The nucleation of crystals in liquids is one of nature’s most ubiquitous phenomena, playing an important role in areas such as climate change and the production of drugs. As the early stages of nucleation involve exceedingly small time and length scales, atomistic computer simulations can provide unique insights into the microscopic aspects of crystallization. In this review, we take stock of the numerous molecular dynamics simulations that, in the past few decades, have unraveled crucial aspects of crystal nucleation in liquids. We put into context the theoretical framework of classical nucleation theory and the state-of-the-art computational methods by reviewing simulations of such processes as ice nucleation and the crystallization of molecules in solutions. We shall see that molecular dynamics simulations have provided key insights into diverse nucleation scenarios, ranging from colloidal particles to natural gas hydrates, and that, as a result, the general applicability of classical nucleation theory has been repeatedly called into question. We have attempted to identify the most pressing open questions in the field. We believe that, by improving (i) existing interatomic potentials and (ii) currently available enhanced sampling methods, the community can move toward accurate investigations of realistic systems of practical interest, thus bringing simulations a step closer to experiments.

Molecular adsorption on surfaces plays a central role in catalysis, corrosion, desalination, and many other processes of relevance to industry and the natural world. Few adsorption systems are more ubiquitous or of more widespread importance than those involving water and carbon, and for a molecular level understanding of such interfaces water monomer adsorption on graphene is a fundamental and representative system. This system is particularly interesting as it calls for an accurate treatment of electron correlation effects, as well as posing a practical challenge to experiments. Here, we employ many-body electronic structure methodologies that can be rigorously converged and thus provide faithful references for the molecule-surface interaction. In particular, we use diffusion Monte-Carlo (DMC), coupled cluster (CCSD(T)), as well as the random phase approximation (RPA) to calculate the strength of the interaction between water and an extended graphene surface. We establish excellent, sub-chemical, agreement between the complementary high-level methodologies, and an adsorption energy estimate in the most stable configuration of approximately -100 meV is obtained. We also find that the adsorption energy is rather insensitive to the orientation of the water molecule on the surface, despite different binding motifs involving qualitatively different interfacial charge reorganisation. In producing the first demonstrably accurate adsorption energies for water on graphene this work also resolves discrepancies amongst previously reported values for this widely studied system. It also paves the way for more accurate and reliable studies of liquid water at carbon interfaces with cheaper computational methods, such as density functional theory and classical potentials.