Geometric structure of ${\text{TiO}}_2\left(110\right)\left(1\times 1\right)$: Confirming experimental conclusions

Low-energy electron-diffraction and surface x-ray diffraction data acquired from ${\text{TiO}}_2\left(110\right)\left(1\times 1\right)$ are reanalyzed to confirm the integrity of the previously reported optimized geometries. This work is performed in response to ab initio density-functional theory calculations that suggest that the atomic displacements determined from low-energy electron-diffraction measurements may be compromised by the limited number of optimized atom positions. Performing structural optimizations as a function of depth into the selvedge, this present study validates the previous experimental structure determinations.

Figure 1

(Color online) Ball-and-stick models of ${\text{TiO}}_2\left(110\right)\left(1\times 1\right)$. Larger (smaller) spheres are oxygen (titanium) atoms. The numerical labeling of the atoms is to allow identification. Symmetry paired (equivalent) atoms are denoted by ${}^{\ast }$ $\left({}^{\prime }\right)$. (a) An example of the type of slab used by Thompson and Lewis for their ab initio calculations on ${\text{TiO}}_2\left(110\right)\left(1\times 1\right)$ (Refs. 7, 8). A five-trilayer slab is depicted. The upper and lower halves of the slab are indistinguishable, as indicated by the mirror plane. Trilayer units are picked out by use of alternate darker/lighter shading, along with dashed lines. (b) Atoms optimized in Ref. 3 during determination of ${\text{TiO}}_2\left(110\right)\left(1\times 1\right)$ geometry from LEED-IV data. (c) The layering scheme employed in the present study to investigate how the depth of the optimized selvedge impacts upon the LEED-IV/SXRD solutions.

Figure 2

(Color online) (a) Best fit $R_{\text{p}}$’s (LEED-IV) (solid circle markers) and ${\chi }^2$’s (SXRD) (solid square markers) are plotted as a function of the number of layers optimized. The layering scheme is illustrated in Fig. 1c. (b) Displacement of O(1) (bridging oxygen) and Ti(2) (fivefold titanium) also plotted as a function of the number optimized layers. These two atoms can be identified by reference to Fig. 1c. There are three plots for each atom, corresponding to the displacements obtained from LEED-IV (solid circle markers), SXRD (solid square markers), and ab initio DFT-GGA calculations (crosses) (Refs. 7, 8). To plot the latter on the same $x$ axis the near equivalence, in terms of adjustable atoms, of $\left(n+1\right)/2$ LEED-IV/SXRD layers and an ab initio $n$-trilayer slab was employed. For clarity, an upper $x$ axis showing the corresponding number of trilayers is included.