Molecular origins of homogeneous crystal nucleation

We review the molecular principles underlying the homogeneous nucleation of a crystal phase from the melt phase, as elucidated by molecular simulation methods. Classical nucleation theory serves as the starting point for describing the nature of nucleation processes, but it does not derive from molecular principles itself. Density functional theory and molecular simulations offer tools for delving into the molecular origins of nucleation. Here, we emphasize the rapid development of molecular simulation methodologies for studying crystal nucleation from the melt. These methodologies are broadly categorized as free energy sampling methods, dynamical or mean first-passage time methods, and composite approaches that take advantage of both. The crucial selection of order parameters to distinguish the crystal phase from the liquid phase and important features of the reaction coordinate are emphasized. The system size dependence of the nucleation free energy barrier is also examined.