We first explore negative-ion formation in fullerenes C44 to C136 through low-energy electron elastic scattering total cross sections calculations using our Regge-pole methodology. Then, the formed negative ions C44ˉ to C136ˉ are used to investigate the catalysis of water oxidation to peroxide and water synthesis from H2 and O2. The exploited fundamental mechanism underlying negative-ion catalysis involves hydrogen bond strength-weakening/breaking in the transition state. Density Functional Theory transition state calculations found C60ˉ optimal 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.