Activation free energies for formation and dissociation of N–N, C–C, and C–H bonds in a Na–Ga melt

[Display omitted] •Bond energies of N–N, C–C, and C–H in Na–Ga melts and C–H in Ga melts were estimated.•The atomic bondings related to C-added Na-flux GaN growth were discussed.•The atomic bondings related to graphene growth with CH4 and molten Ga were discussed.•First-principles molecular dynamics simulations were employed for the calculations.•The Na–Ga and Ga melts influence the above bonding states as catalysts. Bonding energies of N–N, C–C, and C–H in Na–Ga melts and C–H in Ga melts were investigated using first-principles calculations. Activation free energies for formation and dissociation of the above bonds were estimated via the blue-moon ensemble method using constrained molecular dynamics simulations. The dissociation activation energies of the N–N, C–C, and C–H bonds in the Na–Ga melt were about 1.13, 2.71, and 1.58 eV, respectively, and that of the C–H bond in the Ga melt was about 1.40 eV.