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The adsorption and hydrogenation of carbon dioxide on γ-Al₂O₃(110) surface-supported copper clusters of different sizes are investigated using density functional theory calculations. Our results show that the activation of CO₂ is most obvious at the Cu/γ-Al₂O₃ interface containing the size-selected Cu₄ cluster. It is interesting that the CO₂ activation is more pronounced at the partially hydroxyl-covered interface. The catalytic mechanisms of CO₂ conversion to methanol at the dry and hydroxylated Cu₄/γ-Al₂O₃ interfaces via the formate route and the pathway initiated through the hydrogenation of carbon monoxide produced by the reverse water–gas shift reaction are further explored. On both interfaces, the formate pathway is identified as the preferred reaction pathway, in which the hydrogenation of HCOO to H₂COO is the rate-limiting step (RLS). However, since the surface OH group can act as a hydrogen source in some elementary reactions, unlike the dry surface, the production of H₂COOH species along the formate pathway is found at the hydroxylated interface. In addition, the introduction of OH at the interface leads to an increase in the kinetic barrier of the RLS, indicating that surface hydroxylation has a negative effect on the catalytic activity of CO₂ conversion to CH₃OH at the Cu/γ-Al₂O₃ interface.