Role of the core-valence interaction for pseudopotential calculations with exact exchange

Engel, E.; Hock, Adam S.; Schmid, Rochus; Dreizler, R. M.; Chetty, Naven

doi:10.1103/physrevb.64.125111

Cited by 116 publications

(63 citation statements)

References 59 publications

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“…As shown by Porezag et al [34], these errors are larger for first row species compared to heavier atoms and increase with more unpaired electrons, explaining why N 2 has the largest error (first row, and 3 unpaired spins) and why Cl 2 (second row, 1 unpaired spin) has the smallest. Our LDA all-electron and pseudopotential energies are in excellent agreement with previous results [18] without a NLCC. This study also showed that the all-electron results are in good agreement with the pseudopotentials values after including a NLCC, indicating that this is the dominant error for LDA pseudopo-tentials.…”

Section: Study Of Several Dimerssupporting

confidence: 90%

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

Al-Saidi

Rappe

2008

Phys. Rev. B

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We report Hartree-Fock (HF) based pseudopotentials suitable for plane-wave calculations. Unlike typical effective core potentials, the present pseudopotentials are finite at the origin and exhibit rapid convergence in a plane-wave basis; the optimized pseudopotential method [A. M. Rappe et al. , Phys. Rev. B 41 1227-30 (1990] improves plane-wave convergence. Norm-conserving HF pseudopotentials are found to develop long-range non-Coulombic behavior which does not decay faster than 1/r, and is non-local. This behavior, which stems from the nonlocality of the exchange potential, is remedied using a recently developed self-consistent procedure [J. R. Trail and R. J. Needs, J. Chem. Phys. 122, 014112 (2005)]. The resulting pseudopotentials slightly violate the norm conservation of the core charge. We calculated several atomic properties using these pseudopotentials, and the results are in good agreement with all-electron HF values. The dissociation energies, equilibrium bond lengths, and frequency of vibrations of several dimers obtained with these HF pseudopotentials and plane waves are also in good agreement with all-electron results.

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Section: Study Of Several Dimerssupporting

confidence: 90%

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

Al-Saidi

Rappe

2008

Phys. Rev. B

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“…Unlike with traditional density functional theory, Hartree-Fock pseudopotentials require extra care in their construction. This arises from the non-local form of the Hartree-Fock exchange potential 22,23,24,25 . The presence of the non-local exchange potential in Hartree-Fock or Hartree-Fock/DFT hybrids will often yield pseudopotentials with an unphysical, long-range tail.…”

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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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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“…[6][7][8][9] Furthermore, this scheme, usually denoted as exact-exchange OEP (EXX-OEP) or exchange-only OEP, has been implemented for calculations of atoms, molecules, and solids. [10][11][12][13][14][15][16][17][18][19][20][21] As the correct asymptotic behavior (−1/r) of the potential is obtained for finite systems, properties of interest, such as electron affinities or ionisation potentials, tend to be improved. 12 Making approximations to the EXX-OEP equations has also received considerable interest.…”

Section: Introductionmentioning

confidence: 99%

Kohn-Sham band gaps and potentials of solids from the optimised effective potential method within the random phase approximation

Klimeš

Kresse

2014

The Journal of Chemical Physics

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We present an implementation of the optimised effective potential (OEP) scheme for the exactexchange (EXX) and random phase approximation (RPA) energy functionals and apply these methods to a range of bulk materials. We calculate the Kohn-Sham (KS) potentials and the corresponding band gaps and compare them to the potentials obtained by standard local density approximation (LDA) calculations. The KS gaps increase upon going from the LDA to the OEP in the RPA and finally to the OEP for EXX. This can be explained by the different depth of the potentials in the bonding and interstitial regions. To obtain the true quasi-particle gaps the derivative discontinuities or G0W0 corrections need to be added to the RPA-OEP KS gaps. The predicted G0W0@RPA-OEP quasi-particle gaps are about 5% too large compared to the experimental values. However, compared to G0W0 calculations based on local or semi-local functionals, where the errors vary between different materials, we obtain a rather consistent description among all the materials.

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Role of the core-valence interaction for pseudopotential calculations with exact exchange

Cited by 116 publications

References 59 publications

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

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

Hybrid density functional calculations of the band gap ofGaxIn1−xN

Kohn-Sham band gaps and potentials of solids from the optimised effective potential method within the random phase approximation

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