We investigate defects in bulk zinc oxide by performing embedded cluster calculations within the density functional theory using the PBE functional. We obtain and discuss equilibrium structures and vibrational spectra of interstitial hydrogen species and of hydrogen complexes at zinc vacancies and at substitutional atoms like copper, beryllium, manganese and calcium in zinc positions. All of these defects differ in their vibrational frequencies which can be assigned to existing experimental data with an agreement that surpasses the results of earlier calculations within the local (spin) density approximation. This leads to a better understanding of these bulk defects and helps to answer some open questions, as e.g. the assignment of a signal observed in infra red spectra at 3326 cm(-1). Furthermore, the computed vibrational spectra may serve as a benchmark and assist in the interpretation of future experimental results.