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Vibrational properties of tetrahedral amorphous carbon from first principles
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16.The C atoms are described by a pseudopotential with nonlocality. The H atoms are described with a local pseudopotential. The wave functions are expanded in plane wave with a 45 Ry energy cutoff. The dynamical matrix is obtained by displacing each atom and computing the resulting forces. The Brillouin zone is sampled with the point.
17.To obtain continuous curves we used for the plots a Gaussian smearing with equal to 60 (Fig. 1), 50 (Fig. 2), 30 (Fig. 4).
18.To perform the projection we have defined for each bond a “stretching” vector in the space of the displacements. The components of each vector involves the displacement of two atoms in the direction of the bond and with opposite orientations. These vectors, in general, are not orthonormal. We obtain a set of orthonormal vectors by multiplying the initial set by the square root of the inverse of the overlap matrix. We obtain the projected DOS on the stretch modes using the full set of orthonormalized vectors and partial decompositions on and C–C bonds selecting from the full orthonormalized set the vectors originated from the corresponding bonds.
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20.The mean square dispersions have been computed before smearing the DOS.
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