We give a continuum description of the solvation of an electron in the image state of a metal surface by a layer of polar adsorbates. In the model, we account for the interaction of the dipole moment of the adsorbate with the electric field exerted by the electron, which is perpendicular to the surface. We also include the dipolar interactions between the adsorbates. With this simple model, it is easy to make an analysis of the self-trapping of electron. Depending upon the values of the parameters, the self-trapped state can have any arbitrary size. Also, there are regimes in which (1) there is no localized state, (2) a localized and delocalized state coexist, with the delocalized state being a saddle point on the potential energy surface, and the localized state a minimum and (3) both the states exist as stable minima, and there is a barrier between the two. In the second case, self-trapping would be a barrierless process while for the third, it would be an activated process. We find that our model can explain the salient features of the experimental results of Harris et al. [Science 297, 1163 (2002)]. At the parameter value required to fit the experimental data, self-trapping is barrierless.

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