Lattice dynamics of hydrogen-substituted graphene systems

The hydrogen substituted graphenes are investigated by using the density-functional theory. And the localized vibrational modes（LVMs） are calculated within the framework of density-functional perturbation theory. It is found that the number of LVMs at high-frequency part of the spectrum is equal to the number of hydrogen atoms in one vacancy，and LVMs from samples with different substituents have different frequencies. The results and analyses indicate that the measuring of LVMs is an efficient method to determine the classification of substituents as well as their corresponding concentrations in proton-irradiated graphene/graphite samples. This method can also be applied to other doped systems.