Skip to main content
Log in

Electron correlation studies by means of local-scaling transformations and electron-pair density functions

  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Electron correlation is one long standing problem of computational electronic structure theory. Even more, with the advent of the density functional theory and, in particular, with its Kohn–Sham implementation, the separation of the non-dynamical and dynamical components of the electron correlation has became an unavoidable requirement towards construction of reliable exchange-correlation functionals. In this paper, we address the analysis of the separation of the non-dynamical and dynamical electron correlation effects from two complementary viewpoints, namely, analysis of the correlation energy components and the analysis of the electron-pair density. The former approach will make use of the local-scaling transformations and the latter will be based on the study of intracule and extracule densities.

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

Access this article

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

Reference

  1. Methods and Techniques in Computational Chemistry, METECC-94, ed. E. Clementi (STEF, Cagliari, 1993).

  2. P.-O. Löwdin (1959) Adv. Chem. Phys. 2 207

    Google Scholar 

  3. K Ruedenberg L.M. Cheung S.T. Elbert (1979) Int. J. Quant. Chem. 16 1069

    Google Scholar 

  4. B.O. Roos (1980) Int. J. Quant. Chem. Symp. 14 175

    Google Scholar 

  5. O. Sinanoğlu (1964) Adv. Chem. Phys. 6 315

    Google Scholar 

  6. K. Nakayama K. Hirao R. Lindh (1999) Chem. Phys. Lett. 300 303

    Google Scholar 

  7. J.D. Goddard G. Orlova (1999) J. Chem. Phys. 111 7705

    Google Scholar 

  8. J.P. Perdew A. Savin K. Burke (1995) Phys. Rev. A 51 4531

    Google Scholar 

  9. J. Gräfenstein D. Cremer (2000) Chem. Phys. Lett. 316 569

    Google Scholar 

  10. P.R.T. Schipper O.V. Gritsenko E.J. Baerends (1999) J. Chem. Phys. 111 329

    Google Scholar 

  11. V.A. Rassolov (1999) J. Chem. Phys. 110 3672

    Google Scholar 

  12. J. Cioslowski (1991) Phys. Rev. A 43 1223

    Google Scholar 

  13. E. Valderrama E.V. Ludeña J. Hinze (1997) J. Chem. Phys. 106 9227

    Google Scholar 

  14. A.J. Thakkar (1987) NoChapterTitle R. Erdahl V.H. Smith SuffixJr (Eds) Density Matrices and Density Functionals Reidel Dordrecht 553–581

    Google Scholar 

  15. R.J. Boyd J.M. Ugalde (1992) NoChapterTitle S. Fraga (Eds) Computational Chemistry, Part A Elsevier Amsterdam 273–299

    Google Scholar 

  16. E. Valderrama J.M. Ugalde R.J. Boyd (2000) NoChapterTitle J. Cioslowski (Eds) Advances in the Theory of Many-Electron Densities and Reduced Density Matrices Kluwer Academic/Plenum Publishers Holland 231–248

    Google Scholar 

  17. J. Cioslowski G. Liu (1996) J. Chem. Phys. 105 8187

    Google Scholar 

  18. C. Sarasola L. Dominguez M. Aguado J.M. Ugalde (1992) J. Chem. Phys. 96 6778

    Google Scholar 

  19. X. Fradera M. Duran J. Mestres (1997) J. Chem. Phys. 107 3576

    Google Scholar 

  20. J.M. Ugalde R.J. Boyd (1986) Int. J. Quant. Chem. 29 1

    Google Scholar 

  21. R.J. Boyd C. Sarasola J.M. Ugalde (1988) J. Phys. B 21 2555

    Google Scholar 

  22. J. Wang A.N. Tripathi V.H. Smith SuffixJr (1992) J. Chem. Phys. 97 9188

    Google Scholar 

  23. J. Cioslowski G. Liu (1999) J. Chem. Phys. 110 1882

    Google Scholar 

  24. J. Cioslowski G. Liu J. Rychlewski W. Cancek J. Komasa (1999) J. Chem. Phys. 111 3401

    Google Scholar 

  25. T. Koga (1990) J. Chem. Phys. 93 5856

    Google Scholar 

  26. T. Tsuneda T. Suzumura K. Hirao (1999) J. Chem. Phys. 110 10664

    Google Scholar 

  27. P.R.T. Schipper O.V. Gritsenko E.J. Baerends (1998) Phys. Rev. A 57 1729

    Google Scholar 

  28. T. Koga H. Matsuyama (1999) Int. J. Quant. Chem. 74 455

    Google Scholar 

  29. J.M. Ugalde C. Sarasola (1994) Phys. Rev. A 49 3081

    Google Scholar 

  30. T. Koga H. Matsuyama (1997) J. Chem. Phys. 107 10062

    Google Scholar 

  31. J.M. Mercero J.E. Fowler C. Sarasola J.M. Ugalde (1999) Phys. Rev. A 59 4255

    Google Scholar 

  32. E.V. Ludeña R. López-Boada V. Karasiev R. Pino E. Valderrama J. Maldonado R. Colle J. Hinze (1999) Adv. Quant. Chem. 33 47

    Google Scholar 

  33. E.V. Ludeña R. López-Boada V. Karasiev E. Valderrama J. Maldonado (1999) J. Comp. Chem. 20 155

    Google Scholar 

  34. J. Cioslowski (1988) Phys. Rev. Lett. 60 2141

    Google Scholar 

  35. E.S. Kryachko E.V. Ludeña (1991) J. Chem. Phys. 95 9054

    Google Scholar 

  36. E.K.U. Gross M. Petersilka T. Grabo ACS Series (1996) Density Funct. Methods Chem. 629 42

    Google Scholar 

  37. A. Görling M. Ernzerhof (1995) Phys. Rev. A 51 4501

    Google Scholar 

  38. R. McWeeny (1959) Proc. R. Soc. Lond. A 253 242

    Google Scholar 

  39. R. McWeeny (1960) Rev. Mod. Phys. 32 335

    Google Scholar 

  40. E. Valderrama E.V. Ludeña J. Hinze (1999) J. Chem. Phys. 110 2343

    Google Scholar 

  41. J. Linderberg H. Shull (1960) J. Mol. Spectr. 5 1

    Google Scholar 

  42. O. Jitrik C.F. Bunge (1997) Phys. Rev. A 56 2614

    Google Scholar 

  43. E.R. Davidson S.A. Hagstrom S.J. Chakravorty V.M. Umar C. Froese-Fischer (1991) Phys. Rev. A 44 7071

    Google Scholar 

  44. S.J. Chakravorty S.R. Gwaltney E.R. Davidson F.A. Parpia C. Froese-Fischer (1993) Phys. Rev. A 47 3649

    Google Scholar 

  45. E.V. Ludeña R. Lopez-Boada J. Maldonado T. Koga E.S. Kryachko (1993) Phys. Rev. A 48 1937

    Google Scholar 

  46. A.J. Thakkar N.J. Moore (1981) Int. J. Quant. Chem. Symp. 15 393

    Google Scholar 

  47. A.J. Thakkar A.N. Tripathi V.H. Smith Jr (1984) Int. J. Quant. Chem. 26 157

    Google Scholar 

  48. X. Fradera C. Sarasola J.M. Ugalde R.J. Boyd (1999) Chem. Phys. Lett. 304 393

    Google Scholar 

  49. E. Valderrama J.M. Mercero J.M. Ugalde (2001) J. Phys. B 34 275

    Google Scholar 

  50. T. Koga H. Matsuyama (1997) J. Phys. B 30 5631

    Google Scholar 

  51. T. Koga (1998) J. Chem. Phys. 108 2515

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jesus M. Ugalde.

Additional information

Work supported by grant 9/UPV-00203.215-13527/2001of the Office of Universities and Research of the The Goverment of the Basque Country and, by grant BQU2001-0208 of the Spanish Ministry of Education and Science.

Partially supported by grant G-97000741 of CONICIT of Venezuela.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Valderrama, E.G., Ugalde, J.M. Electron correlation studies by means of local-scaling transformations and electron-pair density functions. J Math Chem 37, 211–231 (2005). https://doi.org/10.1007/s10910-004-1465-5

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-004-1465-5

Keywords

Navigation