First-Principles Study on the Surface Energies of Rutile TiO<sub>2</sub>(110) vs (011)-2×1 Surfaces

First-principles calculations based on density functional theory have been used to study the surface energies of the rutile TiO 2 (110) and (011)-2×1 surfaces. We investigate the effect of the slab thickness on the predicted surface energy and find that slab thicknesses of at least 5 layers are necessary to converge the surface energy to within 0.01 J/m 2 for both rutile TiO 2 (110) and (011)-2×1 surfaces. For the rutile TiO 2 (110) surface, it should be noted that the surface energy oscillates with the number of layers (odd-even oscillations). However, the calculated surface energies of the rutile TiO 2 (011)-2×1 surface are closer to the linear relationship for the number of layers larger than 4. Finally, our calculated results indicate that the rutile TiO 2 (011)-2×1 surface has a significantly higher surface energy than the rutile TiO 2 (110) surface.