Local exact exchange potentials within the all-electron FLAPW method and a comparison with pseudopotential results

Abstract

We present a general numerical approach to construct local Kohn-Sham potentials from orbital-dependent functionals within the all-electron full-potential linearized augmented-plane-wave (FLAPW) method, in which core and valence electrons are treated on an equal footing. As a practical example, we present a treatment of the orbital-dependent exact-exchange (EXX) energy and potential. A formulation in terms of a mixed product basis, which is constructed from products of LAPW basis functions, enables a solution of the optimizedeffective-potential (OEP) equation with standard numerical algebraic tools and without shape approximations for the resulting potential. We find that the mixed product and LAPW basis sets must be properly balanced to obtain smooth and converged EXX potentials without spurious oscillations. The construction and convergence of the exchange potential are analyzed in detail for diamond. Our all-electron results for C, Si, SiC, Ge, and GaAs semiconductors as well as Ne and Ar noble-gas solids are in very favorable agreement with plane-wave pseudopotential calculations. This confirms the adequacy of the pseudopotential approximation in the context of the EXX-OEP formalism and clarifies a previous contradiction between FLAPW and pseudopotential results.

Precise response functions in all-electron methods: Application to the optimized-effective-potential approach

“…We have implemented the IBC for both and demonstrated explicitly for the case of rock-salt scandium nitride that it improves the convergence with respect to the LAPW basis and the number of unoccupied states considerably. While without the correction the solution of the OEP equation requires a highly converged LAPW basis with a large number of local orbitals, 20 no extra local orbitals are needed when we use the IBC. A similar statement can be made about the number of unoccupied states in the sum-over-states expression related to perturbation theory.…”

“…The added local orbitals are placed at energies in the conduction band according to the recipe of Ref. 20. For simplicity, we have employed the same number of additional local orbitals for Sc and N. In this case, the MPB consists of 13 spherical functions, 7 at the Sc atom and 6 at the N atom.…”

“…In Ref. 20 we showed that the spurious oscillations can be avoided by augmenting the LAPW basis with local orbitals leading to a smooth and physical potential, at the expense of a very costly calculation. As shown in Fig.…”

“…One way to deal with this issue is to crank up the LAPW basis such that it can describe the Hilbert spaces for the unperturbed and perturbed potentials at the same time-leading to large computational costs as we have seen in Ref. 20. In this paper, we pursue a different approach, which improves the precision of the calculated response functions considerably without the need of using larger basis sets and at the expense of only a small computational overhead.…”

“…It has been shown that the EXX functional leads to KS band gaps that are in much better agreement with experiment. [15][16][17][18][19][20] By definition, the KS band gaps do not contain the derivative discontinuity, 9,21 which indicates that the effect of neglecting correlation is roughly of the same magnitude as the discontinuity but of different sign. 22,23 Also, localized d-and f -electron states appear at larger binding energies compared to local or semilocal functionals, which is a result of the exactly compensated self-interaction error.…”