  We have developed a formulation of density functional perturbation theory for
the calculation of vibrational frequencies in molecules and solids, which uses
numerical atomic orbitals as a basis set for the electronic states. The
(harmonic) dynamical matrix is extracted directly from the first order change
in the density matrix with respect to infinitesimal atomic displacements from
the equilibrium configuration. We have applied this method to study the
vibrational properties of a number of hydrogen-related complexes and light
impurities in silicon. The diagonalization of the dynamical matrix provides the
vibrational modes and frequencies, including the local vibrational modes (LVMs)
associated with the defects. In addition to tests on simple molecules, results
for interstitial hydrogen, hydrogen dimers, vacancy-hydrogen and
self-interstitial-hydrogen complexes, the boron-hydrogen pair, substitutional
C, and several O-related defects in c-Si are presented. The average error
relative to experiment for the aprox.60 predicted LVMs is about 2% with most
highly harmonic modes being extremely close and the more anharmonic ones within
5-6% of the measured values.
