Because the sampling of protonation states is tightly coupled to the sampling of side chain dihedral degrees of freedom, we computed the free energy profiles associated with the rotation of the dihedrals in the side chain of the central amino acid in the capped tripeptide systems (Table ) by means of umbrella sampling. As the first step, we performed 20 ns MD simulations with a time-dependent potential on the dihedral angle with a force constant of 418.4 kJ mol -1 rad -2 . The center of this potential was moved from 0 • to 360 • with a rate of 18 • ns -1 . From these simulations, frames with dihedral angles closest to 0 • , 10 • , 20 • , etc.