The mechanisms of dinitrogen hydrogenation by two different complexes--[(eta(5)-C(5)Me(4)H)(2)Zr](2)(mu(2),eta(2),eta(2)-N(2)), synthesized by Chirik and co-workers [Nature 2004, 427, 527], and {[P(2)N(2)]Zr}(2)(mu(2),eta(2),eta(2)-N(2)), where P(2)N(2) = PhP(CH(2)SiMe(2)NSiMe(2)CH(2))(2)PPh, synthesized by Fryzuk and co-workers [Science 1997, 275, 1445]--are compared with density functional theory calculations. The former complex is experimentally known to be capable of adding more than one H(2) molecule to the side-on coordinated N(2) molecule, while the latter does not add more than one H(2). We have shown that the observed difference in the reactivity of these dizirconium complexes is caused by the fact that the former ligand environment is more rigid than the latter. As a result, the addition of the first H(2) molecule leads to two different products: a non-H-bridged intermediate for the Chirik-type complex and a H-bridged intermediate for the Fryzuk-type complex. The non-H-bridged intermediate requires a smaller energy barrier for the second H(2) addition than the H-bridged intermediate. We have also examined the effect of different numbers of methyl substituents in [(eta(5)-C(5)Me(n)H(5)(-)(n))(2)Zr](2)(mu(2),eta(2),eta(2)-N(2)) for n = 0, 4, and 5 (n = 5 is hypothetical) and [(eta(5)-C(5)H(2)-1,2,4-Me(3))(eta(5)-C(5)Me(5))(2)Zr](2)(mu(2),eta(2),eta(2)-N(2)) and have shown that all complexes of this type would follow a similar H(2) addition mechanism. We have also performed an extensive analysis on the factors (side-on coordination of N(2) to two Zr centers, availability of the frontier orbitals with appropriate symmetry, and inflexibility of the catalyst ligand environment) that are required for successful hydrogenation of the coordinated dinitrogen.