  Density functional calculations of optimized geometries for the migration of
single hydrogen and hydroxyl groups on graphene are performed. It is shown that
the migration energy barrier for the hydroxyl group is three times larger than
for hydrogen. Crucial role of supercell size for the values of the migration
barriers are discussed. The paired migration of hydrogen and hydroxyl groups
has also been examined. It could be concluded that hydroxyl groups based
magnetism is rather stable in contrast with unstable hydrogen based magnetism
of functionalized graphene. The role of water in the migration of hydroxyl
groups is also discussed, with the results of the calculations predicting that
the presence of water weakens the covalent bonds and makes these groups more
fluid. Increasing of number of water molecules associated with hydroxyl group
provides grown of the migration energy.
