Ab initio investigations at the coupled-cluster single double (triple) [CCSD(T)] and MRCISD level with augmented triple and quadruple zeta basis sets have identified various stationary points on the Li-/(H-2)(n),n=1-3, hypersurfaces. The electrostatic complexes, Li-(H-2)(n), are very weakly bound (D-e< 0.25 kcal/mol with respect to H-2 loss) and H-2/H-2 interactions play a contributing role in determining the equilibrium structures within the electrostatic constraint of a linear or near-linear Li--H-H orientation. The covalent molecular ion, LiH2-, is found to have a linear centrosymmetric structure and to be bound with respect to Li-+H-2 in agreement with previous calculations. The interaction of LiH2- with additional H-2 is purely electrostatic but with a D-e larger than those of the Li-(H-2)(n) complexes. LiH2-(H-2) is found to have a linear equilibrium structure and LiH2-(H-2)(2) is found to have two almost isoenergetic structures: linear with an H-2 on either end of the LiH2-, and C-2v with both H-2 on the same end of the LiH2-. Of particular interest is the dramatic change in the nature of the transition state for LiH2- production depending on the number of H-2 molecules present. For n=1, the reaction proceeds through a conical intersection between the lowest energy B-1(2) and (1)A(1) electronic surfaces in C-2v symmetry. For n=2, the reaction occurs on a single surface in a pericyclic mechanism through a transition state consisting of a planar five-member ring where simultaneously two H-2 bonds are broken while two LiH bonds and one new H-2 bond are formed. For n=3, the reaction proceeds by direct insertion of Li- into one of the H-2 molecules with the two additional H-2 molecules providing substantial stabilization of the transition state by taking on part of the negative charge in a weakly covalent interaction. The results are discussed in comparison to the isoelectronic B+/(H-2)(n) systems where significant sigma bond activation through a cooperative interaction mechanism has been identified recently.