For each side chain dihedral angle of the titratable amino acids, the coefficient i was optimized in an iterative fashion: After an initial guess, we computed the free energy profiles associated with rotation of the dihedral, as well as five unbiased 100 ns trajectories at pH = pK a with different starting conditions and a biasing potential (V bias (λ), Equation 5 in Aho et al. ) without barrier. Prior to these constant pH MD simulations, we recomputed the correction potential, V MM (λ), by fitting a third-order polynomial to the ∂V /∂λ λ values obtained from thermodynamic integration simulations performed with the current value of i . Free energy profiles were inspected visually for artificial minima, while distributions of both dihedral angles and λ-coordinates were compared between the five unbiased replica runs based on their similarity. The coefficient i was gradually increased until the distributions in the different replicas were sufficiently similar (KSS < 0.03), while at the same time no additional minima appeared in the free energy profiles. Because with the corrected potentials, the Kolmogorov-Smirnov statistics for Asp, Glu, His, and C-terminus are 0.028, 0.015, 0.027, and 0.022, we conclude that the corrections improve the convergence of both the λ and dihedral degrees of freedom in constant pH simulations.