  The dynamics for molecule formation, relaxation, diffusion, and desorption on
amorphous solid water is studied in a quantitative fashion. We aim at
characterizing, at a quantitative level, the formation probability,
stabilization, energy relaxation and diffusion dynamics of CO$_2$ and NO$_2$ on
cold amorphous solid water following atom+diatom recombination reactions.
Accurate machine-learned energy functions combined with fluctuating charge
models were used to investigate the diffusion, interactions, and recombination
dynamics of atomic oxygen with CO and NO on amorphous solid water (ASW). Energy
relaxation to the ASW and into water-internal-degrees of freedom were
determined from analysis of the vibrational density of states. The surface
diffusion and desorption energetics was investigated from extended and
nonequilibrium MD simulations. The reaction probability on the nanosecond time
scale is determined in a quantitative fashion and demonstrates that surface
diffusion of the reactants leads to recombination for initial separations up to
20 \AA\/. After recombination both, CO$_2$ and NO$_2$, stabilize by energy
transfer to water internal and surface phonon modes on the picosecond time
scale. The average diffusion barriers and desorption energies agree with those
reported from experiments. After recombination, the triatomic products diffuse
easily which contrasts with the equilibrium situation in which both, CO$_2$ and
NO$_2$, are stationary on the multi-nanosecond time scale.
