Metal complexes containing one or several bis(triorganylphosphine)palladium fragments attached to the C60 core and coordinated in olefinic h2 mode have been previously described. The number of carbon atoms of the single walled carbon nanotubes (SWCNTs) is the useful numerical and structural electrochemical properties contributing to the relationship between the structures of the h2_CmPd(dppf), h2_CmPd(dppr), and h2_CmPd(dppcym)2 (m=60 and 70) ligands (A to E) and [SWCNT(5,5)-armchair-CnH20] (n=20 to 190) 1 to 18 and the production of the [SWCNT (5,5)-armchair-CnH20][R] (R=h2-CmPd(dppf), h2-CmPd(dppr), and h2-CmPd(dppcym)2, n=20 to 300 and m=60 and 70) complexes 30 to 174. In this study, the relationship between the number of carbon atoms index and the first and second free energies of electron transfer (DGet(n), n=1,2) using the Rehm-Weller equation based on the first and second oxidation potentials (oxE1 and oxE2) of A to E for the predicted complexes 30 to 174 between 1 and 29 with exohedral metallofullerenes A to E, as [SWCNT(5,5)-armchair-CnH20][R] (R=h2-CmPd(dppf), h2-CmPd(dppr), and h2-CmPd(dppcym)2, n=20 to 300 and m=60 and 70) 30 to 174 was assessed. Here, the first and second free activation energies of electron transfer and the wavelengths of the electromagnetic photons in the photoelectron transfer process, DG#et(n) and l(n) (nm), respectively, for 30 to 174 in accordance with the Marcus theory and Planck's equation were also calculated.