Canonical titration simulations

Abstract

We present a Monte Carlo approach for performing titration simulations in the canonical ensemble.

On the Validity of Constant pH Simulations

“…We then use the surface Widom insertion method to obtain the pH inside the system. 49 Briefly, the idea behind the surface Widom method involves bringing a virtual proton from infinity to a randomly chosen colloidal active site. If the selected site is unoccupied (bearing charge −q), it "reacts" with the virtual proton, causing its charge to transition to 0.…”

“…The reactive MC simulation then determines how many of the polyelectrolyte groups will become protonated in equilibrium. The acceptance probabilities for deprotonation/protonation moves are given by ,− where N H is the number of free hydronium ions inside the simulation cell at a given moment and N A is the Avogadro number. Note that for canonical (closed) systems, the acceptance probabilities do not explicitly depend on pH.…”

“…Recently, we have developed a new method for canonical titration simulations utilizing the surface Widom insertion algorithm that enables us to easily calculate equilibrium pH. 49 In such systems, the traditional Widom insertion method cannot be used since at high pH, there may be few or no hydronium ions present inside the simulation cell, preventing us from accurately determining the chemical potential of these ions. The difficulty of calculating pH in canonical reactive simulations is probably one of the reasons for the widespread use of the incorrect RR-cpH algorithm in the soft matter and biophysics literature.…”

“…Contrary to a common misconception, the RR-cpH algorithm is not a canonical algorithm . For isolated systems, the total number of protons is conserved, and the titration algorithm must use the correct canonical acceptance probabilities for the protonation/deprotonation moves, which do not explicitly depend on the pH inside the simulation cell. ,− In a canonical (isolated) system, pH is not a control parameterit cannot be specified a priori, but can only be calculated a posteriori , after the simulation has fully equilibrated, and the number of protonated groups has been determined . Therefore, if one wants to modify the RR-cpH algorithm to properly include the explicit ions, one must take into account that the simulation cell is implicitly in contact with an external reservoir of acid and salt. , A protonation/deprotonation move should then be combined with the simultaneous insertion/deletion of an anion from the reservoir, in accordance with the correct grand canonical (GC) acceptance probability. ,, Furthermore, since in such a simulation polyelectrolyte is confined within the cell, while ions can freely exchange between the system and the reservoir, the two will be at different electrostatic potentials. , This is known as the “Donnan potential”, φ D .…”

“…This requires a separate simulation of the reservoir, in which, the Widom insertion method is used to obtain the chemical potential of all the ions. − Furthermore, the calculation of the Donnan potential within the GC formalism makes such simulations slow. Recently, we have developed a new method for canonical titration simulations utilizing the surface Widom insertion algorithm that enables us to easily calculate equilibrium pH . In such systems, the traditional Widom insertion method cannot be used since at high pH, there may be few or no hydronium ions present inside the simulation cell, preventing us from accurately determining the chemical potential of these ions.…”