In order to evaluate the free energy associated with supplying an additional carbon atom to a catalyst cluster, we performed umbrella sampling and used the weighted histogram analysis in our classical molecular dynamic simulation. We assumed a one-dimensional reaction coordinate and derived the free energy. The derived free energy distribution was consistent with the observed phenomena and we found a reaction barrier of 0.6 eV near the cluster surface. Beyond the reaction barrier, the free energy increased with increasing density of the carbon atoms, and this indicated that the saturation started from the cluster center. (C) 2015 Elsevier B.V. All rights reserved.