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Advances in Physical Chemistry
Volume 2012 (2012), Article ID 135172, 10 pages
Research Article

Microscopic Rate Constants of Crystal Growth from Molecular Dynamic Simulations Combined with Metadynamics

1Institute of Enzymology, Research Centre for Natural Sciences, Hungarian Academy of Sciences, Karolina út 29, Budapest 1113, Hungary
2Institute of Chemistry, Eötvös Loránd University, P.O. Box 32, Budapest 1518, Hungary

Received 3 April 2012; Revised 24 July 2012; Accepted 26 July 2012

Academic Editor: Dennis Salahub

Copyright © 2012 Dániel Kozma and Gergely Tóth. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Atomistic simulation of crystal growth can be decomposed into two steps: the determination of the microscopic rate constants and a mesoscopic kinetic Monte Carlo simulation. We proposed a method to determine kinetic rate constants of crystal growth. We performed classical molecular dynamics on the equilibrium liquid/crystal interface of argon. Metadynamics was used to explore the free energy surface of crystal growth. A crystalline atom was selected at the interface, and it was displaced to the liquid phase by adding repulsive Gaussian potentials. The activation free energy of this process was calculated as the maximal potential energy density of the Gaussian potentials. We calculated the rate constants at different interfacial structures using the transition state theory. In order to mimic real crystallization, we applied a temperature difference in the calculations of the two opposite rate constants, and they were applied in kinetic Monte Carlo simulation. The novelty of our technique is that it can be used for slow crystallization processes, while the simple following of trajectories can be applied only for fast reactions. Our method is a possibility for determination of elementary rate constants of crystal growth that seems to be necessary for the long-time goal of computer-aided crystal design.