Nucleation of NaCl crystals from solution: Rate prediction and influence of noisy order parameters on the committor

Abstract

We report on a transition interface sampling study of the homogeneous crystal nucleation of NaCl from supersaturated solutions under ambient conditions. We predict the rate and the free energy of the nucleation process and show that they are in line with previous results and with classical nucleation theory. While adequate for rate calculations, the order parameter used exhibits strong temporal fluctuations, which lead to an apparent inconsistency between forward- and backward-projected committor functions. By introducing a temporally smoothed order parameter, we restore consistency in the committor and obtain a more faithful representation of progress along the nucleation pathway. The optimal smoothing window corresponds to a timescale of ∼3 ns, suggesting that only ion attachment events persisting on nanosecond timescales contribute to crystal growth, whereas faster fluctuations reflect transient rearrangements. These findings highlight the importance of temporal persistence, in addition to structural criteria (crystallinity and coordination), for defining meaningful order parameters in nucleation studies.