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We have developed a formulation of density functional perturbation theory forthe calculation of vibrational frequencies in molecules and solids, which usesnumerical atomic orbitals as a basis set for the electronic states. The(harmonic) dynamical matrix is extracted directly from the first order changein the density matrix with respect to infinitesimal atomic displacements fromthe equilibrium configuration. We have applied this method to study thevibrational properties of a number of hydrogen-related complexes and lightimpurities in silicon. The diagonalization of the dynamical matrix provides thevibrational modes and frequencies, including the local vibrational modes (LVMs)associated with the defects. In addition to tests on simple molecules, resultsfor interstitial hydrogen, hydrogen dimers, vacancy-hydrogen andself-interstitial-hydrogen complexes, the boron-hydrogen pair, substitutionalC, and several O-related defects in c-Si are presented. The average errorrelative to experiment for the aprox.60 predicted LVMs is about 2% with mosthighly harmonic modes being extremely close and the more anharmonic ones within5-6% of the measured values.Comment: 18 pages, 1 figur

Ab initiolocal vibrational modes of light impurities in silicon