We report a detailed density functional theory (B3LYP) analysis of the gas-phase H2O2 formation from H-2 and O-2 on Au-3, Au-4(+), Au-5, and Au-5(-), We find that H-2, which interacts only weakly with the Au clusters, is dissociatively added across the Au-O bond, upon interaction with AunO2. One H atom is captured by the adsorbed O-2 to form the hydroperoxy intermediate (OOH), while the other H atom is captured by the Au atom. Once formed, the hydroperoxy intermediate acts as a precursor for the closed-loop catalytic cycle. An important common feature of all the pathways is that the rate-determining step of the catalytic cycle is the second H-2 addition to form H2O2. The H2O2 desorption is followed by O-2 addition to AunH2 to form the hydroperoxy intermediate, thus leading to the closure of the cycle. On the basis of the Gibbs free energy of activation, out of these four clusters, Au4(+) is most active for the formation of the H2O2. The 0 K electronic energy of activation and the Delta G(act) at the standard conditions are 12.6 and 16.6 kcal/mol respectively. The natural bond orbital charge analysis suggests that the Au clusters remain positively charged (oxidic) in almost all the stages of the cycle. This is interesting in the context of the recent experimental evidence for the activity of cationic Au in CO oxidation and water-gas shift catalysts. We have also found preliminary evidence for a correlation between the activation barrier for the first H-2 addition and the 02 binding energy on the Au cluster. It suggests that the minimum activation barrier for the first H-2 addition is expected for the Au clusters with 7.0-9.0 kcal/mol O-2 binding energy, i.e., in the midrange of the expected interaction energy. This represents a balance between more favorable H-2 dissociation when the Au-n-O-2 interaction is weaker and high O-2 coverage when the interaction is stronger. On the basis of this work, we predict that the hydroperoxy intermediate formation can be both thermodynamically and kinetically viable only in a narrow range of the O-2 binding energy (10.0-12.0 kcal/mol)-a useful estimate for computationally screening Au-cluster-based catalysts. We also show that a competitive channel for the OOH desorption exists. Thus, in propylene epoxidation both OOH radicals and H2O2 can attack the active Ti in/on the Au/TS-1 and generate the Ti-OOH sites, which can convert propylene to propylene oxide.