Hydrogen tunneling on a metal surface: A density-functional study of H and D atoms on Cu(0Â 0Â 1)

Using density-functional calculations, we present a theoretical investigation of the adsorption, self-trapping and diffusion of atomic hydrogen on Cu(0 0 1). The hydrogen motion is treated quantum-mechanically, by mapping out three-dimensional potential energy surfaces and solving a Schrödinger equation for H and D numerically. The ground-state energy levels and tunneling matrix elements are used to calculate the hop rate of hydrogen over a wide range of temperatures. We demonstrate how to include couplings of a tunneling adsorbate to the electronic and lattice degrees of freedom of the substrate on a first-principles basis. The results agree well with scanning tunneling microscopy data by Lauhon and Ho.