Platinum and similar metals are suitable catalysts in response to fuel cells, however, because of being costly, their use is limited. So in this study, the catalytic efficiency of some organometallic compounds with the general formula TMCmHm on the reaction rate of "Hydrazine- Oxygen "fuel cell was studied via density Functional Theory (DFT). To perform the respect calculations, the PW91 method and 6-31 G(d) basis set were used. Bonds’ length of O=O and N-N increased in response to their adsorption onto TMCmHm and theoretical study of N2H4-O2 fuel cell the partial transfer of negative charge from organometallic compounds to their π * orbitals. Bond length of O=O increased by 24% due to its adsorption on ScC5H5 and N-N on ScC5H5 increased by 11%. The optimal structure of each studied organometallic compound was plotted by performing natural bond orbital calculations (NBO). The energy of the highest occupied molecular orbital (EHOMO) and the lowest unoccupied molecular orbital (ELUMO) were calculated. Besides, , the gap energies (Eg), chemical hardness (ɳ), chemical potential (µ), and electrophilicity (ω) were calculated in each case. Then, the optimal structure of O2/TMCmHm and N2H4/ TMCmHm pairs was plotted; the adsorption energy of O2 and N2H4 on each of TMCmHm was evaluated. The kinetic adsorption of O2 and N2H4 on the Sc C5H5 compound was investigated by the 6-31 G * method. The potential energy of O2/TMCmHm and N2H4/ TMCmHm pairs in the initial and final position and the transient state were estimated, and the respect kinetic parameters were calculated.