STM simulations

Keywords Atomic scale characterization surface structure epoxidation reaction 111 cleaved silver surface oxide STM simulations DFT slab calculations ab initio phase diagram free energy non-stoichiometry oxygen adatoms site specificity epoxidation mechanism catalytic reactivity oxametallacycle intermediate transition state catalytic cycle. 

STM simulations. STM image simulations were performed with the GREEN code [31,32]. The STM current is evaluated within a one-electron... 

Fig. 13. Structures (left) and STM simulations (right) for oxide overlayers with different stoichiometry on Ag lll. The O coverage in each overlayer is given on the far left and the stoichiometry on the far right. Oxygen (silver) atoms appear as dark grey (light grey) balls. The black squares on the right depict the location of Ag adatoms responsible for the bright features in the STM simulations. The extra O atoms, which are in excess of those in the reference Agx gO oxide (top), are circled in black.

If the barrier energy is lower than this critical value, rotational motion will be fast at 6 K and the STM image will be smeared out and STM simulations will need to include time averaging. If the barrier is larger, then the image may have threefold or sixfold symmetry depending on the energies of the local minima. 

We shall initially dispense with the fullerene moleeule itself because of the compli-eated nature of the JT effects that are possible in this large and highly symmetric molecule (see Sect. 5.2.1). Instead, we eonsider a simple (gi e JT system exemplified by a hypothetical triatomic molecule of the form X3 of the kind exemplifled by Na3, i.e. one constructed from atoms whose valenee electrons reside in i-type atomic orbitals. The molecule is adsorbed onto a similarly hypothetieal, atomically flat surface so that each atom is equidistant from the surface. The surfaee, therefore, is merely a platform to support the molecule so that it can be imaged via STM. In this way, we attempt to isolate, using simple STM simulations, the features of the image that can be attributed solely to the JT nature of the molecule. 

Fig. 20 STM simulation of an X3 molecule subject to a strong JT effect (to the extent that each configuration has an internal angle of 110°)...

Fig. 21 STM simulations for systems subject to a static vs. dynamic JT effect. The top row corresponds to the excited state and the bottom to the ground state. In (a), infinitely strong coupling locks the molecule into one particular well. Finite but strong coupling (so that the system jumps between three wells) is shown in (b). Further reduction in localisation leads to essentially free pseudorotation, producing the time-averaged images in (c)...

The overall conclusion is that it is possible to generate STM simulations of features that have been found in real images starting from molecules that are Dxh, Dsj or Dj,d distorted. If a particular type of distortion is chosen, then there are always several ways in which that distortion can be applied to Ceo- One cannot simply pick one particular distorted form rather, it is necessary to look for other forms that are equal in energy (even if adsorbed onto a surface) and to then account for interconversion by hopping or pseudorotation, as this is likely to be fast on the STM time-scale. 

Fig. 23 Plot to show the electronic orbital associated with a Dsd minimum (well C). Light-grey lobes represent wave functions with a positive polarity. The adjacent STM simulations show the images expected for the different cases discussed in the text, as viewed along the z-axis...

In what follows, we present our results on highly resolved STM images of clean surfaces of icosahedral Al7oPd2iMn9, which we compare with STM simulations on the model In the STM simulations we consider the same topographic... 

The STM simulations are based on a simplified atomic charge model [31], in which a spherical shape of the valence charge density is assumed for the atoms. These spherical shells of fixed radius (solid sphere) are superimposed in three dimensions for all atomic positions considered in the simulation. From this superposition the z(x,y) (z parallel to the plane normal) contour of the uppermost shells is... 

Figure 12-16. left) Experimental STM image of Si(lll) 7x7 reconstruction witii U =1.6V sample bias, (right) Solid sphere STM simulation using the structure model of Si 7x7 reconstruction by... 

---