  Crystallization is one of the most important physicochemical processes which
has relevance in material science, biology, and the environment. Decades of
experimental and theoretical efforts have been made to understand this
fundamental symmetry-breaking transition. While experiments provide equilibrium
structures and shapes of crystals, they are limited to unraveling how molecules
aggregate to form crystal nuclei that subsequently transform into bulk
crystals. Computer simulations, mainly molecular dynamics (MD), can provide
such microscopic details during the early stage of a crystallization event.
Crystallization is a rare event that takes place in timescales much longer than
a typical equilibrium MD simulation can sample. This inadequate sampling of the
MD method can be easily circumvented by the use of enhanced sampling (ES)
simulations. An ES method enhances the fluctuations of a system's slow degrees
of freedom, called collective variables (CVs), by applying a bias potential,
and thereby transforms the system from one state to the other within a short
timescale. The most crucial part of an ES method is to find suitable CVs which
often needs intuition and several trial-and-error optimization steps. Over the
years, a plethora of CVs has been developed and applied in the study of
crystallization. In this review, we provide a brief overview of CVs that have
been developed and used in ES simulations to study crystallization from melt or
solution. These CVs can be categorized mainly into four types: (i) spherical
particle-based, (ii) molecular template-based, (iii) physical property-based,
and (iv) CVs obtained from dimensionality reduction techniques. We present the
context-based evolution of CVs, discuss the current challenges, and propose
future directions to further develop effective CVs for the study of
crystallization of complex systems.
