Factor Group Analysis of Molecular Vibrational Modes of Graphene and Density Functional Calculations

The molecular vibrational modes of graphene were analyzed theoretically by factor group analysis.The molecular vibrational modes of graphene and the spectral characteristics of each vibrational mode were calculated successfully.The molecular vibrational frequency and mode of graphene were also calculated by first-principles density functional theory based on establishment of the graphene Bravais crystal unit cell.The number of vibrational modes and corresponding vibrational frequency spectral properties calculated were consistent with the results obtained using factor group analysis.The above calculations and systematic comparison between the infrared and Raman spectra of graphene and graphite were used to determine why the infrared active vibrational modes A 2u and E 1u with D 6h point group did not appear on the experimental infrared spectrum of graphene.