2 ) 2 , was used for each distance coordinate, with minima r (eq) 1,2 , spaced by 0.5 Å between 2.5 Å and 9.0 Å for a grid of 196 bias windows, with a spring constant of k 1 = k 2 = 10 kCal/mol/ Å2 . Each bias window was sampled for at least 1 ns, recording ion configurations every 0.25 ps and water configurations every 1 ps. The Weighted Histogram Analysis Method (WHAM) was then used to construct an unbiased FES from biased simulations, and to compute unbiased histograms and averages. In the electrode simulations, CO 3 was also held at the interface by a harmonic bias with a 10 kCal/mol/ Å2 in order to probe the interfacial double layer.