  Hydrogen and deuterium chemisorption on a single layer of graphene has been
studied by path-integral molecular dynamics simulations. Finite-temperature
properties of these point defects were analyzed in the range from 200 to 1500
K, by using a tight-binding potential fitted to density-functional
calculations. On one side, vibrational properties of the adatoms are studied at
their equilibrium positions, linked to C atoms. The vibrations display an
appreciable anharmonicity, as derived from comparison between kinetic and
potential energy, as well as between vibrational energy for hydrogen and
deuterium. On the other side, adatom motion has been studied by quantum
transition-state theory. At room temperature, quantum effects are found to
enhance the hydrogen diffusivity on the graphene sheet by a factor of 20.
