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Assessment of quality and reliability of band structures from exact-exchange-only Kohn–Sham, hybrid, and GW methods

  • Egor Trushin
  • Andreas GörlingEmail author
Regular Article
Part of the following topical collections:
  1. Topical issue: Special issue in honor of Hardy Gross

Abstract

Band gaps for a large number of semiconductors obtained with the exact-exchange(EXX)-only Kohn–Sham method are compared to those from various generalized Kohn–Sham methods based on hybrid functionals and with experimental values. EXX band gaps are shown to be of superior quality than the band gaps from most of the considered hybrid methods, band gaps obtained with the hybrid functional HSE06 have a similar quality as EXX ones. The EXX method is found to yield d-electron binding energies that are clearly superior to those determined within the local density approximation and to be comparable to d-electron binding energies from GW approaches. EXX plane-wave pseudopotential calculations and EXX all-electron calculations are shown to yield very similar KS transition energies demonstrating that the plane-wave pseudopotential approach is well-suited for EXX methods. Previous discrepancies between pseudopotential and all-electron calculations, most likely, have to be attributed to technical problems in early all-electron EXX calculations.

References

  1. 1.
    P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964) CrossRefADSGoogle Scholar
  2. 2.
    W. Kohn, L.J. Sham, Phys. Rev. 140, 1133 (1965) MathSciNetCrossRefADSGoogle Scholar
  3. 3.
    R.G. Parr, W. Yang, Density-functional theory of atoms and molecules (Oxford University Press, Oxford, 1989) Google Scholar
  4. 4.
    A. Seidl, A. Görling, P. Vogl, J.A. Majewski, M. Levy, Phys. Rev. B 53, 3764 (1996) CrossRefADSGoogle Scholar
  5. 5.
    R.T. Sharp, G.K. Horton, Phys. Rev. 90, 317 (1953) CrossRefADSGoogle Scholar
  6. 6.
    J.D. Talman, W.F. Shadwick, Phys. Rev. A 14, 36 (1976) CrossRefADSGoogle Scholar
  7. 7.
    M. Städele, J.A. Majewski, P. Vogl, A. Görling, Phys. Rev. Lett. 79, 2089 1997 Google Scholar
  8. 8.
    A. Görling, Phys. Rev. Lett. 83, 5459 (1999) CrossRefADSGoogle Scholar
  9. 9.
    M. Städele, J.A. Majewski, P. Vogl, A. Görling, Phys. Rev. B 59, 10031 1999 CrossRefADSGoogle Scholar
  10. 10.
    A. Görling, J. Chem. Phys. 123, 062203 (2005) CrossRefADSGoogle Scholar
  11. 11.
    H. Schulz, M. Greiner, E. Trushin, A. Görling (unpublished) Google Scholar
  12. 12.
    G. Onida, L. Reining, A. Rubio, Rev. Mod. Phys. 74, 601 (2002), and references therein CrossRefADSGoogle Scholar
  13. 13.
    F. Bechstedt, F. Fuchs, G. Kresse, Phys. Status Solidi B 246, 1877 (2009), and references therein CrossRefADSGoogle Scholar
  14. 14.
    F. Caruso, P. Rinke, X. Ren, A. Rubio, M. Scheffler, Phys. Rev. B 88, 075105 (2013) CrossRefADSGoogle Scholar
  15. 15.
    F. Caruso, M. Dauth, M.J. van Setten, P. Rinke, J. Chem. Theory Comput. 12, 5076 (2016) CrossRefGoogle Scholar
  16. 16.
    C. Rostgaard, K.W. Jacobsen, K.S. Thygesen, Phys. Rev. B 81, 085103 (2010) CrossRefADSGoogle Scholar
  17. 17.
    F. Fuchs, J. Furthmüller, F. Bechstedt, M. Shishkin, G. Kresse, Phys. Rev. B 76, 115109 (2007) CrossRefADSGoogle Scholar
  18. 18.
    A. L. Kutepov, Phys. Rev. B 95, 195120 (2017) CrossRefADSGoogle Scholar
  19. 19.
    M. Shishkin, M. Marsman, G. Kresse, Phys. Rev. Lett. 99, 246403 (2007) CrossRefADSGoogle Scholar
  20. 20.
    D.C. Langreth, J.P. Perdew, Solid State Commun. 17, 1425 (1975) CrossRefADSGoogle Scholar
  21. 21.
    D.C. Langreth, J.P. Perdew, Phys. Rev. B 15, 2884 (1977) CrossRefADSGoogle Scholar
  22. 22.
    F. Furche, Phys. Rev. B 64, 195120 (2001) CrossRefADSGoogle Scholar
  23. 23.
    M. Fuchs, X. Gonze, Phys. Rev. B 65, 235109 (2002) CrossRefADSGoogle Scholar
  24. 24.
    A. Görling, Int. J. Quantum Chem. 69, 265 (1998) CrossRefGoogle Scholar
  25. 25.
    A. Görling, Phys. Rev. A 57, 3433 (1998) CrossRefADSGoogle Scholar
  26. 26.
    Y.-H. Kim, A. Görling, Phys. Rev. B 66, 035114 (2002) CrossRefADSGoogle Scholar
  27. 27.
    A. Görling, in Time-dependent density functional theory, Lecture notes in physics (Springer, Heidelberg, 2006), Vol. 706, p. 137 Google Scholar
  28. 28.
    A. Grüneis, M. Marsman, J. Harl, L. Schimka, G. Kresse, J. Chem. Phys. 131, 154115 (2009) Google Scholar
  29. 29.
    A. Heßelmann, A. Görling, Mol. Phys. 108, 359 (2010) CrossRefADSGoogle Scholar
  30. 30.
    M. Hellgren, U. von Barth, J. Chem. Phys. 132, 044101 (2010) CrossRefADSGoogle Scholar
  31. 31.
    A. Heßelmann, A. Görling, Phys. Rev. Lett. 106, 093001 (2011) CrossRefADSGoogle Scholar
  32. 32.
    A. Heßelmann, A. Görling, Mol. Phys. 109, 2473 (2011) CrossRefADSGoogle Scholar
  33. 33.
    X. Ren, A. Tkatchenko, P. Rinke, M. Scheffler, Phys. Rev. Lett. 106, 153003 (2011) CrossRefADSGoogle Scholar
  34. 34.
    P. Bleiziffer, A. Heßelmann, A. Görling, J. Chem. Phys. 136, 134102 (2012) CrossRefADSGoogle Scholar
  35. 35.
    P. Bleiziffer, A. Heßelmann, A. Görling, J. Chem. Phys. 139, 084113 (2013). Note that in Eqs. (30), (31), and (48)–(51) of this reference there is a sign error in the denominators of the right hand side. They should read 1 − σ () instead of 1 + σ(). CrossRefADSGoogle Scholar
  36. 36.
    P. Bleiziffer, M. Krug, A. Görling, J. Chem. Phys. 142, 244108 (2015) CrossRefADSGoogle Scholar
  37. 37.
    J. Erhard, P. Bleiziffer, A. Görling, Phys. Rev. Lett. 117, 143002 (2016) MathSciNetCrossRefADSGoogle Scholar
  38. 38.
    N. Colonna, M. Hellgren, S. de Gironcoli, Phys. Rev. B 90, 125150 (2014) CrossRefADSGoogle Scholar
  39. 39.
    Y.M. Niquet, X. Gonze, Phys. Rev. B 70, 245115 (2004) CrossRefADSGoogle Scholar
  40. 40.
    E. Trushin, M. Betzinger, S. Blügel, A. Görling, Phys. Rev. B 94, 075123 (2016) CrossRefADSGoogle Scholar
  41. 41.
    S. Sharma, J.K. Dewhurst, C. Ambrosch-Draxl, Phys. Rev. Lett. 95, 136402 (2005) CrossRefADSGoogle Scholar
  42. 42.
    M. Betzinger, C. Friedrich, S. Blügel, A. Görling, Phys. Rev. B 83, 045105 (2011) CrossRefADSGoogle Scholar
  43. 43.
    M. Betzinger, C. Friedrich, A. Görling, S. Blügel, Phys. Rev. B 85, 245124 (2012) CrossRefADSGoogle Scholar
  44. 44.
    R.J. Magyar, A. Fleszar, E.K.U. Gross, Phys. Rev. B 69, 045111 (2004) CrossRefADSGoogle Scholar
  45. 45.
    E. Engel, Phys. Rev. B 80, 161205 (2009) CrossRefADSGoogle Scholar
  46. 46.
    A. Makmal, R. Armiento, E. Engel, L. Kronik, S. Kümmel, Phys. Rev. B 80, 161204 (2009) CrossRefADSGoogle Scholar
  47. 47.
    A.V. Krukau, O.A. Vydrov, A.F. Izmaylov, G.E. Scuseria, J. Chem. Phys. 125, 224106 (2006) CrossRefADSGoogle Scholar
  48. 48.
    M.J. Lucero, T.M. Henderson, G.E. Scuseria, J. Phys.: Condens. Matter 24, 145504 (2012) ADSGoogle Scholar
  49. 49.
    N. Troullier, J.L. Martins, Phys. Rev. B 43, 1993 1991 CrossRefADSGoogle Scholar
  50. 50.
    E. Engel, A. Höck, R.N. Schmid, R.M. Dreizler, N. Chetty, Phys. Rev. B 64, 125111 (2001) CrossRefADSGoogle Scholar
  51. 51.
    A.J. Garza, G.E. Scuseria, J. Phys. Chem. Lett. 7, 4165 (2016) CrossRefGoogle Scholar
  52. 52.
    M. Cardona, M.L.W. Thewalt, Rev. Mod. Phys. 77, 1173 (2005) CrossRefADSGoogle Scholar
  53. 53.
    J. Klimes, G. Kresse, J. Chem. Phys. 140, 054516 (2014) CrossRefADSGoogle Scholar
  54. 54.
    P. Carrier, S.-H. Wei, Phys. Rev. B 70, 035212 (2004) CrossRefADSGoogle Scholar
  55. 55.
    J. Klimes, M. Kaltak, G. Kresse, Phys. Rev. B 90, 075125 (2014) CrossRefADSGoogle Scholar
  56. 56.
    T. Kotani, M. van Schilfgaarde, Solid State Commun. 121, 461 (2002) CrossRefADSGoogle Scholar
  57. 57.
    E.A. Kraut, R.W. Grant, J.R. Waldrop, S.P. Kowalczyk, Phys. Rev. Lett. 44, 1620 (1980) CrossRefADSGoogle Scholar
  58. 58.
    W.R.L. Lambrecht, B. Segall, S. Strite, G. Martin, A. Agarwal, H. Morkoç, A. Rockett, Phys. Rev. B 50, 14155 (1994) CrossRefADSGoogle Scholar
  59. 59.
    R. Weidemann, H.-E. Gumlich, M. Kupsch, H.-U. Middelmann, U. Becker, Phys. Rev. B 45, 1172 (1992) CrossRefADSGoogle Scholar
  60. 60.
    X.-Z. Li, R. Gmez-Abal, H. Jiang, C. Ambrosch-Draxl, M. Scheffler, New J. Phys. 14, 023006 (2012) CrossRefADSGoogle Scholar
  61. 61.
    L. Ley, R.A. Pollak, F.R. McFeely, S.P. Kowalczyk, D.A. Shirley, Phys. Rev. B 9, 600 (1974) CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Lehrstuhl für Theoretische Chemie, Universität Erlangen-NürnbergErlangenGermany

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