Vibrational spectroscopy of hydrogens in diamond: a quantum mechanical treatment†
The electronic and vibrational features of the VHn (n = 1 to 4) family of defects in diamond (hydrogen atoms saturating the dangling bonds of the atoms surrounding a vacancy) are investigated at the quantum mechanical level by using the periodic supercell approach, an all electron Gaussian type basis set, hybrid functionals, and the CRYSTAL code. Most of the results have been collected for supercells containing 64 atoms; however, in order to explore the effect of the defect concentration on both the IR and Raman spectra, supercells containing 216, 512 and 1000 atoms have also been considered in the VH4 case. For each system, all the possible spin states are considered; their relative stability, band structure, charge and spin density distributions are thoroughly described. All the investigated systems present specific IR and Raman spectra, with vibrational spectroscopic features that can in principle be used as fingerprints for their characterization. This is particularly true for the C–H stretching, that ranges between 2500 and 4400 cm−1. The stretching modes are strongly affected by anharmonicity that has been evaluated in this work; it turns out to be extremely sensitive to the H load and spin state of the system, and ranges from −335 cm−1 for VH1 to +85 cm−1 for VH4. All of the investigated defects have very low C–H stretching IR intensity, so that they essentially appear as silent, the exception being VH1. The situation is different for the Raman spectra: the stretching modes of all defects do have similar large intensity; unfortunately here it is the experimental evidence that is lacking.