Abstract: The interactions of hydrogen molecules (H2) and the Cu (111) surface have been studied by using density functional theory based first-principles calculations. The results show that the dissociation of H₂ depends mainly on the initial distance from H₂ to the surface (h_H) and the initial H₂ configurations. The H₂ molecules of vertical adsorption on Cu (111) are not dissociated for the initial h_H of 0.3-4.0 Å, and the undissociated H₂ is physically adsorbed on the Cu (111) surface. When H₂ molecules are adsorbed on Cu (111) surface in parallel, some of the H₂ are dissociated into two hydrogen atoms, which occupy hcp and fcc sites and form stable chemisorption on the Cu (111) surface. The critical distance of H₂ dissociation at bri sites is 1.35 Å for parallel adsorption along the211 direction and 0.65-0.86 Å for other cases.