Theory of resonant Raman scattering of tetrahedral amorphous carbon

We present a practical method to compute the vibrational resonant Raman spectra in solids with delocalized excitations. We apply this approach to the study of tetrahedrous amorphous carbon. We determine the vibrational eigenmodes and eigenvalues using density functional theory in the local density approximation and the Raman intensities using a tight binding approximation. The computed spectra are in good agreement with the experimental ones measured with visible and uv lasers. We analyze the Raman spectra in terms of vibrational modes of microscopic units. We show that, at any frequency, the spectra are dominated by the stretching vibrations. We identify a very rapid inversion in the relative Raman intensities of the ${\mathrm{sp}}^2$ and ${\mathrm{sp}}^3$ carbon sites with the frequency of the incident laser beam. In particular, the spectra are dominated by ${\mathrm{sp}}^2$ atoms below 4 eV and by ${\mathrm{sp}}^3$ atoms above 6 eV.