Self-Consistent Potential Correction for Charged Periodic Systems.

Supercell models are often used to calculate the electronic structure of local deviations from the ideal periodicity in the bulk or on the surface of a crystal or in wires. When the defect or adsorbent is charged, a jellium counter charge is applied to maintain overall neutrality, but the interaction of the artificially repeated charges has to be corrected, both in the total energy and in the one-electron eigenvalues and eigenstates. This becomes paramount in slab or wire calculations, where the jellium counter charge may induce spurious states in the vacuum. We present here a self-consistent potential correction scheme and provide successful tests of it for bulk and slab calculations.

Application of the Lany-Zunger polaron correction for calculating surface charge trapping.

Defect calculations, using density functional theory in a local or semi-local approximation, in transition metal oxides are severely handicapped by the electron self-interaction error. The underestimation of the band gap may cause incorrect occupation of defect states and wrong formation energies, and the underestimated localization of the states disfavors the formation of small polarons. These problems can be avoided by using higher level approximations (GW or a correctly chosen hybrid functional), but those methods are computationally too expensive to be used for calculating surface defects in a periodic slab model. Lany and Zunger have suggested a convenient (low-cost) solution for solving the band-gap and charge delocalization problem, by applying a correction scheme to the standard local or semi-local approximations. Most importantly, the linearity of the total energy as a function of the fractional occupation numbers, is restored, leading to the fulfillment of the generalized Koopmans' theorem. The method works well in the bulk but, as we show here, it is not accurate on the surface due to the different screening environment. We also show that by making the atom- and angular-momentum dependent parameters of the Lany-Zunger polaron-correction also coordination dependent, it is possible to correctly describe charge trapping in small polaron states on the anatase (1 0 1) and rutile (1 1 0) surfaces at a low computational cost.