Molecular simulations of aqueous electrolyte solubility: 1. The expanded-ensemble osmotic molecular dynamics method for the solution phase

We have developed a molecular-level simulation technique called the expanded-ensemble osmotic molecular dynamics (EEOMD) method, for studying electrolyte solution systems. The EEOMD method performs simulations at a fixed number of solvent molecules, pressure, temperature, and overall electrolyte chemical potential. The method combines elements of constant pressure-constant temperature molecular dynamics and expanded-ensemble grand canonical Monte Carlo. The simulated electrolyte solution systems contain, in addition to solvent molecules, full and fractional ions and undissociated electrolyte molecular units. The fractional particles are coupled to the system via a coupling parameter that varies between 0 (no interaction between the fractional particle and the other particles in the system) and 1 (full interaction between the fractional particle and the other particles in the system). The time evolution of the system is governed by the constant pressure-constant temperature equations of motion and accompanied by random changes in the coupling parameter. The coupling-parameter changes are accepted with a probability derived from the expanded-ensemble osmotic partition function corresponding to the prescribed electrolyte chemical potential. The coupling-parameter changes mimic insertion/deletion of particles as in a crude grand canonical Monte Carlo simulation; if the coupling parameter becomes 0, the fractional particles disappear from the system, and as the coupling parameter reaches unity, the fractional particles become full particles. The method is demonstrated for a model of NaCl in water at ambient conditions. To test our approach, we first determine the chemical potential of NaCl in water by the thermodynamic integration technique and by the expanded-ensemble method. Then, we carry out EEOMD simulations for different specified values of the overall NaCl chemical potential and measure the concentration of ions resulting from the simulations. Both computations give consistent results, validating the EEOMD methodology.