Hydrogen vibrational modes on graphene and relaxation of the C–H stretch excitation from first-principles calculations

Abstract

Density functional theory (DFT) calculations are used to determine the vibrational modes of hydrogen adsorbed on graphene in the low-coverage limit. Both the calculated adsorption energy of a H atom of 0.8 eV and calculated C-H stretch vibrational frequency of 2552 cm(-1) are unusually low for hydrocarbons, but in agreement with data from electron energy loss spectroscopy on hydrogenated graphite. The clustering of two adsorbed H atoms observed in scanning tunneling microscopy images shows its fingerprint also in our calculated spectra. The energetically preferred adsorption on different sublattices correlates with a blueshift of the C-H stretch vibrational modes in H adatom clusters. The C-H bending modes are calculated to be in the 1100 cm(-1) range, resonant with the graphene phonons. Moreover, we use our previously developed methods to calculate the relaxation of the C-H stretch mode via vibration-phonon interaction, using the Born-Oppenheimer surface for all local modes as obtained from the DFT calculations. The total decay rate of the H stretch into other H vibrations, thereby creating or annihilating one graphene phonon, is determined from Fermi's golden rule. Our calculations using the matrix elements derived from DFT calculations show that the lifetime of the H stretch mode on graphene is only several picoseconds, much shorter than on other semiconductor surfaces such as Ge(001) and Si(001).