For systems with many titratable sites, multiple λ-groups are introduced. Because the analytical expressions for the correction, biasing and pH dependent terms in equation 5 are additive, we no longer consider them explicitly in what follows and focus exclusively on the interpolation of the force field potential energies between the multiple protonation states of the system. For N λ-coordinates, there are 2 N such states and the interpolation generalizes to: 13