Several experiments have suggested that chemisorption of digermane onto the Ge(0 0 1) surface takes place in the form of dissociated fragments GeH and GeH2 of the molecule. Using the pseudo-potential method and the local density approximation, we have determined the equilibrium site for GeH2 on the bare and hydrogenated Ge(0 0 1) surfaces. Following a previous study for SiH2 on Si(0 0 1), we have considered one GeH2 radical per 2 x 2 surface unit cell in an intra-row position with the dangling bonds at the other end of the dimers being (i) empty (i.e. on the bare surface), (ii) partially saturated by one hydrogen per unit cell, and (iii) fully saturated by hydrogen. For situation (i), the empty sites of the Ge-dimers are tilted asymmetrically (i.e. zig-zag in the intra-row direction). For situation (ii), the hydrogenated dimer is of length 0.242 nm and becomes nearly symmetric, but the other dimer has a length of 0.239 nm and remains tilted by approximately 6degrees. For situation (iii), both dimers become symmetric with an elongated length of 0.243 nm, and the Ge(0 0 1) surface exhibits full electrical passivation, with the fundamental band gap region becoming free of surface states. (C) 2002 Elsevier Science Ltd. All rights reserved.