We first explore negative-ion formation in fullerenes C44, C60, C70, C98, C112, C120, C132 and C136 through low-energy electron elastic scattering total cross sections calculations using our Regge-pole methodology. Water oxidation to peroxide and water synthesis from H₂ and O₂ are then investigated using the anionic catalysts C44ˉ to C136ˉ. The fundamental mechanism underlying negative-ion catalysis involves hydrogen bond strength-weakening in the transition state. DFT transition state calculations found C60ˉ numerically stable for both water and peroxide synthesis, C100ˉ increases the energy barrier the most and C136ˉ the most effective catalyst in both water synthesis and oxidation to H2O2.