A general relation between the largest nucleus and all nuclei distributions for free energy calculations

Abstract

Prediction of nucleation rates in first order phase transitions requires the knowledge of the barrier associated with the free energy profile W. Molecular simulations offer a direct route through W = − kT ln  p a, where k is Boltzmann’s constant, T is temperature, and p a is the probability distribution of the size of any nucleus. However, in practice, the extremely scarce spontaneous occurrence of large nuclei impedes the full determination of p a, and a numerical bias must be introduced, which is generally done on the size of the largest nucleus in the system, leading to the probability size distribution of the largest nucleus p l. Although p l is known to be system size dependent, unlike p a, it has extensively been used as an approximation for p a. This communication demonstrates an improved relation between p a and p l, which cures this approximation and allows an accurate calculation of free energy barriers from biased simulations.