Reconstruction of charged surfaces: General trends and a case study of Pt(110) and Au(110)

The stability of missing-row reconstructions of (110) surfaces with respect to surface charging has been investigated using ab initio theory, taking Pt and Au as representative systems. A thermodynamic formulation is derived to compare the relative stability of charged surfaces either in constant-potential or constant-charge mode. By generalizing Koopmans' theorem to charged metallic surfaces, we obtain an expression for the surface (excess) energy as a function of charge (or potential) in terms of the neutral surface energy, work function, and the position of the image plane. A surface is shown to reconstruct in constant-charge mode if and only if it reconstructs in constant-potential mode. We next address the question of whether a positive (negative) surface charge can lift (induce) the reconstruction, as suggested in the literature. This turns out not to be the case. Instead the following consistent picture arises: at small surface charges, the effect of the charge follows the difference of the work functions; i.e., positive charge favors a surface having a smaller work function and vice versa. Larger charges, either positive or negative, tend to stabilize the reconstructed surface or, more generally, the 1xr reconstruction with larger r. The latter essentially results in that the 1x2 reconstruction in either Pt or Au is never lifted in our study, although the 1x3 surface in Au eventually becomes more stable.