Estimation of the ice melting point in molecular dynamics simulations based on the finite-size effects

Predicting the ice melting point using molecular dynamics (MD) simulations is nontrivial due to uncertainty associated with the stochastic nature of the simulation and effect of finite domain sizes on the simulated ice-water phase transition. We developed a method based on the percolation theory to make use of the finite size effects to allow determination of a unique critical phase transition temperature as the melting point. The method involves construction of melting/freezing probability curves from multiple simulations with varying temperatures for different domain sizes. While the domain sizes affect the apparent melting/freezing probability and hence generate different curves with a wider probability distribution for a smaller size, the intersection of these curves is unique and locates the melting point. Based on MD simulations using the Tip4p/Ice water model, we tested and demonstrated the effectiveness of this method in locating the critical ice-water phase transition at a melting temperature of 268.78 K. Our analysis also showed that the apparent melting probability at this critical point is \ensuremath{\sim}0.69, not 0.5 assumed in the ad hoc method used previously. Our method, making no assumption about the system size, may provide a generic framework for analyzing phase transitions influenced by the finite size effects in MD simulations.