We hypothesized that a nitrogen transportation process mediated by cyanide (CN) ions causes the observed increase in growth rate by carbon addition in the Na-flux growth of GaN. Using first-principles calculations, we investigated the probability of the nitrogen transportation process from the viewpoint of change of free energy. In addition, to verify whether the CN can separate into N and C atoms, we estimated the C-N bond energy on the GaN crystal surface by the blue-moon method using constrained molecular dynamics simulations. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim