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First-principles techniques are used to investigate the interaction of hydrogen with gallium vacancies in wurtzite GaN. The calculations reveal that hydrogen can either compensate a vacancy by donating an electron to a vacancy acceptor level, or passivate the vacancy by forming a hydrogen-vacancy complex. A gallium vacancy can bind up to four hydrogen atoms, and hydrogen removal energies are computed as a function of the number of hydrogen atoms. Removal energies are found to depend strongly on Fermi level and complexes containing more than two hydrogen atoms are predicted to be unstable in n-type GaN. Hydrogen vibration frequencies are computed and compared with previously reported infrared absorption measurements for hydrogen-implanted GaN. © 2001 American Institute of Physics.