Theoretical determination of work functions and adsorption energies of atoms on metal surfaces from small-cluster calculations: A local-spin-density approach

Some results of ionization-potential, work-function, and binding-energy calculations are presented for atomic hydrogen adsorbed on small clusters of transition metals. All electronic calculations are made by using a linear combination of Gaussian-type orbitals (LCGTO) model-potential (MP) local-spin-density (LSD) method. Three metals are considered: Ag, Pd, and Ni. For the nickel, a nonvanishing spin polarization is taken into account. Size effects are analyzed and it is shown that it is possible to reduce them considerably. We show that the work function Φ may be obtained easily from a small-cluster calculation by using the derivative of the cluster energy with respect to the number of electrons; in this way one eliminates the relaxation effects of the electronic distribution and the nonzero derivative of energy with respect to the magnetic moment in a finite system. Furthermore, we define a new scheme to calculate the binding energy ${\mathit{E}}_{\mathit{M}\mathrm{-}\mathrm{H}}$ of hydrogen on transition metals M. More precisely, the electron and proton contributions are treated separately. The electron contribution is the work function in the limit of zero coverage of the surface and includes, by this route, the effect of delocalization of the electrons in the solid. Then the binding energy of the proton is directly obtained from a small-cluster calculation because of the localized character of its interaction with the solid. Particular attention is paid to the case of nickel where the size effects, analyzed on the basis of the ionization potential, are compared to the recent experimental results of Parks et al. The agreement, quite satisfactory, shows that the significant size effects observed in clusterlike calculations are not due to the LSD approximation. Finally, our results from indirect calculations for Φ and ${\mathit{E}}_{\mathit{M}\mathrm{-}\mathrm{H}}$ compare well with experimental results for infinite metals.