Optimized norm-conserving Hartree-Fock pseudopotentials for plane-wave calculations

Al-Saidi, W. A.; Rappe, Andrew M.

doi:10.1103/physrevb.77.075112

Cited by 36 publications

(36 citation statements)

References 38 publications

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“…A correction procedure is necessary to remove this tail and restore the correct long-range behavior of the pseudopotential while maintaining the eigenvalue spectrum and logarithmic derivatives. Recent work 22,26,27 has shown that this approach yields highly accurate Hartre-Fock pseudopotentials.…”

Section: Recently Wu Et Al (Wsc)mentioning

confidence: 99%

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Hybrid density functional calculations of the band gap ofGaxIn1−xN

Walter

Rappe

et al. 2009

Phys. Rev. B

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Recent theoretical work has provided evidence that hybrid functionals, which include a fraction of exact (Hartree Fock) exchange in the density functional theory (DFT) exchange and correlation terms, significantly improve the description of band gaps of semiconductors compared with local and semilocal approximations. Based on a recently developed order-N method for calculating the exact exchange in extended insulating systems, we have implemented an efficient scheme to determine the hybrid functional band gap. We use this scheme to study the band gap and other electronic properties of the ternary compound In1−xGaxN using a 64-atom supercell model. The design of novel functional semiconductors with given values of the energy band gap is an area of intense research 1,2,3,4,5 . In particular, much attention is focused on the band gap engineering of group-III nitride semiconductors, whose remarkable optical properties are important for optoelectronic device applications 6,7 . To guide the search for compounds with tailored properties 1 , experimental studies are often accompanied by electronic structure calculations based on density functional theory (DFT)8 . For these calculations, the local-density(LDA) or generalized gradient approximations(GGA) are typically used. Due to the delocalization error of the LDA and GGA exchange and correlation functionals, however, these approaches severely underestimate the materials band gaps 9,10 .As shown by several recent studies 11 , a significant improvement in the description of semiconductor and insulator band gaps is generally obtained by using hybrid functionals 12 , in which some exact (Hartree-Fock) exchange is mixed into the exchange and correlation functional. This reduces the delocalization and derivative discontinuity errors of (semi)local functionals 2,9,10,11 . However, because of the considerable computational cost of evaluating the non-local exact exchange term, hybrid functionals have been mostly applied to systems with small unit cells 13 . For the modeling of systems where a large supercell is needed, an additional screened exchange approximation is usually made to relieve the computational burden 2,11 . Recently Wu et al. (WSC)14 introduced an order-N method to calculate the exact exchange in extended insulating systems. The WSC method is based on a localized Wannier function representation of the occupied (valence) space, so that the exchange interaction between two orbitals decays rapidly with the distance between their centers. A truncation can thus be introduced, which greatly reduces the computational cost. The effectiveness of the WSC method was demonstrated by ground state electronic minimizations for crystalline silicon in supercells with 64 and 216 atoms.In this paper, we extend the WSC scheme to compute hybrid functional band gaps. To this end, the system's first (few) empty conduction state(s) is(are) determined starting from the ground state calculated via the WSC method. With hybrid functionals, this requires the computation of the pair exchange ...

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Section: Recently Wu Et Al (Wsc)mentioning

confidence: 99%

“…27. The Ga and In pseudopotentials were obtained from scalar-relativistic solutions, while the N pseudopotential was non-relativistic.…”

Section: Recently Wu Et Al (Wsc)mentioning

confidence: 99%

Hybrid density functional calculations of the band gap ofGaxIn1−xN

Walter

Rappe

et al. 2009

Phys. Rev. B

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“…The Hartree-Fock approximation was used and the non-analytic behaviour of HF pseudopotentials was treated using the localization and optimization scheme of Al-Saidi, Walter and Rappe 47 . Including exchange exactly in the pseudopotentials is required to ensure accurate core-valence interaction within the current formalism.…”

Section: -39mentioning

confidence: 99%

Optimized effective potential using the Hylleraas variational method

et al. 2012

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In electronic structure calculations the optimized effective potential (OEP) is a method that treats exchange interactions exactly using a local potential within density-functional theory (DFT). We present a method using density functional perturbation theory combined with the Hylleraas variational method for finding the OEP by direct minimization which avoids any sum over unoccupied states. The method has been implemented within the plane-wave, pseudopotential formalism. Band structures for zinc blende semiconductors Si, Ge C, GaAs, CdTe and ZnSe, wurtzite semiconductors InN, GaN and ZnO and the rocksalt insulators CaO and NaCl have been calculated using the OEP and compared to calculations using the local density approximation (LDA), a selection of generalized gradient approximations (GGAs) and Hartree-Fock (HF) functionals. The band gaps found with the OEP improve on the calculated results for the LDA, GGAs or HF, with calculated values of 1.16eV for Si, 3.32eV for GaN and 3.48eV for ZnO. The OEP energies of semi-core d-states are also greatly improved compared to LDA.

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“…By using Eq. (B1) and a method similar to that described by Al-Saidi and co-workers 83 to generate a norm-conserving screened pseudopotential V aPS (r), we can then use a similar unscreening process described by Eq. (47) to determine a suitableṼ a loc (r) for each atom.…”

Section: Discussionmentioning

confidence: 99%

“…This extension of ideas presented in the original PAW formalism 38 was first introduced by Paier and co-workers. 4 In principle, the correct treatment of the charge moments in PAW approach should have accuracy advantages over norm-conserving pseudoptential methods 73,74,76,78,83,84 which explicitly control only the diagonal L = 0 pair charges. We also show that the treatment of core effects in the Fock exchange are best implemented in terms of frozencore orbitals which can be accomplished with high accuracy within the PAW method.…”

Section: Discussionmentioning

confidence: 99%

Adaptation of the projector-augmented-wave formalism to the treatment of orbital-dependent exchange-correlation functionals

Holzwarth

2011

Phys. Rev. B

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This paper presents the formulation and numerical implementation of a self-consistent treatment of orbitaldependent exchange-correlation functionals within the Projector Augmented Wave (PAW) method of Blöchl [Phys. Rev. B 50 17953 (1994)] for electronic structure calculations. The methodology is illustrated with binding energy curves for C in the diamond structure and LiF in the rock salt structure, comparing results from the Hartree-Fock (HF) formalism and the Optimized Effective Potential (OEP) formalism in the so-called KLI approximation [Krieger, Li, and Iafrate, Phys. Rev. A 45, 101 (1992)] with those of the local density approximation (LDA). While the work here uses pure Fock exchange only, the formalism can be extended to treat orbital-dependent functionals more generally.2

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Optimized norm-conserving Hartree-Fock pseudopotentials for plane-wave calculations

Cited by 36 publications

References 38 publications

Hybrid density functional calculations of the band gap ofGaxIn1−xN

Hybrid density functional calculations of the band gap ofGaxIn1−xN

Optimized effective potential using the Hylleraas variational method

Adaptation of the projector-augmented-wave formalism to the treatment of orbital-dependent exchange-correlation functionals

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