Self-Consistent Model of Hydrogen Chemisorption

Abstract

The chemisorption of a hydrogen atom on a transition-metal surface is treated theoretically on the basis of the Anderson Hamiltonian in Hartree-Fock approximation, which includes the interelectronic interaction within the $1s$ orbital. One-electron theory is shown to be inadequate for this problem. The localized states which may occur are discussed. A simple expression for the chemisorption energy $\ensuremath{\Delta}E$ is obtained, and a variational method is given for obtaining its self-consistent value. The metal eigenfunctions enter $\ensuremath{\Delta}E$ only through a function $\ensuremath{\Delta}(\ensuremath{\epsilon})$, and the foregoing results are exemplified and applied when this function is semielliptical. When the band is half-filled, a single analytic formula for the one-electron part of $\ensuremath{\Delta}E$ is obtained, in accord with the Kohn-Majumdar theorem. With some further assumptions, $\ensuremath{\Delta}E$ and the charge on the atom are calculated for adsorption on Ti, Cr, Ni, and Cu. The values of the hopping integral between the $1s$ orbital and a neighboring metal $d$ orbital required to fit the experimental $\ensuremath{\Delta}E$ are found to be similar and are reasonable. The correct prediction that ${|\ensuremath{\Delta}E|}_{\mathrm{Ni}}>{|\ensuremath{\Delta}E|}_{\mathrm{Cu}}$ is believed to be significant. A suggestive correlation is found between observations of catalytic ortho-para hydrogen interconversion on Pd-Au alloys and a rigidband calculation of $\ensuremath{\Delta}E$.