Molecular simulations allow the measurement of microscopic details beyond the temporal and spatial resolution of experimental methods. However, the limitation of molecular dynamics simulations to microscopic length and time scales that can be achieved with reasonable computational effort poses challenges. For example, homogeneous crystal nucleation is an ordering process of considerable interest, where an entropic barrier typically prevents it from occurring in brute-force simulations. Details about the early stages of the formation of a crystalline nucleus from the liquid are simplified in conventional theories like the classical nucleation theory or the diffusive interface theory; consequently, these theories do not suffice to explain alternative nucleation mechanisms.
To study activated processes like homogeneous crystal nucleation in simulations, so called rare-event sampling methods have been developed, which typically depend on a judicious choice of suitable order parameters, which can unknowingly bias the process of interest. To circumvent this challenge, it would be beneficial to find a new very general and systematically applicable sampling bias that promotes the phenomenon of crystallization rather than the formation of a particular lattice structure. This work introduces a new approach that enhances the sampling of ordered arrangements in molecular simulations of liquids thereby giving rise to dramatically accelerated crystal nucleation rates, by as much as 30 orders of magnitude. This is achieved by the simultaneous application of thermostat algorithms that control the kinetic and configurational degrees of freedom separately and maintain an induced conversion of potential into kinetic energy. We call the difference between the kinetic and configurational temperatures in this steady state a 'conjugate thermal field'.
The complete process of crystal nucleation has been simulated in liquid Lennard Jones and carbon dioxide (EPM2 model) systems, and similar localized effects on structure and mobility were found in two-dimensional purely repulsive spheres and Lennard Jones disks, as well as a rigid water model (TIP4P-2005 model). All our results agree with the interpretation that the bias enhances the sampling of configurations that sustain vibrational motion patterns, and indicate that it can also be applied to facilitate the simulation of crystal nucleation and crystallization of other materials.