  Diffusion of atoms and molecules is a key process for the chemical evolution
in the star forming regions of the interstellar medium. Accurate data on the
mobility of many important interstellar species is however often not available
and this provides a serious limitation for the reliability of models describing
the physical and chemical processes in molecular clouds. Here we aim to provide
the astrochemical modeling community with reliable data on the ratio between
the energy barriers for diffusion and desorption for adsorbed CO and CO$_2$ on
water ices. To this end, we use a fully atomistic, off-lattice kinetic Monte
Carlo technique to generate dynamical trajectories of CO and CO$_2$ molecules
on the surface of crystalline ice at temperatures relevant for the interstellar
medium. The diffusion to desorption barrier ratios are determined to be 0.31
for CO and 0.39 for CO$_2$ . These ratios can be directly used to improve the
accuracy of current gas-grain chemical models.
