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The preferential adsorption sites, bond lengths, and vibration frequencies for H on the Pd (001) surface are determined by use of the ab initio pseudopotential local-orbital method. From the calculated total energies we derive a coverage-dependent absorption energy in very good agreement with experiment. We establish that at low coverages (θ≤ 1), H occupies fourfold hollow sites. At higher coverages (1< θ≤ 2), islands of bridge-bonded H (local coverage θ= 2) are predicted to coexist with regions of H in hollow sites.