We investigate atomic and electronic structures of the threading edge dislo
cations of GaN using self-consistent-charge density-functional tight-bindin
g approaches. Full-core, open-core, Ca-vacancy, and N-vacancy edge dislocat
ions are fully relaxed in our total-energy scheme. The Ca-vacancy dislocati
on is the most stable in a wide range of Ga chemical potentials, whereas fu
ll-core and open-core dislocations are more stable than others in the Ga-ri
ch region. Partial dehybridization takes place during the lattice relaxatio
n near the dislocation in all cases. The dangling bonds at Ga atoms mostly
contribute to the deep-gap states, whereas those at N atoms contribute to t
he valence-band tails. All the edge dislocations can act as deep trap cente
rs, except the Ga-vacancy dislocation, which may act as an origin of yellow
luminescence.