Exact exchange plane-wave-pseudopotential calculations for slabs

Abstract

The exact exchange of density functional theory is applied to both free-standing graphene and a Si(111) slab, using the plane-wave pseudopotential (PWPP) approach and a periodic repetition of the supercell containing the slab. It is shown that (i) PWPP calculations with exact exchange for slabs in supercell geometry are basically feasible, (ii) the width of the vacuum required for a decoupling of the slabs is only moderately larger than in the case of the local-density approximation, and (iii) the resulting exchange potential vx shows an extended region, both far outside the surface of the slab and far from the middle of the vacuum region between the slabs, in which vx behaves as -e(2)/z, provided the width of the vacuum is chosen sufficiently large. This last result is corroborated by an analytical analysis of periodically repeated jellium slabs. The intermediate -e(2)/z behavior of vx can be used for an absolute normalization of vx and the total Kohn-Sham potential, which, in turn, allows the determination of the work function.

Approximations to the exact exchange potential: KLI versus semilocal

“…However, comparisons between the EXX-OEP and the KLI approximation (EXX-KLI in the following) concern mainly atoms and light molecules/clusters 8,[15][16][17][34][35][36][37][38][39][40][41][42][43][44] and only a few such comparisons were done for periodic systems. 8,11,45,46 From most of these studies, it was concluded that EXX-KLI is a good approximation to EXX-OEP, however, in Refs. 8 and 45 Engel pointed out that in bulk Si and FeO the EXX-KLI potential can not fully reproduce the aspherical features around the atoms seen in the EXX-OEP.…”

Accurate ionization potential of semiconductors from efficient density functional calculations

“…We note in Ref. 16 the OEP was generated by supercell. Limited by the low efficiency of the supercell method, the sheet separation is only 14 Bohr which is definitely not sufficient to achieve the asymptotic value of the OEP at the vacuum edge.…”

“…This is because the wave functions are mainly bound to the slab while less exposed to the vacuum or the asymptotic region. At this point, it is necessary to point out that the exact asymptotic behavior of v xc for solid surface is still unresolved 12,16 . In BJ06c, the asymptotic behav-ior −1/z + C of the exchange part is exact according to the form found in Ref.…”

Asymptotic Behavior of Exact Exchange for Slabs: Beyond the Leading Order

“…This latter result is of particular interest, since e x defines the Slater potential, v Slater = 2e x /n, which is the core contribution to the often used Krieger-Li-Iafrate approximation [44] for the exact v x and its refinement, the localized Hartree-Fock/common energy denominator approximation [45,46]. Both results have subsequently been generalized [34,35] to non-jellium slabs, for which one has a Bravais lattice in the xy-directions,…”