Kinetic analysis of low-barrier nucleation via first-passage time distributions: A CO₂ hydrate case study

The mean first-passage time (MFPT) analysis is widely used for extracting key thermodynamic and kinetic parameters of nucleation from unbiased molecular dynamics (MD) simulations. For high-barrier nucleation events, the MFPT of the largest cluster can be analytically related to the critical nucleus size, nucleation rate, and the Zeldovich factor. However, for low-barrier nucleation, an additional empirical growth term is required to fit the MFPT curve derived from MD simulations, raising concerns about the accuracy of the resulting nucleation properties. In this study, we determine nucleation parameters by solving the first-passage time distributions (FPTD) and their means. Our results show that incorporating the full FPTD allows for a more accurate determination of the nucleation properties, even in low energy-barrier nucleation scenarios. Furthermore, we determine the range of applicability for the analytical expression derived under high-barrier assumptions. For CO₂ hydrate nucleation at 3000 bar and 270 K, we found that the analytical equation can lead to a nucleation rate error of about 50 %, despite yielding a relatively accurate estimate of the critical nucleus size (about 1 % error). This work highlights the limitations of the high-barrier analytical equation and demonstrates the effectiveness of directly solving the FPTD for more accurate nucleation property determination.