Approximations to the exact exchange potential: KLI versus semilocal

Abstract

In the search for an accurate and computationally efficient approximation to the exact exchange potential of Kohn-Sham density functional theory, we recently compared various semilocal exchange potentials to the exact one [F. Tran et al., Phys. Rev. B 91, 165121 (2015)]. It was concluded that the Becke-Johnson (BJ) potential is a very good starting point, but requires the use of empirical parameters to obtain good agreement with the exact exchange potential. In the present work, we extend the comparison by considering the Krieger-Li-Iafrate (KLI) approximation, which is a beyond-semilocal approximation. It is shown that overall the KLI and BJ-based potentials are the most reliable approximations to the exact exchange potential, however, sizeable differences, especially for the antiferromagnetic transition-metal oxides, can be obtained.

Importance of the Kinetic Energy Density for Band Gap Calculations in Solids with Density Functional Theory

“…Our results strongly support the use of the kinetic energy density in the design of KS potentials for band gap calculations or to approximate the exact KS potential as done in our previous works. 69 , 73 To finish, we should also mention that nonmultiplicative MGGA potentials, which include the derivative discontinuity Δ xc in the energy spectrum, are extremely promising for band gap calculations; however, at the moment no such potential leading to satisfying results has been proposed. 12 Therefore, at the moment the mBJLDA potential represents the best alternative to the much more expensive hybrid or GW methods.…”

Challenges for semilocal density functionals with asymptotically nonvanishing potentials

“…However, as discussed in past works that go back to the original AK13 paper, the accuracy of total energies from this functional is not as good [40,45,55,70] as from established GGAs, e.g., the one of Perdew, Burke, and Ernzerhof (PBE) [71]. Instead, one finds that the energetics displayed upon structural relaxation are distorted beyond what seems reasonable even for an exchange-only functional (see Ref.…”

“…Attempts have been made to model such features directly into semilocal xc potentials [34][35][36][37][38][39][40][41][42][43][44][45], partially also with an additional (nonlocal) eigenvalue dependence, e.g., as done by Gritsenko et al (GLLB) [46] and Kuisma et al [47].…”

Orbital nodal surfaces: Topological challenges for density functionals

“…However, while the low computational cost of semilocal functionals has very much contributed to the success of DFT because it enables access to large systems of practical relevance, the functional derivatives of typical semilocal functionals, i.e., their corresponding xc potentials, miss important features of the exact xc potential, in particular discontinuities [3,4] and step structures [5][6][7][8][9] that are relevant, e.g., in charge-transfer situations [10][11][12] and ionization processes [5,[13][14][15][16]. Many attempts have been made to incorporate some of the missing features into semilocal DFT [17][18][19][20][21][22][23][24][25][26][27]. In recent years, it was the Becke-Johnson (BJ) model potential [28] in particular that sparked interest in this respect [22,[29][30][31][32][33][34][35].…”