While global order parameters have been widely used as
reaction coordinates in nucleation and crystallization studies, their use in
nucleation studies is claimed to have a serious drawback. In this work, a local
order parameter is introduced as a local reaction coordinate to drive the
simulation from the liquid phase to the solid phase and vice versa. This local
order parameter holds information regarding the order in the first- and
second-shell neighbors of a particle and has different well-defined values for
local crystallites and disordered neighborhoods but is insensitive to the type of
the crystal structure. The order parameter is employed in metadynamics
simulations to calculate the solid?liquid phase equilibria and free energy
barrier to nucleation. Our results for repulsive soft spheres and the Lennard-
Jones potential, LJ(12?6), reveal better-resolved solid and liquid basins
compared with the case in which a global order parameter is used. It is also
shown that the configuration space is sampled more efficiently in the present
method, allowing a more accurate calculation of the free energy barrier and the solid?liquid interfacial free energy. Another
feature of the present local order parameter-based method is that it is possible to apply the bias potential to regions of interest in
the order parameter space, for example, on the largest nucleus in the case of nucleation studies. In the present scheme for
metadynamics simulation of the nucleation in supercooled LJ(12?6) particles, unlike the cases in which global order parameters
are employed, there is no need to have an estimate of the size of the critical nucleus and to refine the results with the results of
umbrella sampling simulations. The barrier heights and the nucleation pathway obtained from this method agree very well with
the results of former umbrella sampling simulations.