Theoretical studies of the free energies of electron transfer and electron transfer kinetics in nanostructure supramolecular complexes of cis-unsaturated thiocrown ethers and Ce and Gd endohedral metallofullerenes [X-UT-Y][M@C82] (MÂ =Â Ce, Gd)

Unsaturated thiocrown ethers (described as [X-UT-Y], where X and Y indicate the numbers of carbon and sulfur atoms, respectively) 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. 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. The relationship between an index (which was introduced as the ratio of summation of the number of carbon atoms (nc) and the number of sulfur atoms (ns)) and oxidation potential (oxE1) of 1-9, as well as the free energies of electron transfer (ΔGet, 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, were investigated before. In this study, the first and second activation free energies of electron transfer and kinetic rate constants of the electron transfers, ΔGet(n)# and ket (n = 1,2), respectively, which are given by the previous studies for [X-UT-Y][Ce@C82] (12) and [X-UT-Y][Gd@C82] (13) complexes, were calculated in accordance with the Marcus theory.