• Penta-coordinated Cu ions on the malachite (201) and (010) surfaces exhibit stronger activity, highlighting surface anisotropy's role in sulfidation.
• HS− adsorption forms more stable tetra-coordinated structures on (010) and (201) surfaces than the hexa-coordinated structure on (201), as indicated by more negative adsorption energies.
• Sulfidized malachite gains an additional π electron pair and a smaller HOMO-LUMO gap with xanthate, enhancing π backbonding and collector adsorption.
• The findings offer a theoretical basis for designing targeted flotation reagents that leverage coordination chemistry and Jahn-Teller effects in malachite beneficiation.