Density-functional theory calculations based on plane-wave expansion and pseudopotential treatment were carried out for atomic hydrogen on a rigid Cu(100) surface. A global potential energy surface was then obtained by using a three-dimensional spline interpolation. It is found that the minimum of the potential is located at the fourfold hollow site with a diffusion barrier of 88 meV at the bridge site. The vibrational states of atomic hydrogen and deuterium on the Cu(100) surface were calculated on the potential surface. Our calculations show that the vibrational states A(1)(0), A(1)(1), E-1, and B-2(1) of H/Cu(100) exhibit strong localized character and very narrow band widths, whereas other excited vibrational states have considerable delocalized character and broad band widths. The vibrational frequency of 71.2 (51.5) meV for H(D) in the perpendicular direction obtained in this study is in good agreement with the experimentally observed value of 70 (52) meV [Surf. Sci. 248, 35 (1991)]. (C) 2004 American Institute of Physics.