Charge localization in cation-sulfate complexes: Implications for thermodynamic surface complexation models of the mineral/water interface

The applicability of separating charges of oxyanions across inner- and outer-Helmholtz planes according to the charge distribution model was tested by investigating the theoretical charge distribution in 13 metalsulfate complexes (Be2+, mg(2+), Ca2+, Sr2+, Ba2+, Co2+, Ni2+, Cu2+, Zn2+, Pd2+, Cd2+, Al3+, and Ga3+) using the methods of atoms in molecules and of the electron localization function. Density functional theory gas-phase geometry optimization calculations revealed that unbound oxygens of the sulfate molecules contracted to relatively constant S-O bond lengths of 1.432 +/- 0.019 (3 sigma) angstrom irrespective of the bond strength with the metal ions. The populations of the valence basins of the unbound oxygens also remained relatively constant, showing that even the strongest complexation induces very little charge distribution across the sulfate molecule. Maps of the Laplacian of the electron density and of the electron localization function revealed that although charge is relatively localized at the oxygen centers, there is no clear charge separation between the inner- and outer-Helmholtz planes. Thermodynamic adsorption models that avoid subtle distributions of charge across static adsorption planes are suggested to represent a more natural expression of the interface. Models that could instead simulate the changes in the charge-storage capacity of the interface via changes in the capacitance caused by strongly adsorbing molecules are suggested as future alternatives to current-day approaches. It should nonetheless be emphasized that the charge distribution model remains a valuable approach and should have the best applicability at low surface loadings and with molecules with sizes similar or larger to those of the compact layer.