An algebraic variational approach to dissociative adsorption of a diatomic molecule on a smooth metal surface

A general theoretical treatment employing a time-independent algebraic variational method (S-matrix Kohn variational method) for dissociative adsorption of a diatomic molecule on a smooth metal surface is presented. The time-independent scattering treatment using the S-matrix Kohn variational method naturally enables one to obtain accurate state-to-state reaction probabilities for dissociative adsorption of molecules on surfaces. In this paper, the S-matrix Kohn variational method is adapted to the 3D dissociative adsorption of H₂ on Ni(100) surface treated as a flat surface, and the state-to-state transition probabilities are obtained. The dependence of the dissociation probabilities on the initial rovibrational state of H ₂(vjm) is examined. As a result of flat surface approximation, which conserves the rotation quantum number j_z=m, the exchange symmetry of H₂ has an important consequence on the vibrations of the adsorbates. Specially if the rotational state of H₂ satisfies the condition j+m=odd, the vibrational quantum number of two adsorbed hydrogen atoms must be different. The orientational effect of rotation is such that the in-plane rotation (m=j) is more favorable for molecular dissociation on surface than the out-of-plane rotation (m=0).