Efficient method for the simulation of STM images. II. Application to clean Rh(111) andRh(111)+c(4×2)−2S

We apply our recently developed Green-function formalism for the simulation of scanning tunneling microscopy (STM) images to the clean Rh(111) and the $\mathrm{Rh}\mathrm{}\left(111\right)+c(4\mathrm{}\times 2)-2\mathrm{S}$ systems. The former represents a test case in order to study the adequacy of the extended Hückel theory (EHT) as an approximation to the Hamiltonian matrix elements of the entire system. It is shown that, via a suitable parametrization of the atomic-orbital basis set, the EHT provides a reasonable description of the electronic structure of the sample and the tip, together with the interactions at the STM interface. When the same parametrization scheme is applied to the $\mathrm{Rh}\mathrm{}\left(111\right)+c(4\mathrm{}\times 2)-2\mathrm{S}$ system, we find a good agreement with the experimental images by considering a Pt tip with its apex terminated in a Pt or S atom. More specifically, the two inequivalent maxima per unit cell that appear in the images are unambiguously assigned to a S atom adsorbed at the hcp site (brightest maximum) and to another S atom at the fcc site. Furthermore, the simulations for each tip termination can be associated to two different types of experimental images which could be acquired in a reproducible way. At the same time, and after a detailed study on the relevance of most of the parameters involved in the calculation, some general criteria for the estimation of their value, prior to the STM calculation, are established. Finally, an analysis of the tunneling current on the Rh(111) system allows us to identify the $\mathrm{Rh}-d_{z^2}$ orbitals at the surface as the main states responsible for the atomic resolution. It is also found that the most relevant probing orbitals at the tip apex are those with axial symmetry along the surface normal; for the S ended tip, it is the S-$p_z$ orbital which dominates by far the current, whereas, for the Pt-ended tip, first the Pt-$s$ and next the $-d_{z^2}$ provide the major contributions. The better resolution obtained with the former tip is a consequence of the different levels of localization of these probing orbitals. A similar analysis applied to the $\mathrm{Rh}\mathrm{}\left(111\right)+c(4\mathrm{}\times 2)-2\mathrm{S}$ system explains the tip-dependent features in the simulated images, again through the higher localization of the tip $\mathrm{S}{-p}_z$ orbital with respect to the Pt-$s$ orbital, and the simultaneous interaction of these states with the $p_z$ orbitals of the S atoms at the surface. The inequivalence between the two S maxima in the unit cell, on the other hand, arises as a consequence of a better coupling of the substrate to the S-$p_z$ orbitals when the adsorbate is at the hcp site than when it is at the fcc site.