When Langmuir Is Too Simple: ${\mathrm{H}}_2$ Dissociation on Pd(111) at High Coverage

Recent experiments of ${\mathrm{H}}_2$ adsorption on Pd(111) [T. Mitsui et al., Nature (London) 422, 705 (2003)] have questioned the classical Langmuir picture of second order adsorption kinetics at high surface coverage requiring pairs of empty sites for the dissociative chemisorption. Experiments find that at least three empty sites are needed. Through density functional theory, we find that ${\mathrm{H}}_2$ dissociation is favored on ensembles of sites that involve a Pd atom with no direct interaction with adsorbed hydrogen. Such active sites are formed by aggregation of at least 3 H-free sites revealing the complex structure of the “active sites.”

Figure 1

Surface models of the H-covered Pd(111) surface with different H-vacancy densities: (a) fully hydrogenated surface; (b) single vacancy ($1V$); (c) divacancy ($2V$); (d) open trimer configuration ($3V_{\mathrm{O}}$); (e) closed trimer centered around a threefold hollow site ($3V_{\mathrm{H}}$); and (f) closed trimer centered around a Pd atom ($3V_T$). Palladium atoms are represented by large circles, hydrogen atoms by filled smaller circles and vacancies by small gray (red) circles.

Figure 2

Energy profiles for the fcc-fcc hydrogen dissociation pathway at different vacancy structures. The differential heat of adsorption, computed as $d{E}_{\mathrm{a}\mathrm{d}\mathrm{s}}=E_{\mathrm{H}/\mathrm{P}\mathrm{d}}(NV-2)\mathrm{\text{−}}{E}_{\mathrm{H}2}\mathrm{\text{−}}{E}_{\mathrm{H}/\mathrm{P}\mathrm{d}}(NV)$, is plotted as a function of distance to the Pd surface. The molecular axis is parallel to the surface and the 2 H atoms point towards neighboring fcc sites. The gas-phase to chemisorption energy barrier $E_a{}^{\prime }$ is shown for the clean surface case.

Figure 3

Dependence of the activation energy$E_a{}^{\prime }$ on the position of the metal $d$-band center with respect to the Fermi level. Energies are referred to the gas-phase ${\mathrm{H}}_2$.