Direct determination of the nucleation free-energy surface by large-scale metadynamics simulations

Direct determination of the free-energy surface (FES) associated with nucleation remains a long-standing challenge because nucleation occurs on extremely small spatial and temporal scales. Conventional molecular dynamics simulations can capture nucleation events but typically become irreversible once a critical nucleus forms, preventing direct reconstruction of the nucleation free-energy landscape. Here we demonstrate that large-scale metadynamics simulation enables the direct determination of the nucleation FES in an undercooled metallic melt. By introducing a collective variable representing the number of solid atoms, repeated growth and shrinkage of nuclei are sampled, allowing reconstruction of the free-energy profile associated with nucleation. The obtained FES follows classical nucleation theory, showing that the nucleation barrier and critical nucleus radius decrease with increasing undercooling. The derived nucleation-related properties are quantitatively consistent with the Gibbs–Thomson and Gibbs–Helmholtz relations. These results establish metadynamics as a powerful framework for directly resolving nucleation free-energy landscapes in atomistic simulations.