Hydrogenation of olefins catalyzed by a ruthenium II complex, the RuH2(η2-H2)2(P(C6H11)3)2 have been studied using DFT/B3LYP method. The establishment of agostic Ru-C bonds followed by the migration of hydrogen atoms from one cyclohexyl of phosphine ligand is the main particularity of this reaction. Transition states associated with the latter migrations were determined. Each one is trizonal and involves three different areas and ten active atoms. Intrinsic Reaction Coordinate (IRC) calculations allowed following their movements during this reaction. Energy profiles confirm the simultaneous movement of all these active atoms. Molecular orbitals of all involved species were analyzed and related to ruthenium atomic orbitals. Obtained results highlight the catalytic effect of Ru atom able, thanks to its versatility, to redistribute its AOs and to control the exchange process of concerned ligands. Those transition states are currently among the most complicated ones to be calculated up today.