Pseudo-grand canonical molecular dynamics via volumetrically controlled osmotic pressure

Molecular dynamics simulations are typically constrained to have a fixed number of particles, which limits our capability to simulate chemical and physical processes where the composition of the system changes during the simulation time. Typical examples are the calculation of nucleation and crystal growth rates in heterogeneous solutions where the driving force depends on the composition of the fluid. Constant chemical potential molecular dynamics simulations would instead be required to compute time-independent growth and nucleation rates. While this can, in principle, be achieved through the addition and deletion of particles using the grand canonical partition function, this is very inefficient in the condensed phase due to the low acceptance probability of these events. Adaptive resolution schemes, which use a reservoir of non-interacting particles that can be transformed into solute particles, circumvent this problem, but at the cost of relatively complicated code implementations. In this work, a simpler approach is proposed that uses harmonic volumetric restraints to control the solute osmotic pressure, which can be considered a proxy for the system's chemical potential. The osmotic pressure regulator is demonstrated to reproduce the expected properties of ideal gases and ideal solutions. Using the mW water model, the osmotic pressure regulator is shown to provide a constant growth rate for ice in the presence of an electrolyte solution, unlike what standard molecular dynamics simulations would produce.