Neurotransmitters are the compounds which allow the transmission of signals from one neuron to the next across synapses. They are the brain chemicals that communicate information throughout brain and body. Fullerenes are a family of carbonallotropes, molecules composed entirely of carbon, that take the forms of spheres, ellipsoids, and cylinders. Various empty carbon fullerenes (Cn) with different carbon atoms have been obtained and investigated. Topological indices have been successfully used to construct effective and useful mathematical methods to establish clear relationships between structural data and the physical properties of these materials. In this study, the number of carbon atoms in the fullerenes was used as an index to establish a relationship between the structures of neurotransmitters (NTs) acetylcholine (AC) 1, dopamine (DP) 2, serotonin (SE) 3, and epinephrine (EP) 4 as the well-known redox systems and fullerenes C n (n = 60, 70, 76, 82, and 86) which create [NT].Cn; A-1 to A-5 up to D-1 to D-5. The relationship between the number of carbon atoms and the free energy of electron transfer (ΔG et(n); n = 1-4) is assessed using the Rehm-Weller equation for A-1 to A-5 up to D-1 to D-5 supramolecular [NT].Cn complexes. The calculations are presented for the four reduction potentials ( (Red.) E 1 to (Red.) E 4 ) of fullerenes C n . The results were used to calculate the four free energy values of electron transfer (ΔG et(1) to ΔG et(4)) of the supramolecular complexes A-1 to A-8 up to D-1 to D-8 for fullerenes C60 to C120. The first to fourth free activation energy values of electron transfer and the maximum wavelength of the electron transfers, ΔG (#) et(n) and λ et (n = 1-4), respectively, were also calculated in this study for A-1 to A-8 up to D-1 to D-8 in accordance with the Marcus theory.