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.

Figure 1

The band structure of a hydrogen saturated diamond (001) slab, without (a) and with (b)–(d) an $N_C{V}_C$ center in the middle of the slab. The neutral case is shown in (b), while (c) and (d) show the charged case without and with SCPC correction, respectively. Solid and dashed lines correspond to spin-up and spin-down states, respectively. Green lines denote defect-related states and the red line is the Fermi level.

Figure 2

Planar average of the extra charge and of the electrostatic potential along the surface normal for an ${\mathrm{O}}_2(-)$ molecule on the surface of an anatase-${\mathrm{TiO}}_2$ (001) slab, without (a) and with (b) the SCPC correction. In (b) the green curve shows the corrective potential and the inset in (b) shows a magnification of the Coulomb-tail due to the negative charge on ${\mathrm{O}}_2$, which is not removed by the correction.