Skip to main content
SpringerLink
Log in

Relativistic Density Functional Theory

  • Reference work entry
  • First Online:
Handbook of Relativistic Quantum Chemistry

Abstract

This chapter gives an overview of relativistic density functional theory. Both its foundations, the existence theorem and the Kohn–Sham equations, and its core quantity, the exchange–correlation (xc) energy functional, are discussed. It is first outlined how a workable relativistic Kohn–Sham scheme can be obtained within the framework of quantum electrodynamics and which alternatives for its implementation are available. Particular emphasis is then placed on the relativistic corrections to the xc-functional. The modification of its functional form due to the relativistic motion of the electrons and their retarded interaction via exchange of photons is distinguished from the effect resulting from insertion of a relativistic density into the functional. The difference between the relativistic xc-functional and its nonrelativistic form is studied in detail for the case of the exchange functional (which can be handled exactly via the optimized effective potential method). This analysis is complemented by some first-principles results for the correlation functional, relying on a perturbative approach. Finally, the accuracy of approximate relativistic xc-functionals, the local density and the generalized gradient approximation, is assessed on the basis of the exact results.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 599.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 699.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Engel E, Dreizler RM (2011) Density functional theory: an advanced course. Springer, Berlin

    Book  Google Scholar 

  2. Rajagopal AK, Callaway J (1973) Phys Rev B 7:1912

    Article  CAS  Google Scholar 

  3. Rajagopal AK (1978) J Phys C 11:L943

    Article  CAS  Google Scholar 

  4. MacDonald AH, Vosko SH (1979) J Phys C 12:2977

    Article  CAS  Google Scholar 

  5. Eschrig H, Seifert G, Ziesche P (1985) Solid State Commun 56:777

    Article  CAS  Google Scholar 

  6. Hohenberg P, Kohn W (1964) Phys Rev 136B:864

    Article  Google Scholar 

  7. Engel E, Müller H, Speicher C, Dreizler RM (1995) In: Gross EKU, Dreizler RM (eds) Density functional theory. NATO ASI series B, vol 337. Plenum, New York, p 65

    Google Scholar 

  8. Engel E (2002) In: Schwerdtfeger P (ed) Relativistic electronic structure theory, part 1, chapter 10. Fundamentals. Elsevier, Amsterdam, p 524

    Google Scholar 

  9. Eschrig H, Servedio VDP (1999) J Comput Chem 20:23

    Article  CAS  Google Scholar 

  10. Eschrig H (2003) The fundamentals of density functional theory. Edition am Gutenbergplatz, Leipzig

    Google Scholar 

  11. Lieb EH (1983) Int J Quantum Chem 24:243

    Article  CAS  Google Scholar 

  12. Huang KN, Aoyagi M, Chen MH, Crasemann B, Mark H (1976) At Data Nucl Data Tables 18:243

    Article  CAS  Google Scholar 

  13. Labzowsky L, Goidenko I, Tokman M, Pyykkö P (1999) Phys Rev A 59:2707

    Article  CAS  Google Scholar 

  14. Liberman D, Waber JT, Cromer DT (1965) Phys Rev 137A:27

    Article  Google Scholar 

  15. Ramana MV, Rajagopal AK (1981) J Phys C 14:4291

    Article  Google Scholar 

  16. Diener G, Gräfenstein J (1989) J Phys Condens Matter 1:8445

    Article  Google Scholar 

  17. Jansen HJF (1999) Phys Rev B 59:4699

    Article  CAS  Google Scholar 

  18. Wang F, Liu WJ (2003) J Chin Chem Soc (Taipei) 50:597

    Article  CAS  Google Scholar 

  19. Anton J, Fricke B, Engel E (2004) Phys Rev A 69:012505

    Article  Google Scholar 

  20. Laskowski R, Madsen GKH, Blaha P, Schwarz K (2004) Phys Rev B 69:140408(R)

    Google Scholar 

  21. Ramana MV, Rajagopal AK (1981) Phys Rev A 24:1689

    Article  CAS  Google Scholar 

  22. Engel E, Facco Bonetti A, Keller S, Andrejkovics I, Dreizler RM (1998) Phys Rev A 58:964

    Article  CAS  Google Scholar 

  23. Görling A, Levy M (1994) Phys Rev A 50:196

    Article  Google Scholar 

  24. Facco Bonetti A (2000) Implizite Dichtefunktionale: Untersuchung eines störungstheoretische Zugangs für das Korrelationsenergie funktional. Ph.D. thesis, Univ. Frankfurt

    Google Scholar 

  25. Engel E, Ködderitzsch D, Ebert H (2008) Phys Rev B 78:235123

    Article  Google Scholar 

  26. Kotani T (1998) J Phys Condens Matter 10:9241

    Article  CAS  Google Scholar 

  27. Kotani T (2000) J Phys Condens Matter 12:2413

    Article  CAS  Google Scholar 

  28. Furche F (2001) Phys Rev B 64:195120

    Article  Google Scholar 

  29. Fuchs M, Gonze X (2002) Phys Rev B 65:235109

    Article  Google Scholar 

  30. Sharp RT, Horton GK (1953) Phys Rev 90:317

    Article  Google Scholar 

  31. Talman JD, Shadwick WF (1976) Phys Rev A 14:36

    Article  CAS  Google Scholar 

  32. Ködderitzsch D, Ebert H, Engel E (2008) Phys Rev B 77:045101

    Article  Google Scholar 

  33. Shadwick BA, Talman JD, Norman MR (1989) Comput Phys Commun 54:95

    Article  CAS  Google Scholar 

  34. Engel E, Keller S, Facco Bonetti A, Müller H, Dreizler RM (1995) Phys Rev A 52:2750

    Article  CAS  Google Scholar 

  35. Hisaka K et al (Particle Data Group) (1992) Phys Rev D 45(11):Part II

    Google Scholar 

  36. Engel E, Keller S, Dreizler RM (1996) Phys Rev A 53:1367

    Article  CAS  Google Scholar 

  37. Becke AD (1988) Phys Rev A 38:3098

    Article  CAS  Google Scholar 

  38. Lee C, Yang W, Parr RG (1988) Phys Rev B 37:785

    Article  CAS  Google Scholar 

  39. Vosko SH, Wilk L, Nusair M (1980) Can J Phys 58:1200

    Article  CAS  Google Scholar 

  40. Harris J, Jones RO (1978) J Chem Phys 68:3316

    Article  CAS  Google Scholar 

  41. Gunnarsson O, Jones RO (1985) Phys Rev B 31:7588

    Article  CAS  Google Scholar 

  42. Lagowski JB, Vosko SH (1989) Phys Rev A 39:4972

    Article  CAS  Google Scholar 

  43. Perdew JP, Burke K, Ernzerhof M (1996) Phys Rev Lett 77:3865

    Article  CAS  Google Scholar 

  44. Ralchenko Y, Kramida AE, Reader J, Team NA (eds) (2008) NIST atomic spectra database (version 3.1.5), [Online]. Available: http://physics.nist.gov/asd3 2 Sept 2008. National Institute of Standards and Technology, Gaithersburg

  45. Perdew JP, Chevary JA, Vosko SH, Jackson KA, Pederson MR, Singh DJ, Fiolhais C (1992) Phys Rev B 46:6671

    Article  CAS  Google Scholar 

  46. Davidson ER, Hagstrom SA, Chakravorty SJ, Umar VM, Froese Fischer C (1991) Phys Rev A 44:7071

    Article  CAS  Google Scholar 

  47. Chakravorty SJ, Gwaltney SR, Davidson ER, Parpia FA, Froese Fischer C (1993) Phys Rev A 47:3649

    Article  CAS  Google Scholar 

  48. Facco Bonetti A, Engel E, Dreizler RM, Andrejkovics I, Müller H (1998) Phys Rev A 58:993

    Article  CAS  Google Scholar 

  49. Akhiezer IA, Peletminskii SV (1960) Zh. Eksp. Teor. Fiz. 38:1829 [Sov. Phys. JETP 11, 1316 (1960)]

    Google Scholar 

  50. Zapolsky HS (1960) Lns report, Cornell University

    Google Scholar 

  51. Jancovici B (1962) Nuovo Cim XXV:428

    Google Scholar 

  52. Freedman BA, McLerran LD (1977) Phys Rev D 16:1130, 1147, 1169

    Google Scholar 

  53. Perdew JP (1991) In: Ziesche P, Eschrig H (eds) Electronic structure of solids 1991. Akademie Verlag, Berlin, p 11

    Google Scholar 

  54. Ramana MV, Rajagopal AK (1979) J Phys C 12:L845

    Article  CAS  Google Scholar 

  55. MacDonald AH (1983) J Phys C 16:3869

    Article  CAS  Google Scholar 

  56. Xu BX, Rajagopal AK, Ramana MV (1984) J Phys C 17:1339

    Article  CAS  Google Scholar 

  57. Oliver GL, Perdew JP (1979) Phys Rev A 20:397

    Article  CAS  Google Scholar 

  58. Engel E, Keller S, Dreizler RM (1998) In: Dobson JF, Vignale G, Das MP (eds) Electronic density functional theory: recent progress and new directions. Plenum, New York, p 149

    Chapter  Google Scholar 

  59. Mayer M, Häberlen OD, Rösch N (1996) Phys Rev A 54:4775

    Article  CAS  Google Scholar 

  60. Varga S, Engel E, Sepp WD, Fricke B (1999) Phys Rev A 59:4288

    Article  CAS  Google Scholar 

  61. Liu W, van Wüllen C (2000) J Chem Phys 113:2506

    Article  CAS  Google Scholar 

  62. Schmid RN, Engel E, Dreizler RM, Blaha P, Schwarz K (1998) Adv Quantum Chem 33:209

    Article  CAS  Google Scholar 

  63. Perdew JP (1986) Phys Rev B 33:8822

    Article  Google Scholar 

  64. Painter GS, Averill FW (1983) Phys Rev B 28:5536

    Article  CAS  Google Scholar 

  65. van Wüllen C (1995) J Chem Phys 103:3589

    Article  Google Scholar 

  66. Pyykkö P (1988) Chem Rev 88:563

    Article  Google Scholar 

  67. Takeuchi N, Chan CT, Ho KM (1989) Phys Rev B 40:1565

    Article  CAS  Google Scholar 

  68. Dewaele A, Loubeyre P, Mezouar M (2004) Phys Rev B 70:094112

    Article  Google Scholar 

  69. Brewer L (1977) Tech. Rep. Report LBL-3720 Rev., Lawrence Berkeley Laboratory, Univ. of California, Berkeley

    Google Scholar 

Download references

Acknowledgements

I am very grateful to R. M. Dreizler and D. Ködderitzsch for many valuable discussions on the topics of this contribution.

Author information

Authors and Affiliations

  1. Center for Scientific Computing, J.W. Goethe-Universität Frankfurt, Max-von-Laue-Str. 1, D-60438, Frankfurt/Main, Germany

    Eberhard Engel

Authors
  1. Eberhard Engel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eberhard Engel .

Editor information

Editors and Affiliations

  1. Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering and Center for Computational Science and Engineering, Peking University, Beijing, China

    Wenjian Liu

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer-Verlag Berlin Heidelberg

About this entry

Cite this entry

Engel, E. (2017). Relativistic Density Functional Theory. In: Liu, W. (eds) Handbook of Relativistic Quantum Chemistry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40766-6_18

Download citation

Publish with us

Policies and ethics

Search

Navigation