a 2D-sheet comprising of several kekulenes. [ABSTRACT FROM AUTHOR]

A series of novel two-dimensional, metal trihalides MX 3 , have been explored recently because of their unusual Dirac half-metallicity, intriguing topological spintronic properties arising from both inherent magnetization and large relativistic spin-orbit coupling effects exhibited by these 2D metal halides. Moreover due to large spin-orbit coupling which results in unusual band gaps combined with their stopping power and higher Curie temperature, 2D materials such as BiI 3 find important applications in room temperature radiation detectors. Hence the present work is devoted to relativistic topological characterization of two classes of 2D trihalides. We outline techniques for incorporation of relativistic parameters into topological expression through 2-component Wannier spinors obtained by localization methods. Mathematical expressions of several structurally based topological indices are proposed in terms of parameters that can be derived from relativistic quantum computations including spin-orbit coupling for the first time. [ABSTRACT FROM AUTHOR]