To test our hypothesis, we investigated the accuracy of the polynomial fit to the correction potential. In Figure we show the mean error of the correction potential with respect to the computed free energy difference associated with deprotonation, as a function of the fitting order. With an error of 4 kJ mol -1 , the third-order fit, used above to address the convergence issues, does not yield a sufficiently accurate representation of the underlying free energy profile. Increasing the order of the polynomial fit reduces the error and, as shown in Figure , at least seventh order fit is required to provide a uniform distribution of the λ-coordinate for the Asp tripeptide in constant pH MD simulations at pH = pK a .