Ab initio reflectance difference spectra of the bare and adsorbate covered Cu(110) surfaces

The reflectance difference spectra of the bare Cu(110) surface, of the oxygen induced $(2\times 1)\mathrm{O}$ reconstruction, and of the carbon monoxide covered Cu(110) surface are calculated using density functional theory and the independent particle approximation. Generally, good agreement with experiment is found at energies below $2\mathrm{eV}$, where a resonance between two surface states dominates the spectrum for the bare surface. The resonance is progressively quenched from the bare surface, over the oxygen covered surface, to the CO covered surface. At higher energies, a rather deep minimum in the reflectance difference spectrum is calculated for all three surfaces, which agrees qualitatively with experiment, but details such as the shape and depth of the minimum are not in good agreement with experiment. We argue that a treatment beyond standard density functional theory is required at higher energies, in particular, for adsorbate covered surfaces. The calculated spectra and the surface band structures are carefully analyzed with respect to transitions between specific electronic states, confirming previous experimental and theoretical assignments. An essential result of the study is that the anisotropy of the intraband plasma frequency tensor (Drude-like term) is important and must be calculated on the same level of theory as the interband contributions to the dielectric function. Only then the results converge with increasing layer numbers.

Figure 1

Energy bands of the bare Cu(110) surface between the $\overline{\Gamma }$ and $\overline{Y}$ points for 23 and 24 layers. The energies are given with respect to the Fermi energy. Surface bands are indicated by filled circles at the $\overline{Y}$ point.

Figure 2

Reflectance difference spectrum for 23 and 24 layers (two upper panels) and the averaged RD spectrum obtained by averaging the results for 23, 24, and 25 layers as discussed in the text.

Figure 3

Real part of the surface dielectric anisotropy (SDA) for the 23 and 24 layer Cu(110) slabs. The thin line shows the SDA considering only interband contributions. The SDA arising from the anisotropic intraband term, whose magnitude is given by the intraband plasma frequency, is the negative of the curve shown with a dashed line. The SDA considering both interband and intraband contributions is plotted with a thick line.

Figure 4

Band structure of the bare 24 layer Cu(110) slab with important contributions marked by small squares. For explanation of the states, see the text.

Figure 5

Band structure of the $(2\times 1)\mathrm{O}$ and $(2\times 1)\mathrm{C}\mathrm{O}$ surfaces (12 layer slab). Because of the doubled cell size in the $\left[1\overline{1}0\right]$ direction, the Brillouin zone is folded back with respect to the Brillouin zone of the bare surface, and the number of bands is doubled.

Figure 6

RDS of the bare, of the oxygen, and of the carbon-monoxide-covered Cu(110) surface. The left panel shows the RD spectra calculated in this work, the right panel the experimentally measured spectra (Ref. 22). For the $(2\times 1)\mathrm{O}$ reconstruction, also the RD spectrum arising only from transitions in the vicinity of the $\overline{Y}$ point is shown using a dashed line.