Towards a Greater Accuracy in DFT Calculations: From GGA to Hybrid Functionals

Abstract

The accuracy of a DFT calculation depends in a crucial way on the choice of the exchange-correlation functional, for which a variety of approximations are available. Local functionals, or functionals belonging to the generalized-gradient approximation (GGA) or meta-GGA classes are the simplest ones and the most computationally efficient. Furthermore, they give sufficiently accurate results for many applications. Nevertheless, for a number of purposes, an increased accuracy is required, which can only be obtained by means of hybrid functionals. Hybrid functionals are derived by mixing a GGA (or local, or meta-GGA) functional with the Hartree-Fock exchange. Two different families of hybrid functionals exist: the so-called global hybrids and the range separated hybrids. Quite recently, hybrids combining the main features of the functionals belonging to both families have been proposed and tested. We have constructed new hybrid functionals based on some recently proposed local and GGA functionals. Global hybrids, range-separated hybrids, as well as global hybrids with range separation will be presented and their performances discussed.

Keywords

Barrier Height Correlation Energy Mean Absolute Error Atomization Energy Hybrid Functional 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work has been supported by the Agence Nationale de la Recherche under the project Dinf DFT ANR BLANC n. 0425.

References

  1. 1.
    Hohenberg P, Kohn W (1964) Phys Rev B 136:864 CrossRefGoogle Scholar
  2. 2.
    Kohn W, Sham LJ (1965) Phys Rev A 140:1133 Google Scholar
  3. 3.
    Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. Oxford University Press, New York Google Scholar
  4. 4.
    Perdew JP, Zunger A (1981) Phys Rev 23:5048 CrossRefGoogle Scholar
  5. 5.
    Vosko SH, Wilk L, Nusair M (1980) Can J Phys 58:1200 CrossRefGoogle Scholar
  6. 6.
    Perdew JP, Wang Y (1992) Phys Rev B 45:13244 CrossRefGoogle Scholar
  7. 7.
    Perdew JP, Burke K, Ernzerhof M (1996) Phys Rev Lett 77:3865 CrossRefGoogle Scholar
  8. 8.
    Becke AD (1988) Phys Rev A 38:3098 CrossRefGoogle Scholar
  9. 9.
    Lee C, Yang W, Parr RG (1988) Phys Rev B 37:785 CrossRefGoogle Scholar
  10. 10.
    Tao J, Perdew JP, Staroverov VN, Scuseria GE (2003) Phys Rev Lett 91:146401 CrossRefGoogle Scholar
  11. 11.
    Becke AD (1993) J Chem Phys 98:1372 CrossRefGoogle Scholar
  12. 12.
    Adamo C, Barone V (1999) J Chem Phys 110:6158 CrossRefGoogle Scholar
  13. 13.
    Ernzerhof M, Scuseria GE (1999) J Chem Phys 110:5029 CrossRefGoogle Scholar
  14. 14.
    Iikura H, Tsuneda T, Yanai T, Hirao K (2001) J Chem Phys 115:3540 CrossRefGoogle Scholar
  15. 15.
    Heyd J, Scuseria GE, Ernzerhof M (2003) J Chem Phys 118:8207 CrossRefGoogle Scholar
  16. 16.
    Heyd J, Scuseria GE (2004) J Chem Phys 120:7274 CrossRefGoogle Scholar
  17. 17.
    Vydrov OA, Heyd J, Krukau AV, Scuseria GE (2006) J Chem Phys 125:074106 CrossRefGoogle Scholar
  18. 18.
    Ragot S, Cortona P (2004) J Chem Phys 121:7671 CrossRefGoogle Scholar
  19. 19.
    Tognetti V, Cortona P, Adamo C (2008) J Chem Phys 128:034101 CrossRefGoogle Scholar
  20. 20.
    Tognetti V, Cortona P, Adamo C (2008) Chem Phys Lett 460:536 CrossRefGoogle Scholar
  21. 21.
    Hermet J, Cortona P, Adamo C (2012) Chem Phys Lett 519–520:145 CrossRefGoogle Scholar
  22. 22.
    Wang Y, Perdew JP (1991) Phys Rev B 43:8911 CrossRefGoogle Scholar
  23. 23.
    Tognetti V, Cortona P, Adamo C (2007) Chem Phys Lett 439:381 CrossRefGoogle Scholar
  24. 24.
    Tognetti V, Adamo C, Cortona P (2007) Chem Phys 337:161 CrossRefGoogle Scholar
  25. 25.
    Tognetti V, Cortona P, Adamo C (2009) Theor Chem Acc 122:257 CrossRefGoogle Scholar
  26. 26.
    Tognetti V, Joubert L, Cortona P, Adamo C (2009) J Phys Chem A 113:12322 CrossRefGoogle Scholar
  27. 27.
    Tognetti V, Cortona P, Adamo C (2009) AIP Conf Proc 1102:147 CrossRefGoogle Scholar
  28. 28.
    Tognetti V, Cortona P, Adamo C (2010) Int J Quant Chem 110:2320 CrossRefGoogle Scholar
  29. 29.
    Tognetti V, Adamo C, Cortona P (2010) Interdiscip Sci Comput Life Sci 2:163 CrossRefGoogle Scholar
  30. 30.
    Lieb EH, Oxford S (1981) Int J Quant Chem 19:427 CrossRefGoogle Scholar
  31. 31.
    Zhang Y, Yang W (1998) Phys Rev Lett 80:890 CrossRefGoogle Scholar
  32. 32.
    Chan K-I, Handy NC (1999) Phys Rev A 59:3075 CrossRefGoogle Scholar
  33. 33.
    Frisch MJ et al. (2007) Gaussian development version, revision G01. Gaussian, Inc, Wallingford Google Scholar
  34. 34.
    Curtiss LA, Raghavachari K, Trucks GW, Pople JA (1991) J Chem Phys 94:7221 CrossRefGoogle Scholar
  35. 35.
    Zheng J, Zhao Y, Truhlar DG (2009) J Chem Theory Comput 5:808 CrossRefGoogle Scholar
  36. 36.
    Zheng J, Zhao Y, Truhlar DG (2007) J Chem Theory Comput 3:569 CrossRefGoogle Scholar
  37. 37.
    Zhao Y, Truhlar DG (2005) J Chem Theory Comput 1:415 CrossRefGoogle Scholar
  38. 38.
    Zhao Y, Truhlar DG (2005) J Phys Chem A 109:5656 CrossRefGoogle Scholar
  39. 39.
    Brémond E, Pilard D, Ciofini I, Chermette H, Adamo C, Cortona P (2012) Theor Chem Acc 131:1184 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.CEA-DAM, DIFArpajonFrance
  2. 2.Laboratoire d’Électrochimie, Chimie des Interfaces et Modélisation pour l’Énergie (UMR 7575), Centre National de la Recherche ScientifiqueChimie ParisTechParis Cedex 05France
  3. 3.Laboratoire Structure, Propriétés et Modélisation des SolidesUMR 8580, École Centrale ParisChâtenay-MalabryFrance

Personalised recommendations