Hydrogen atoms in the diamond vacancy defect. A quantum mechanical vibrational analysis

The VH1 defect in diamond (one hydrogen atom saturating one of the four dangling bonds of the carbon atoms surrounding a vacancy) is investigated at the quantum mechanical level by using the periodic supercell approach, an all electron Gaussian type basis set, “hybrid” functionals and two supercells. Both spin states, characterized by Sz = 1/2 and Sz = 3/2 and resulting from the unpaired electrons on the three unsaturated carbon atoms around the vacancy, have been investigated. The doublet state VH1 d turns out to be more stable by 0.34 eV than the quadruplet VH1 q. The band structure, charge and spin density distributions are analyzed. The two states present very different IR spectra, with peaks that can be used for their characterization. In particular the CH stretching peak can vary by as much as 400 cm−1: from about 2800 cm−1 for VH1 q to about 3200 cm−1 for VH1 d in the harmonic approximation. Anharmonicity is quite important but very different in the two cases: for the C-H stretching, about 330 cm−1 for VH1 q and only 190 cm−1 for VH1 d, so that the final anharmonic wavenumbers differ by as much as 500 cm−1