Modeling the structure and electronic properties of $\mathrm{Ti}{\mathrm{O}}_2$ nanoparticles

A self-consistent tight-binding method and density functional theory were used to study structures and electronic properties of anatase nanoparticles. Full geometry optimization resulted in both surface relaxation and a slight overall contraction of the nanoparticles. Analyzing electronic properties using electron localization function and Mulliken populations, we found nonbonding electrons at the edges and corners of the nanoparticle. The results of tight-binding and density functional theory calculations are in good agreement, suggesting the tight-binding scheme to be a useful tool for studies of larger nanoparticles in the range of hundreds to thousands of atoms. The self-consistent tight-binding results on nanoparticles of sizes up to 1365 atoms and some structural, electronic, and energetic trends as a function of nanoparticle size are also reported.

Figure 1

(Color) The anatase bipyramidal nanocrystal before (left) and after (right) the relaxation, viewed from the [001] direction (top) and [100] direction (bottom).

Figure 2

(Color) (a) The ECD through the central plane of the final relaxed anatase nanoparticle. The localization of the ECD around the Ti (blue) and O (red) atoms indicates a high ionic character. (b) The ELF through the central plane of the final relaxed anatase nanoparticle. The colored plumes of the ELF indicate the presence of nonbonding electrons.

Figure 3

(Color) Iso-surface applied at $l\left(r\right)=0.2$ (left), $l\left(r\right)=0.5$ (center) and $l\left(r\right)=0.8$ (right) of the ELF for the relaxed 105 atom anatase nanoparticle.

Figure 4

(Color) SCTB relaxed structures of 99, 105, 417, 453, 495, and 1365 atom nanoparticles.

Figure 5

Radial distribution functions for (a) relaxed SCTB structure of 105 atom nanoparticle and relaxed DFT structure of 105 atom nanoparticle, (b) relaxed SCTB structures of 417, 453, 495, and 1365 atom nanoparticles and bulk anatase. The radial distribution functions were obtained by Gaussian broadening (standard deviation $\sigma =0.1\mathrm{\AA })$ of discrete interatomic distance distributions with the appropriate normalization factors.

Figure 6

(Color) Excess charge relative to bulk for 105 (left) and 1365 (right) atom nanoparticles from SCTB calculations. Red is more positive charge and blue is more negative charge.