Self-Consistent Potential Correction for Charged Periodic Systems

Abstract

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.

Activity and Mechanism Mapping of Photocatalytic NO2 Conversion on the Anatase TiO2(101) Surface

“…40 Note that in charged slabs sometimes charge spill-out occurs into the vacuum if the electrostatic potential of the slab is not corrected selfconsistently. 41 In the cases studied here this did not happen, and tests with the new self-consistent potential correction (SCPC) method 41 have total energy corrections very close to the SLABCC results (see Table S2 in the Supporting Information).…”

“…In these cases, the total energies were corrected a posteriori for the spurious interactions between the repeated images, applying the method of Komsa and Pasquarello, as implemented in the SLABCC code . Note that in charged slabs sometimes charge spill-out occurs into the vacuum if the electrostatic potential of the slab is not corrected self-consistently . In the cases studied here this did not happen, and tests with the new self-consistent potential correction (SCPC) method have total energy corrections very close to the SLABCC results (see Table S2 in the Supporting Information).…”

“…38 In this Letter, we apply an efficient density functional (appropriately correcting the band gap and localization error) 39 and charge correction schemes recently developed by us. 40,41 Using the methods described above, we studied the complex reaction mechanism of deNO 2 in the presence of H 2 O on a set of active sites, both on a perfect and on a defective anatase TiO 2 (101) surface, assuming both dark and UV-illuminated conditions. It was found that the deNO 2 activity trend is, indeed, significantly different from a conventional volcano plot, and the variety of reaction pathways results in multiple activity optima.…”

“…The results can be quite inaccurate if standard local or semilocal implementations of density functional theory (DFT) are used (because those have a strong tendency for charge delocalization) or if the artifacts caused by the repetition of the charge in a periodic (supercell) model of the surface are not corrected appropriately . In this Letter, we apply an efficient density functional (appropriately correcting the band gap and localization error) and charge correction schemes recently developed by us. , …”

Strain Engineering to Release Trapped Hole Carriers in p-Type Haeckelite GaN

“…The strength parameter of the hole state potential is set to λ hs = 3.0 eV, which satisfies the generalized Koopmans condition for the localized in-gap state of Mg and Be impurities in 4|8-GaN. The total energy of negatively charged systems in the periodic boundary condition was corrected by an SCPC correction . The dielectric constant of 4|8-GaN for the SCPC correction was set to 7.0 as obtained by density functional perturbation theory (DFPT) …”