In order to understand the shortfalls of Eq. 3, it's crucial to first recognize that RR-cpH algorithm is inherently grand-canonical. This is evident when examining the weight for a protonation move in Eq. 3, in which appears e -ln pH ∼ e βµ H , where µ H is the electrochemical potential of a hydronium ion. This is precisely the grand canonical weight associated with transferring a hydronium ion from the reservoir into the simulation cell. In the context of the Grand Canonical Monte Carlo (GCMC) simulations of Coulomb systems, maintaining charge neutrality within the simulation cell is paramount, in particular when using Ewald summation to treat long-range Coulomb interaction. Consequently, a grand canonical protonation move necessitates a corresponding grand-canonical insertion move for an anion, and a deprotonation move should be coupled with a GCMC removal of an anion, to preserve the overall charge neutrality inside the system. One can't arbitrarily delete or create ions inside the simulation cell, as is usually done in the framework of RR-cpH algorithm. Instead, ions must be inserted or removed from the system with the correct grand-canonical acceptance probabilities.