The reduction of electron transfer distance leads to an electronic communication between the electrode and redox proteins. This study elaborates upon the relationship between the number of carbon atoms in the fullerenes and the four free energies of electron transfer (DGet(1) to DGet(4)) between the fullerenes Cn (n=60, 70, 76, 82 and 86) and the six most well –known enzyme molecular systems: Laccase Coriolus hirsutus (LCh), Tyrosinase, Laccase Rhus vernicifera (LRv), Cytochrome c peroxidase, Ascorbate oxidase and Cytochrome c oxidase, numbered 1-6, respectively, in the text. The free energies of electron transfer are based on the four reduction potentials (Red.E1 to Red.E4) of the fullerenes, as assessed by applying the electron transfer (ET) equation to create [Laccase Coriolus hirsutus (LCh)].Cn, A-1 to A-5; [Tyrosinase].Cn, B-1 to B-5; [Laccase Rhus vernicifera (LRv)].Cn, C- 1 to C-5; [Cytochrome c peroxidase].Cn, D-1 to D-5; [Ascorbate oxidase].Cn, E-1 to E-5; and [Cytochrome c oxidase].Cn, F-1 to F-5. The results were extended to calculate the four free energies of the electron transfer (DGet(1) to DGet(4)) of other supramolecular complexes of each enzyme 1-6, as a class of electron transfer species, with fullerenes C60 to C120 ([(R)].Cn supramolecular complexes. The study also calculated the first to fourth activation free energies of electron transfer, DG# et(n) (n=1- 4), respectively, as assessed using the Marcus theory and the above equations on the basis of the first to fourth reduction potentials (Red.E1 to Red.E4) of fullerenes Cn (n=60, 70, 76, 82 and 86) for the predicted supramolecular complexes [Laccase Coriolus hirsutus (LCh)].Cn, A-1 to A-5; [Tyrosinase].Cn, B-1 to B-5; [Laccase Rhus vernicifera (LRv)].Cn, C-1 to C-5; [Cytochrome c peroxidase].Cn, D-1 to D-5; [Ascorbate oxidase].Cn, E-1 to E-5; and [Cytochrome c oxidase].Cn, F-1 to F-5. Furthermore, this study determined the wavelengths (l(n); n=1-4; in nm) of the electromagnetic photons for the electron transfer processes and in the nanostructure supramolecular complexes.