Energy of Step Defects on the TiO2 Rutile (110) Surface: An ab initio DFT Methodology

We present a novel methodology for dealing with quantum size effects (QSE) when calculating the energy per unit length and step-step interaction energy of atomic step defects on crystalline solid surfaces using atomistic slab models. We apply it to the TiO2 rutile (110) surface using density functional theory (DFT) for which it is well-known that surface energies converge in a slow and oscillatory manner with increasing slab size. This makes it difficult to reliably calculate step energies because they are very sensitive to supercell surface energies, and yet the surface energies depend sensitively on the choice of slab chemical formula due to the dominance of QSE at computationally practical slab sizes. The commonly used method of calculating surface energies by taking the intercept of a best fit line of total supercell energies against slab size breaks down and becomes highly unreliable for such systems. Our systematic approach, which can be applied to any crystalline surface, bypasses such statistical estimation techniques and cross checks and makes robust what is otherwise a very unreliable process of extracting the energies of steps. We use the calculated step energies to predict island shapes on rutile (110) which compare favorably with published scanning tunneling microscopy (STM) images.