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Mathematical Chemistry
Published in Mihai V. Putz, New Frontiers in Nanochemistry, 2020
Louis V. Quintas, Edgar G. DuCasse
Almost all mathematical chemistry applications are done in the context of a molecular model. The simplest model is the graph model for a molecule. Another example is the nano-chemical approach where the modeling involves the electrons of the atoms in the graph model (Mezey, 1983). Additional examples can be found when the chemical structure is embedded in some topological or algebraic setting. If the surface of a sphere is subdivided into polygonal regions, the result is a polyhedron. In a chemical context, if the vertices of a polyhedron can be identified with the atoms of a molecule, one obtains a model called a polyhedral molecule (King, 1983). Algebraic models come up when one studies the symmetries of a molecular structure. The case of an asymmetric carbon, that is, a carbon atom that is bonded to four chemically distinct branches (ligands) is an extreme example. Permutation groups of labeled graphs, with the labeled parts corresponding to distinct chemical entities, make the labeled graph a model in an algebraic setting (Dugundji, 1983). For more details concerning molecular modeling see Leach (2001, 2008).
Removal of the UV Filter Benzophenone-2 in Aqueous Solution by Ozonation: Kinetics, Intermediates, Pathways and Toxicity
Published in Ozone: Science & Engineering, 2018
Siyuan Wang, Xinghao Wang, Jing Chen, Ruijuan Qu, Zunyao Wang
Setting up the molecular model is an effective method to speculate chemical reactivity from a molecular perspective, giving us much information about the reactive sites and possible reaction products. This method has been widely used to study the inherent chemical reactivity of organic molecules and proved to be feasible and valuable in products identification and toxicity prediction (Li et al. 2016; Xiao et al. 2013; Zhuang et al. 2016). The frontier molecular orbital (FMO) theory is especially helpful in studying the oxidative behaviors of organic molecules, by calculating the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the molecule of target compounds, as well as the Millikan charge of atoms of the molecules (An et al. 2010; Chen et al. 2008).