The US method was used to compute the free energy profile, F (z ′ ), of each solute binding to the interface, with z ′ being a collective variable (CV) corresponding to the distance between the center of mass (COM) of the solute and a weighted 2 COM of the liquid water phase projected along the z-axis. Note that for SO 4 CH - 2 , the COM included the mass of the tail group which was decoupled from the solvent. Additionally note that all thermodynamic quantities shown in Sec. III are reported with respect to the distance, z between the solute COM and the water Gibbs dividing interface (GDI) in order to better compare data for the AWI with that for the ACWI. No reweighting is required to make the transformation z ′ → z (i.e. solute COM distance from the water COM, z ′ → solute COM distance from the GDI, z) since the water GDI is essentially independent of the solute z-position.