To validate the new approach, we used it to calculate the titration isotherms of 11% volume fraction suspension of nanoparticles of radius 60 Å with Z = 600 surface sites. For simplicity, we placed only one nanoparticle into the simulation cell, however, there is no conceptual difficulty in putting as many particles as is desired into the simulation cell. The simulation was performed inside a cubic cell, which in addition to the nanoparticle also contained 600 hydronium ions and four Na + and Cl -ions, corresponding to the concentration of 1mM of salt. To calculate the titration isotherm, we ran the reactive MC simulation with the acceptance probabilities for protonation/deprotonation moves given by Eq. ( ). After equilibration, the number of protonated sites was determined. To make sure the system was well equilibrated, we used 1 million particle moves. To check equilibrium we also monitored the energy of the system. After equilibration, we performed insertions of a virtual proton to calculate the pH using the surface Widom insertion method, Eq. ( ). Virtual insertions were performed at interval of 10,000 particle moves, to make sure the events were uncorrelated. We then replaced one of the initial 600 hydroniums by Na + and repeated the calculation -resulting in a slightly more negatively charged nanoparticle and a slightly higher pH. We repeated this procedure until almost all the hydronium ions were replaced by Na + , resulting in a nanoparticle with no protonated surface groups. We can summarize the sequence of calculations as follows: