We present a quantum dynamical study for the abstraction reaction of hydrogen and its isotope on Cu(111) surface by a four-dimensional planar model. The rigid surface corrugation has been explicitly treated. High vibrational and rotational excitation observed in our product-state distributions indicates that the reactions occur mainly via the Eley-Rideal mechanism as suggested earlier by experiments as well as the three-dimensional flat surface model. The four-dimensional planar model using a cut through the six-dimensional LEPS (London-Eyring-Polanyi-Sato) potential energy surface essentially reproduces the isotope effects observed in experiment in the energy distributions of the reaction product. The unreacted atoms are found either to bounce back from the surface or to diffuse on the surface as atoms. A significant concentration of diffusing atoms on the surface could result in an associative desorption pathway and contribute to the experimental measurement of HD formation.