The mechanism of reaction of binuclear zirconium dinitrogen complex [p(2)n(2)]Zr(mu-eta(2)-N-2)Zr[p(2)n(2)] (1, where p(2)n(2) = (PH3)(2)(NH2)(2) as a model of the experimentally used P2N2 = PhP(CH2SiMe2NSiMe2CH2)(2)-PPh ligand), with a hydrogen molecule has been studied by using the density functional method. It is shown that this reaction proceeds via (i) activation of the H-H sigma-bond via a "metathesis-like" transition state where simultaneously Zr-H and N-H bonds are formed and the H-H and one of the N-N pi-bonds are broken, to produce the diazenidohydride complex 3, [p(2)n(2)]Zr(mu-eta(2)-NNH)Zr(H)[p(2)n(2)], and (ii) migration of the Zr-bonded hydride ligand to a position bridging the two Zr atoms to form the diazenido-mu-hydride complex 7, [p(2)n(2)]Zr(mu-eta(2)-NNH)Zr[P(2)n(2)](mu-H). The entire reaction is calculated to be exothermic by 13-15 kcal/mol. The rate-determining step of this reaction is found to be the activation of the H-W bond, which occurs with a 21- kcal/mol barrier. The experimentally observed diazenido-mu-hydride complex 7, [p(2)n(2)]Zr(mu-eta(2)-NNH)Zr[p(2)n(2)](mu-H), is not the lowest energy structure in the potential energy surface. The hydrazono complex [p(2)n(2)]Zr(mu-NNH2)Zr[p(2)n(2)] (with a bridging NH2) and the hydrado complex [p(2)n(2)]Zr(mu-NHNH)Zr[p(2)n(2)] (with two bridging NH units) are calculated to be more stable than the diazenido-mu-hydride complex 7 by about 50 kcal/mol. However, these complexes cannot be generated by the reaction of 1 + H-2 at ambient laboratory conditions because of very high (nearly 60 kcal/mol) barriers separating them from 7.