Skip to main content
SpringerLink
Log in

The self-interaction error and the description of non-dynamic electron correlation in density functional theory

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

Abstract

The self-interaction error (SIE) plays a central role in density functional theory (DFT) when carried out with approximate exchange-correlation functionals. Its origin, properties, and consequences for the development of standard DFT to a method that can correctly describe multi-reference electron systems by treating dynamic and non-dynamic electron correlation on an equal footing, is discussed. In this connection, the seminal work of Colle and Salvetti on wave function-based correlation functionals that do no longer suffer from a SIE is essential. It is described how the Colle–Salvetti correlation functional is an anchor point for the derivation of a functional multi-reference DFT method.

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

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Hohenberg P, Kohn W (1964) Phys Rev 136:B864–B871

    Article  Google Scholar 

  2. Kohn W, Sham LJ (1965) Phys Rev 140:A1133–A1138

    Article  Google Scholar 

  3. Slater J (1951) Phys Rev 81:385–390

    Article  CAS  Google Scholar 

  4. Becke AD (1988) Phys Rev A 38:3098–3100

    Article  CAS  Google Scholar 

  5. Perdew JP (1991) Electronic structure of solids 91. In: Ziesche P, Eschrig H (eds) Akademie-Verlag, Berlin, pp 11–20

  6. Perdew JP, Wang Y (1992) Phys Rev B 45:13244–13249

    Article  Google Scholar 

  7. Adamo C, Barone V (1998) J Chem Phys 108:664–675

    Article  CAS  Google Scholar 

  8. Vosko S, Wilk L, Nusair M (1980) Can J Phys 58:1200–1211

    Article  CAS  Google Scholar 

  9. Lee C, Yang W, Parr R (1988) Phys Rev B 37:785–789

    Article  CAS  Google Scholar 

  10. Becke AD (1993) J Chem Phys 98:1372–1377

    Article  CAS  Google Scholar 

  11. Becke AD (1993) J Chem Phys 98:5648–5652

    Article  CAS  Google Scholar 

  12. Becke AD (1996) J Chem Phys 104:1040–1046

    Article  CAS  Google Scholar 

  13. Perdew JP, Burke K, Ernzerhof M (1996) Phys Rev Lett 77:3865–3868

    Article  Google Scholar 

  14. Perdew JP, Burke K, Ernzerhof M (1997) Phys Rev Lett 78:1396(E)

    Google Scholar 

  15. Van Voorhis T, Scuseria GE (1998) J Chem Phys 109:400–410

    Article  Google Scholar 

  16. Zhao Y, Schultz NE, Truhlar DG (2005) J Chem Phys 123:161103

    Article  CAS  Google Scholar 

  17. Cremer D (2001) Mol Phys 99:1899–1940

    Article  CAS  Google Scholar 

  18. Gräfenstein J, Hjerpe AM, Kraka E, Cremer D (2000) J Phys Chem A 104:1748–1761

    Article  CAS  Google Scholar 

  19. Gräfenstein J, Kraka E, Filatov M, Cremer D (2002) Int J Mol Sci 3:360–394

    Article  Google Scholar 

  20. Ziegler T, Rauk A, Baerends EJ (1977) Theor Chim Acta 43:261–271

    Article  CAS  Google Scholar 

  21. Lie GC, Clementi E (1974) J Chem Phys 60:1275–1287

    Article  CAS  Google Scholar 

  22. Lie GC, Clementi E (1974) J Chem Phys 60:1288–1296

    Article  CAS  Google Scholar 

  23. Colle R, Salvetti O (1975) Theor Chim Acta 37:329–334

    Article  CAS  Google Scholar 

  24. Colle R, Salvetti O (1979) Theor Chim Acta 53:55–63

    Article  CAS  Google Scholar 

  25. Colle R, Salvetti O (1983) J Chem Phys 79:1404–1407

    Article  CAS  Google Scholar 

  26. Savin A (1988) Int J Quantum Chem S 22:59–69

    Article  CAS  Google Scholar 

  27. Kraka E (1992) Chem Phys 161:149–153

    Article  CAS  Google Scholar 

  28. Kraka E, Cremer D, Nordholm S (1992) Molecules in natural science and biomedicine. In: Maksic ZB, Eckert-Maksic M (eds) Ellis Horwood, Chichester, pp 351–374

  29. Colle R, Salvetti O (1990) J Chem Phys 93:534–544

    Article  CAS  Google Scholar 

  30. Miehlich B, Savin A, Stoll H (1997) Mol Phys 91:527–536

    Article  CAS  Google Scholar 

  31. Panas I (1995) Chem Phys Lett 245:171–177

    Article  CAS  Google Scholar 

  32. Leininger T, Stoll H, Werner HJ, Savin A (1997) Chem Phys Lett 275:151–160

    Article  CAS  Google Scholar 

  33. Filatov M, Shaik S (1999) Chem Phys Lett 304:429–437

    Article  CAS  Google Scholar 

  34. Filatov M, Shaik S (2000) Chem Phys Lett 332:409–419

    Article  CAS  Google Scholar 

  35. Gräfenstein J, Cremer D (2000) Chem Phys Lett 316:569–577

    Article  Google Scholar 

  36. Gräfenstein J, Cremer D (2000) Phys Chem Chem Phys 2:2091–2103

    Article  Google Scholar 

  37. McDouall JJW (2003) Mol Phys 101:361–371

    Article  CAS  Google Scholar 

  38. San-Fabian E, Pastor-Abia L (2003) Int J Quantum Chem 91:451–460

    Article  CAS  Google Scholar 

  39. Gräfenstein J, Cremer D (2005) Mol Phys 103:279–308

    Article  CAS  Google Scholar 

  40. Goll E, Werner HJ, Stoll H (2005) Phys Chem Chem Phys 7:3917–3923

    Article  CAS  Google Scholar 

  41. Gusarov S, Malmqvist PA, Lindh R, Roos BO (2004) Theor Chem Acc 112:84–94

    CAS  Google Scholar 

  42. Yamanaka S, Nakata K, Takada T, Kusakabe K, Ugaide JM, Yamaguchi K (2006) Chem Lett 35:242–247

    Article  CAS  Google Scholar 

  43. Perdew JP, Zunger A (1981) Phys Rev B 23:5048–5079

    Article  CAS  Google Scholar 

  44. Fermi E, Amaldi E (1934) Accad Ita Roma 6:119–149

    CAS  Google Scholar 

  45. Thomas LH (1927) Proc Camb Philol Soc 23:542–548

    Article  CAS  Google Scholar 

  46. Fermi E (1927) Rend Accad Lincei 6:602–607

    CAS  Google Scholar 

  47. Polo V, Kraka E, Cremer D (2002) Theor Chem Acc 107:291–303

    CAS  Google Scholar 

  48. Polo V, Gräfenstein J, Kraka E, Cremer D (2002) Chem Phys Lett 352:469–478

    Article  CAS  Google Scholar 

  49. Cremer D, Filatov M, Polo V, Kraka E, Shaik S (2002) Int J Mol Sci 3:604–638

    Article  CAS  Google Scholar 

  50. Polo V, Gräfenstein J, Kraka E, Cremer D (2003) Theor Chem Acc 109:22–35

    CAS  Google Scholar 

  51. Gräfenstein J, Kraka E, Cremer D (2004) J Chem Phys 120:524–539

    Article  CAS  Google Scholar 

  52. Gräfenstein J, Kraka E, Cremer D (2004) Phys Chem Chem Phys 6:1096–1112

    Article  CAS  Google Scholar 

  53. He Y, Gräfenstein J, Kraka E, Cremer D (2000) Mol Phys 98:1639–1658

    Article  CAS  Google Scholar 

  54. Polo V, Kraka E, Cremer D (2002) Mol Phys 100:1771–1790

    Article  CAS  Google Scholar 

  55. Cremer D (1998) Encyclopedia of computational chemistry. In: Schleyer PvR, Allinger NL, Clark T, Gasteiger J, Kollman PA, Schaefer HF, Schreiner P (eds) John Wiley, Chichester, vol 3, pp 1706–1735

  56. Raghavachari K, Trucks GW, Pople JA, Head-Gordon M (1989) Chem Phys Lett 157:479–483

    Article  CAS  Google Scholar 

  57. Crawford TD, Schaefer HF (2000) Reviews in computational chemistry. In: Lipkowitz KB, Boyd DB (eds) VCH, Weinheim, vol 14, pp 33–136

  58. He Z, Cremer D (1991) Int J Quantum Chem Symp 25:43–70

    Article  CAS  Google Scholar 

  59. He Z, Cremer D (1993) Theor Chim Acta 85:305–323

    Article  CAS  Google Scholar 

  60. Grimme S, Antony J, Schwabe T, Mück-Lichtenfeld C (2007) Org Biomol Chem 5:741–758

    Article  CAS  Google Scholar 

  61. Gräfenstein J, Cremer D (2009) J Chem Phys 130

  62. Leininger T, Stoll H, Werner HJ, Savin A (1997) Chem Phys Lett 275:151–160

    Article  CAS  Google Scholar 

  63. Adamson RD, Dombroski JP, Gill PMW (1999) J Comput Chem 20:921–927

    Article  CAS  Google Scholar 

  64. Kamiya M, Tsuneda T, Hirao K (2002) J Chem Phys 117:6010–6015

    Article  CAS  Google Scholar 

  65. Harris J (1984) Phys Rev A 29:1648–1659

    Article  CAS  Google Scholar 

  66. Ruedenberg K, Cheung LM, Elbert ST (1979) Int J Quantum Chem 16:1069–1101

    Article  Google Scholar 

  67. Roos BO (1980) Int J Quantum Chem Symp 14:175–189

    CAS  Google Scholar 

  68. Bobrowicz FW, Goddard WA III (1977) Methods of electronic structure theory. In: Schaefer HF III (ed) Modern theoretical chemistry, vol 3. Plenum Press, New York, pp 79–127

  69. Andersson K, Roos B (199x) Modern electron structure theory. In: Yarkony DR (ed) Advanced series in physical chemistry, vol 2, Part I. World Scientific, Singapore, pp 55–109

  70. McDouall JJW, Peasley K, Robb MA (1988) Chem Phys Lett 148:183–189

    Article  CAS  Google Scholar 

  71. Wolinski K, Sellers HL, Pulay P (1987) Chem Phys Lett 140:225–231

    Article  CAS  Google Scholar 

  72. Jastrow R (1955) Phys Rev 98:1479–1484

    Article  Google Scholar 

  73. Stoll H, Pavlidou C, Preuss H (1978) Theor Chim Acta 49:143–149

    Article  CAS  Google Scholar 

  74. Staroverov VN, Davidson ER (2000) Chem Phys Lett 330:161–168

    Article  CAS  Google Scholar 

  75. Staroverov VN, Davidson ER (2001) Chem Phys Lett 340:142–150

    Article  CAS  Google Scholar 

  76. Konkoli Z, He Z, Cremer D (1997) Theor Chem Acc 96:71–74

    CAS  Google Scholar 

  77. Ruzsinsky A, Perdew JP Csonka G, Vydrov OA, Scuseria GE (2006) J Chem Phys 125:194112

    Article  CAS  Google Scholar 

  78. Ruzsinsky A, Perdew JP, Csonka G, Vydrov OA, Scuseria GE (2007) J Chem Phys 126:104102

    Google Scholar 

  79. Cohen AJ, Mori-Sánchez P, Yang WT (2008) Science 321:792–794

    Article  CAS  Google Scholar 

  80. Körzdörfer T, Kümmel S, Mundt M (2008) J Chem Phys 129:014110

    Article  CAS  Google Scholar 

  81. Kümmel S, Perdew JP (2003) Mol Phys 101:1363–1368

    Article  CAS  Google Scholar 

  82. Singh R, Massa L, Sahni V (1999) Phys Rev A 60:4135–4139

    Article  CAS  Google Scholar 

  83. Tao J, Gori-Giorgi P, Perdew JP, McWeeny R (2001) Phys Rev A 63:032513

    Article  CAS  Google Scholar 

  84. Caratzoulas S, Knowles PJ (2000) Mol Phys 98:1811–1821

    Article  CAS  Google Scholar 

  85. Moscardó F (2007) Theor Chem Acc 118:631–635

    Article  CAS  Google Scholar 

  86. Moscardó F, San-Fabián E, Pastor-Abia L (2006) Theor Chem Acc 115:334–342

    Article  CAS  Google Scholar 

Download references

Acknowledgments

DC thanks the University of the Pacific for support. Support by the NSF under grant CHE 071893 is acknowledged.

Author information

Authors and Affiliations

  1. Department of Chemistry, University of Gothenburg, 412 96, Göteborg, Sweden

    Jürgen Gräfenstein

  2. Department of Chemistry, University of the Pacific, 3601 Pacific Ave., Stockton, CA, 95211-0110, USA

    Dieter Cremer

  3. Department of Physics, University of the Pacific, 3601 Pacific Ave., Stockton, CA, 95211-0110, USA

    Dieter Cremer

Authors
  1. Jürgen Gräfenstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dieter Cremer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dieter Cremer.

Additional information

Dedicated to the memory of Professor Oriano Salvetti and published as part of the Salvetti Memorial Issue.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gräfenstein, J., Cremer, D. The self-interaction error and the description of non-dynamic electron correlation in density functional theory. Theor Chem Acc 123, 171–182 (2009). https://doi.org/10.1007/s00214-009-0545-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00214-009-0545-9

Keywords

Search

Navigation