2.

Radial distribution functions between metal cations and the sulfate sulfur atom, for the versions of the Mamatkulov model with the ion charge indicated. Black corresponds to λ = 0, red to λ = 1 and the intervening colors blue, green, purple, orange and brown correspond to λ values of 0.168, 0.332, 0.501, 0.664 and 0.838, respectively. The upper three panels are for simulations with polarizable water (SWM4-NDP model) and the lower three panels are for simulations with nonpolarizble water (SPC/E model).