Skip to main content
SpringerLink
Log in

Douglas–Kroll–Hess Theory: a relativistic electrons-only theory for chemistry

  • Regular Article
  • Published:
Theoretical Chemistry Accounts Aims and scope Submit manuscript

Abstract

A unitary transformation allows to separate (block-diagonalize) the Dirac Hamiltonian into two parts one part: solely describes electrons, while the other gives rise to negative-energy states, which are the so-called positronic states. The block-diagonal form of the Hamiltonian no longer accounts for the coupling of both kinds of states. The positive-energy (‘electrons-only’) part can serve as a ‘fully’ relativistic electrons-only theory, which can be understood as a rigorous basis for chemistry. Recent developments of the Douglas–Kroll–Hess (DKH) method allowed to derive a sequence of expressions, which approximate this electrons-only Hamiltonian up to arbitrary-order. While all previous work focused on the numerical stability and accuracy of these arbitrary-order DKH Hamiltonians, conceptual issues and paradoxa of the method were mostly left aside. In this work, the conceptual side of DKH theory is revisited in order to identify essential aspects of the theory to be distinguished from purely computational consideration.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Einstein A (1905). Ann Phys (Leipzig) 17:891–921

    Google Scholar 

  2. Bagus PS, Lee YS, Pitzer KS (1975). Chem Phys Lett 33:408–411

    Article  CAS  Google Scholar 

  3. Pyykkö P, Desclaux J-P (1979). Acc Chem Res 12:276–281

    Article  Google Scholar 

  4. Ziegler T, Snijders JG, Baerends EJ (1981). J Chem Phys 74:1271–1284

    Article  CAS  Google Scholar 

  5. Pitzer KS (1979). Acc Chem Res 12:271–276

    Article  CAS  Google Scholar 

  6. Pyykkö P (1988). Chem Rev 88:563–594

    Article  Google Scholar 

  7. Schwerdtfeger P (eds). (2002). Relativistic electronic structure theory. Part 1. Fundamentals. Elsevier, Amsterdam

    Google Scholar 

  8. Schwerdtfeger P (eds) (2004). Relativistic electronic structure theory. Part 2. Applications. Elsevier, Berlin

    Google Scholar 

  9. Hess BA (eds) (2003). Relativistic effects in heavy-element chemistry and physics. Wiley, New York

    Google Scholar 

  10. Hirao K, Ishikawa Y (eds) (2004). Recent advances in relativistic effects in chemistry. World Scientific Publishing, Singapore

    Google Scholar 

  11. Feynman RP (1961). Quantum electrodynamics. Benjamin, New York

    Google Scholar 

  12. Gupta SN. (1977). Quantum electrodynamics. Gordon and Breach Science Publishers, New York

    Google Scholar 

  13. Mohr PJ, Plunien G, Soff G (1998). Phys Rep 293:227–369

    Article  CAS  Google Scholar 

  14. Dirac PAM (1928). Proc Roy Soc London A 117:610–624

    Google Scholar 

  15. Dirac PAM (1928). Proc Roy Soc London A 118:351–361

    Google Scholar 

  16. Thaller B (1992). The Dirac equation. Springer, Berlin Heidelberg New York

    Google Scholar 

  17. Goidenko I, Labzowsky L, Eliav E, Kaldor U, Pyykkö P (2003). Phys Rev A 67:020102, 1–3

    Google Scholar 

  18. Schwabl F (2004). Quantenmechanik für Fortgeschrittene, 3rd edn. Springer, Berlin Heidelberg New York

    Google Scholar 

  19. Reiher M, Hinze J (2002). Four-component ab initio methods for electronic structure calculations of atoms, molecules, and solids. In: Hess BA (eds). Relativistic effects in heavy-element chemistry and physics. Wiley, Chichester

    Google Scholar 

  20. Jensen HJA, Saue T, Visscher L et al (2004) DIRAC, a relativistic ab initio electronic structure program, Release DIRAC04.0, http://dirac.chem.sdu.dk

  21. Pyykkö P (1986). Relativistic theory of atoms and molecules—a bibliography 1916–1985. Volume 41 of Lecture Notes in Chemistry. Springer, Berlin Heidelberg New York

    Google Scholar 

  22. Pyykkö P (1993). Relativistic theory of atoms and molecules II – a bibliography 1986–1992. Volume 60 of Lecture Notes in Chemistry. Springer, Berlin Heidelberg New York

    Google Scholar 

  23. Pyykkö P (2000). Relativistic theory of atoms and molecules, vol III – A Bibliography 1993–2000. Springer, Berlin Heidelberg New York

    Google Scholar 

  24. Pyykkö P (2004) Database ‘RTAM’—relativistic quantum chemistry database 1915–2004; http://www.csc.fi/rtam/

  25. Wolf A, Reiher M, Hess BA (2002). Two-component methods and the generalised Douglas–Kroll transformation. In: Schwerdtfeger P (eds). Relativistic quantum chemistry, vol I. Theory; Theoretical and computational chemistry. Elsevier, Amsterdam, pp. 622–663

    Google Scholar 

  26. Wolf A, Reiher M, Hess BA (2004). Transgressing theory boundaries: the generalized Douglas–Kroll transformation. In: Hirao K, Ishikawa Y (eds). Recent advances in relativistic effects in chemistry. World Scientific Publishing, Singapore, pp. 137–190

    Google Scholar 

  27. Reiher M, Wolf A, Hess BA (2005) Relativistic quantum chemistry: from quantum electrodynamics to quasi-relativistic methods. In: Rieth M, Schommers W (eds) Handbook of theoretical and computational nanotechnology. American Scientific Publishers, Stevenson Ranch (in press)

  28. van Lenthe E, Baerends E-J, Snijders JG (1993). J Chem Phys 99:4597–4610

    Article  Google Scholar 

  29. van Lenthe E, Baerends E-J, Snijders JG (1994). J Chem Phys 101:9783–9792

    Article  Google Scholar 

  30. Chang C, Pélissier M, Durand P (1986). Phys Scr 34:394–404

    CAS  Google Scholar 

  31. Barysz M, Sadlej AJ (2002). J Chem Phys 116:2696–2704

    Article  CAS  Google Scholar 

  32. Heully JL, Lindgren I, Lindroth E, Lundquist S, Mårtensson-Pendrill AM (1986). J Phys B 19:2799–2815

    Article  CAS  Google Scholar 

  33. Kutzelnigg W (1997). Chem Phys 225:203–222

    Article  CAS  Google Scholar 

  34. Barysz M, Sadlej AJ, Snijders JG (1997). Int J Quant Chem 65:225–239

    Article  CAS  Google Scholar 

  35. Wolf A, Reiher M, Hess BA (2002). J Chem Phys 117:9215–9226

    Article  CAS  Google Scholar 

  36. Douglas M, Kroll NM (1974). Ann Phys 82:89–155

    Article  CAS  Google Scholar 

  37. Hess BA (1986). Phys Rev A 33:3742–3748

    Article  CAS  Google Scholar 

  38. Reiher M, Wolf A (2004). J Chem Phys 121:2037–2047

    Article  CAS  Google Scholar 

  39. Hess BA (1985). Phys Rev A 32:756–763

    Article  CAS  Google Scholar 

  40. Foldy LL, Wouthuysen SA (1950). Phys Rev 78:29–36

    Article  Google Scholar 

  41. Reiher M, Wolf A (2004). J Chem Phys 121:10945–10956

    Article  CAS  Google Scholar 

  42. Jansen G, Hess BA (1989). Phys Rev A 39:6016–6017

    Article  Google Scholar 

  43. Barysz M, Sadlej AJ (2001). J Mol Struct (Theochem) 573:181–200

    Article  CAS  Google Scholar 

  44. Nakajima T, Hirao K (2000). J Chem Phys 113:7786–7789

    Article  CAS  Google Scholar 

  45. van Wüllen C (2004). J Chem Phys 120:7307–7313

    Article  Google Scholar 

  46. Kutzelnigg W (1989). Z Phys D 11:15–28

    Article  CAS  Google Scholar 

  47. Kutzelnigg W (1990). Z Phys D 15:27–50

    Article  CAS  Google Scholar 

  48. Brummelhuis R, Siedentop H, Stockmeyer E (2002). Doc Math 7:167–182

    Google Scholar 

  49. Kedziera D, Barysz M (2004). Chem Phys Lett 393:521–527

    Article  CAS  Google Scholar 

  50. Kedziera D, Barysz M (2004). J Chem Phys 121:6719–6727

    Article  Google Scholar 

  51. van Wüllen C (2005). Chem Phys 311:105–112

    Article  Google Scholar 

  52. Wolf A, Reiher M, Hess BA (2004). J Chem Phys 120:8624–8631

    Article  CAS  Google Scholar 

  53. Neese F, Wolf A, Fleig T, Reiher M, Hess BA (2005). J Chem Phys 122:204107

    Article  Google Scholar 

  54. Samzow R, Hess BA (1991). Chem Phys Lett 184:491–495

    Article  CAS  Google Scholar 

  55. Samzow R, Hess BA, Jansen G (1992). J Chem Phys 96:1227–1231

    Article  CAS  Google Scholar 

  56. Hess BA, Marian CM, Wahlgren U, Gropen O (1996). Chem Phys Lett 251:365–371

    Article  CAS  Google Scholar 

  57. Boettger JC (2000). Phys Rev B 62:7809–7815

    Article  CAS  Google Scholar 

  58. Mayer M, Krüger S, Rösch N (2001). J Chem Phys 115:4411–4423

    Article  CAS  Google Scholar 

  59. Matveev A, Rösch N (2003). J Chem Phys 118:3997–4012

    Article  CAS  Google Scholar 

  60. Majumder S, Matveev AV, Rösch N (2003). Chem Phys Lett 382:186–193

    Article  CAS  Google Scholar 

  61. Nakajima T, Hirao K (2003). J Chem Phys 119:4105–4111

    Article  CAS  Google Scholar 

  62. Peralta JE, Scuseria GE (2004). J Chem Phys 120:5875–5881

    Article  CAS  Google Scholar 

  63. Nasluzov VA, Rösch N (1996). Chem Phys 210:413–425

    Article  CAS  Google Scholar 

  64. Kellö V, Sadlej AJ (1998). Int J Quant Chem 68:159–174

    Article  Google Scholar 

  65. Fukuda R, Hada M, Nakatsuji H (2002). J Chem Phys 118:1015–1026

    Article  Google Scholar 

  66. Fukuda R, Hada M, Nakatsuji H (2002). J Chem Phys 118:1027–1035

    Article  Google Scholar 

  67. Malkin I, Malkina OL, Malkin VG (2002). Chem Phys Lett 361:231–236

    Article  CAS  Google Scholar 

  68. Malkin I, Malkina OL, Malkin VG, Kaupp M (2004). Chem Phys Lett 396:268–276

    Article  CAS  Google Scholar 

  69. Nakajima T, Hirao K (2000). Chem Phys Lett 329:511–516

    Article  CAS  Google Scholar 

  70. Lee YS, McLean AD (1982). J Chem Phys 76:735–736

    Article  CAS  Google Scholar 

  71. Stanton RE, Havriliak S (1984). J Chem Phys 81:1910–1918

    Article  CAS  Google Scholar 

  72. Siedentop H, Stockmeyer E (2005). Phys Lett A 341: 473–478

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Physikalische Chemie, Friedrich-Schiller-Universität Jena, Helmholtzweg 4, 07743, Jena, Germany

    Markus Reiher

Authors
  1. Markus Reiher
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Markus Reiher.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reiher, M. Douglas–Kroll–Hess Theory: a relativistic electrons-only theory for chemistry. Theor Chem Acc 116, 241–252 (2006). https://doi.org/10.1007/s00214-005-0003-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00214-005-0003-2

Keywords

Search

Navigation