To investigate the stability of the ion complexes and the deprotonation of ammonium to ammonia we use well-tempered metadynamics simulations, and explore the free energy surface using two collective variables: the N-N distance between NO - 3 and NH + 4 , and the coordination number of ammonium with hydrogen defined in Eq. 4. Figure ) shows the free energy surface (FES) as well as the coordination number and nitrogen distances throughout the metadynamics simulation. The average error of the FES is obtained from the diffusion of the CVs and block average analysis (Figure ). The average error on the FES converges to ∼ 0.8 kJ/mol, and the maximum error is 2.2 kJ/mol in the regions of the CVs space that are sampled less frequently. These data show that at the air-ice interface, for the surface coverage considered, it is more favorable for nitrate to be fully separated from ammonium, which is preferentially protonated, similar to that of ammonium nitrate in bulk aqueous Figure : The free energy surface of ammonium nitrate at the air-ice interface at 263 K in the collective variables space defined by the coordination number of ammonium, and the distance between nitrogen atoms. Each of the stars represents the averaged values of the collective variables throughout their respective unbiased trajectories. The pink star is for the ammonia nitrate run, the red star is for the first ammonium nitrate run, and the yellow star is for the restarted ammonium nitrate run.