A formulation of density-functional perturbation theory was developed, 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) dynamic matrix was extracted directly from the first-order change in the density matrix with respect to infinitesimal atomic displacements from the equilibrium configuration. This method was

used to study the vibrational properties of a number of H-related complexes and light impurities in Si. The diagonalization of the dynamic matrix provides the vibrational modes and frequencies, including the local vibrational modes associated with the defects. In addition to tests on simple molecules, results for interstitial H, H dimers, vacancy-H and self-interstitial-H complexes, the B-H pair, substitutional C, and several O-related defects in c-Si, were presented. The average error relative to experiment for the about 60 predicted local vibrational modes was about 2% with most highly harmonic modes being extremely close and the more anharmonic ones within 5 to 6 % of the measured values.

Ab Initio Local Vibrational Modes of Light Impurities in Silicon. J.M.Pruneda, S.K.Estreicher, J.Junquera, J.Ferrer, P.Ordejón: Physical Review B, 2002, 65[7], 075210 (8pp)