Dependence on Adsorption Energy

Spohr investigated the dependence of the shape of the oxygen density profiles on the adsorption energy [56]. The model contains a simple scaling parameter. Do, that determines the adsorption energy (see Eq. (7) and Eq. (8)). 

The density profiles obtained from atomic models (platinum [49] and rigid mercury surfaces [40]), where water-metal interactions are described by pairwise additive atomatom interaction potentials, are similar in shape. Height and width are correlated with the depth and force constant of the interaction potential. A similar correlation between peak height and interaction energy holds for water near a variety of different smooth model surfaces (see Ref. 139 and references therein). 

In experimental studies the liquid mercury electrode has been prototypical for a long time. Modeling the liquid mercury electrode is complicated by the fact that knowledge of mercury-mercury interactions is required. The liquid mercury/liquid water interface was investigated by Heinzinger and coworkers [78, 81] using a pseudopotential ansatz. 

The width is larger than the width of the oxygen and hydrogen peaks near the solid surface. Consequently, in order to compare the liquid/liquid with the liquid/ solid interface, the density distribution near the rigid surface can be convoluted with a width function w(z) due to the mercury motion according to 

The width function is the normalized shape of the first mercury peak in the density profile, approximated as a Gaussian distribution of width r = 1.3 A 

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Dependence on Adsorption Energy. The models described in the previous sections have been obtained either by adjusting an empirical potential function to available experimental data like adsorption energies and/or adsorbate frequencies, or by fitting of some set of analytical potential functions to semiempirical or ab initio quantum chemical calculations. Because the metal atom clusters in these calculations are small, and because of the semiempirical nature [35] or the neglect of electron correlation in the Hartree-Fock calculations [36] the interaction potentials can be regarded, at best, semiquantitatively... 

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