Classical simulations of the reactions between HCO+/COH+ and hydrogen atoms, as well as their deuterated variants, have been carried out on an ab initio interpolated potential energy surface. The surface is constructed at the quadratic configuration interaction with single and double excitation level of ab initio calculation. At low energies we observe reaction channels associated with the isomerization of the cation, hydrogen/deuterium exchange, and the combination of isomerization with exchange. The HCO+/DCO+ ions only undergo exchange, and deuteration is more facile than the release of deuterium. The COH+/COD+ ions undergo isomerization or isomerization combined with exchange, the latter being the dominant reaction channel. Deuteration is again more facile than the release of deuterium, in combination with isomerization. These results are consistent with experimental measurements and with hypotheses on the deuteration of molecules in the interstellar medium.