• Hydroxamic acid adsorption on malachite is highly anisotropic across different exposed crystal surfaces, with the (100) surface showing the greatest competitive advantage over water molecules.
• Surface energies of malachite crystal faces follow the order (201)>(100)>(110)>(001)>(010)>(201), revealing significant anisotropy in surface stability.
• Water molecules hinder hydroxamic acid adsorption to varying degrees, with minimal interference on the (100) surface, making it the most favorable for flotation separation.
• First-principle DFT calculations provide theoretical guidance for the precise design of flotation reagents and optimization of mineral surface interfaces to enhance copper oxide ore recovery.