This work presents a study of reactions between neutral and negatively chargedAunclusters(n=2,3) and molecular hydrogen. The binding energies of the first and second hydrogen molecule to the goldclusters were determined using density functional theory(DFT), second order perturbation theory (MP2) and coupled cluster (CCSD(T)) methods. It is found that molecular hydrogen easily binds to neutral Au2 and Au3clusters with binding energies of 0.55 eV and 0.71 eV, respectively. The barriers to H2dissociation on these clusters with respect to AunH2 complexes are 1.10 eV and 0.59 eV for n=2 and 3. Although negatively chargedAu−nclusters do not bind molecular hydrogen, H2dissociation can occur with energy barriers of 0.93 eV for Au−2 and 1.39 eV for Au−3. The energies of the Au2H−2 and Au3H−2 complexes with dissociated hydrogen molecules are lower than the energies of Au−2+H2 and Au−3+H2by 0.49 eV and 0.96 eV, respectively. There is satisfactory agreement between the DFT and CCSD(T) results for binding energies, but the agreement is not as good for barrier heights.