# The Gibbs free energy of homogeneous nucleation: from atomistic nuclei to the planar limit

## TL;DR

This paper presents a method to improve the fitting of macroscopic nucleation models by combining atomistic simulations of nuclei and planar interfaces, reducing errors and enhancing prediction reliability.

## Contribution

It introduces a combined fitting approach using both atomistic and planar interface simulations to better determine nucleation model parameters.

## Key findings

- Fitting parameters from atomistic free energy profiles is highly sensitive to errors.
- Combining planar interface and nucleus simulations reduces fitting errors.
- The new method yields more reliable predictions for large nuclei.

## Abstract

In this paper we discuss how the information contained in atomistic simulations of homogeneous nucleation should be used when fitting the parameters in macroscopic nucleation models. We show how the number of solid and liquid atoms in such simulations can be determined unambiguously by using a Gibbs dividing surface and how the free energy as a function of the number of solid atoms in the nucleus can thus be extracted. We then show that the parameters of a model based on classical nucleation theory can be fit using the information contained in these free-energy profiles but that the parameters in such models are highly correlated. This correlation is unfortunate as it ensures that small errors in the computed free energy surface can give rise to large errors in the extrapolated properties of the fitted model. To resolve this problem we thus propose a method for fitting macroscopic nucleation models that uses simulations of planar interfaces and simulations of three-dimensional nuclei in tandem. We show that when the parameters of the macroscopic model are fitted in this way the numerical errors for the final fitted model are smaller and that the extrapolated predictions for large nuclei are thus more reliable.