Four-dimensional quantum and two-dimensional classical mechanical study of molecule–surface interactions

The collision of a hydrogen molecule with a copper surface has been studied using a semiclassical theory. The four molecular coordinates, the distance from the surface, the vibrational coordinate, and the polar angles, are treated quantum mechanically using a grid method. The kinetic energy is evaluated by a fast Fourier transformation (FFT) technique and the wave function propagated by a Lanczos iterative method. Two translational degrees of freedom for motion at the lattice are treated classically, whereas the normal modes of the solid are quantized using a quantum boson approach. The present calculation indicates that rotational state distributions of the scattered molecule and dissociative chemisorption of the diatom on the metal surface are significantly affected by the phonon coupling.