We determine the stability and properties of interfaces of low-index Au surfaces adhered to TiO2(110), using density functional theory energy density calculations. We consider Au(100) and Au(111) epitaxies on rutile TiO2(110) surface, as observed in
experiments. For each epitaxy, we consider several different interfaces: Au(111)//TiO2(110) and Au(100)//TiO2(110), with and without bridging oxygen, Au(111) on 1x2 added-row TiO2(110) reconstruction, and Au(111) on a proposed 1x2 TiO reconstruction. The density functional theory energy density method computes the energy changes on each of the atoms while forming the interface, and evaluates the work of adhesion to determine the equilibrium interfacial structure.
We propose a method to decompose the total energy of a supercell containing defects into contributions of individual atoms, using the energy density formalism within density functional theory. The spatial energy density is unique up to a gauge transf
ormation, and we show that unique atomic energies can be calculated by integrating over Bader and charge-neutral volumes for each atom. Numerically, we implement the energy density method in the framework of the Vienna ab initio simulation package (VASP) for both norm-conserving and ultrasoft pseudopotentials and the projector augmented wave method, and use a weighted integration algorithm to integrate the volumes. The surface energies and point defect energies can be calculated by integrating the energy density over the surface region and the defect region, respectively. We compute energies for several surfaces and defects: the (110) surface energy of GaAs, the mono-vacancy formation energies of Si, the (100) surface energy of Au, and the interstitial formation energy of O in the hexagonal close-packed Ti crystal. The surface and defect energies calculated using our method agree with size-converged calculations of the difference between the total energies of the system with and without the defect. Moreover, the convergence of the defect energies with size can be found from a single calculation.
