Understanding adsorption of phosphate and sulfate on Fe-(hydr)oxide surfaces is important to predict the fate of these anions in wastewater and in the design of systems to remove and recover phosphates. Quantum chemical calculations were used to estimate relative Gibbs free energies of phosphate and sulfate adsorption like inner-sphere and outer-sphere complexes using three different simulated pH conditions (acid, intermediate, and basic). Bidentate binuclear surface complexes presented the most thermodynamically favorable mode of adsorption for both phosphate and sulfate with -94.4. kJ/mol and -62.3. kJ/mol, respectively, at acid pH condition. Topological analysis was done to understand how the Fe-(hydr)oxide surfaces are affected for the different types of adsorption of phosphate and sulfate. A classification of the O. H...O hydrogen bonds (HBs) formed in all structures discriminating among the surface functional groups, solvation water molecules, and adsorbed molecules was done by the topological analysis of the electron density. HBs nature is mostly electrostatic which agrees with positive values of the Laplacian. This result indicates the existence of positive cooperative effects among these interactions which confers additional stabilization to the systems. © 2012 Elsevier B.V.