Theoretical and Quantitative Structural Relationship Studies of Electrochemical Properties of the Nanostructures of Cis-Unsaturated Thiocrown Ethers and Their Supramolecular Complexes [X-UT-Y][M@C82] (M˭Ce,Gd)

The endohedral lanthanidofullerenes, an important type of organolanthanides, are stabilized by the delocalization of the negative charges on the cages of fullerenes. Since the discovery of these classes of carbon compounds and their unusual structures and properties of these molecules, many potential applications have been suggested. Unsaturated thiocrown ethers with cis-geometry are a group of crown ethers that, in light of the size of their cavities and their conformational restriction compared to a corresponding saturated system (1–9), demonstrate interesting properties for physicochemical studies. Endohedral lanthanidofullerenes M@C_x (x = 82 and M = Ce, Gd) were introduced as a new class of the spherical fullerene group with unique properties. Formation of endohedral metallofullerenes is thought to involve the transfer of electrons from the encapsulated metal atom(s) to the surrounding fullerene cage. Two of these molecules are the Ce@C₈₂ (10) and Gd@C₈₂ (11). The supramolecular complexes of 1–9 with Ce@C₈₂ (10) and Gd@C₈₂ (11) have been shown to possess a host–guest interaction for electron transfer processes, and these behaviors have previously been reported. Topological indices have been successfully used to construct effective and useful mathematical methods for finding good relationships between structural data and the various chemical and physical properties. To establish a good structural relationship between the structures of 1–9 and M@C_x that were introduced here, an index that is represented as μ_cs was utilized. This index is the ratio of summation of the number of carbon atoms (n_c ) and the number of sulfur atoms (n_s ) to the product of these two numbers for 1–9. In this study, the relationship between this index and oxidation potential ( ^oxE₁ ) of 1–9, as well as the free energy of electron transfer (ΔG_et , by the Rehm-Weller equation) between 1–9 and 10 and 11 as X-UT-Y]Ce@C₈₂] (12) and X-UT-Y]Gd@C₈₂] (13) complexes, is presented.

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