Structural and energetic properties of Ir₄H₂ have been determined by applying a relativistic density functional method. As previously obtained for Ir₄H, terminal coordination of H ligands is preferred, in contrast to some other transition metals. Square-planar Ir₄ isomers with an H binding energy of up to 318 kJ mol⁻¹ per atom were determined as the most stable structures of Ir₄H₂. Isomers with a tetrahedral or butterfly structure of the metal framework exhibit average H atom binding energies of up to ∼300 kJ mol⁻¹. For all three types of isomers, a surprisingly large number of stable minima was identified. Unexpectedly, structural as well as energetic properties of Ir₄H₂ complexes are very similar to Ir₄H. Thus binding of an H atom to Ir₄ is only slightly affected by the presence of a second H ligand. In all cases examined, the reaction H₂ + Ir₄→ H₂Ir₄ was found to be exothermic with reaction energies of up to 170 kJ mol⁻¹.