However, as shown in Figure , the distributions are identical between replicas, but not uniform, despite the corrections to the torsion potentials. Because both the pH-dependent potential V pH (λ) and the biasing potential are flat by construction at pH = pK a , the deviations must originate from discrepancies between the correction potential V MM (λ) and the underlying free energy profile associated with deprotonation. The correction potential is obtained as a polynomial fit to the ∂V /∂λ λ values from thermodynamic integration simulations. Because linear response (LR) theory predicts a lin-ear dependence between the hydration free energy and the magnitude of a (point) charge, a first-order fit has often been used to obtain the correction potential for constant pH MD. 9,12