Journal of Mathematical Chemistry

, Volume 37, Issue 3, pp 211–231 | Cite as

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

Article

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.

Keywords

intracule electron correlation local scaling Density Functional Theory electron pair density 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Reference

  1. [1]
    Methods and Techniques in Computational Chemistry, METECC-94, ed. E. Clementi (STEF, Cagliari, 1993).Google Scholar
  2. [2]
    Löwdin, P.-O. 1959Adv. Chem. Phys.2207Google Scholar
  3. [3]
    Ruedenberg, K, Cheung, L.M., Elbert, S.T. 1979Int. J. Quant. Chem.161069Google Scholar
  4. [4]
    Roos, B.O. 1980Int. J. Quant. Chem. Symp.14175Google Scholar
  5. [5]
    Sinanoğlu , O. 1964Adv. Chem. Phys.6315Google Scholar
  6. [6]
    Nakayama, K., Hirao, K., Lindh, R. 1999Chem. Phys. Lett.300303Google Scholar
  7. [7]
    Goddard, J.D., Orlova, G. 1999J. Chem. Phys.1117705Google Scholar
  8. [8]
    Perdew, J.P., Savin, A., Burke, K. 1995Phys. Rev. A514531Google Scholar
  9. [9]
    Gräfenstein, J., Cremer, D. 2000Chem. Phys. Lett.316569Google Scholar
  10. [10]
    Schipper, P.R.T., Gritsenko, O.V., Baerends, E.J. 1999J. Chem. Phys.111329Google Scholar
  11. [11]
    Rassolov, V.A. 1999J. Chem. Phys.1103672Google Scholar
  12. [12]
    Cioslowski, J. 1991Phys. Rev. A431223Google Scholar
  13. [13]
    Valderrama, E., Ludeña, E.V., Hinze, J. 1997J. Chem. Phys.1069227Google Scholar
  14. [14]
    Thakkar, A.J. 1987Erdahl, R.Smith, V.H.,Jr eds. Density Matrices and Density FunctionalsReidelDordrecht553581Google Scholar
  15. [15]
    Boyd, R.J., Ugalde, J.M. 1992Fraga, S. eds. Computational Chemistry, Part AElsevierAmsterdam273299Google Scholar
  16. [16]
    Valderrama, E., Ugalde, J.M., Boyd, R.J. 2000Cioslowski, J. eds. Advances in the Theory of Many-Electron Densities and Reduced Density MatricesKluwer Academic/Plenum PublishersHolland231248Google Scholar
  17. [17]
    Cioslowski, J., Liu, G. 1996J. Chem. Phys.1058187Google Scholar
  18. [18]
    Sarasola, C., Dominguez, L., Aguado, M., Ugalde, J.M. 1992J. Chem. Phys.966778Google Scholar
  19. [19]
    Fradera, X., Duran, M., Mestres, J. 1997J. Chem. Phys.1073576Google Scholar
  20. [20]
    Ugalde, J.M., Boyd, R.J. 1986Int. J. Quant. Chem.291Google Scholar
  21. [21]
    Boyd, R.J., Sarasola, C., Ugalde, J.M. 1988J. Phys. B212555Google Scholar
  22. [22]
    Wang, J., Tripathi, A.N., Smith, V.H.,Jr 1992J. Chem. Phys.979188Google Scholar
  23. [23]
    Cioslowski, J., Liu, G. 1999J. Chem. Phys.1101882Google Scholar
  24. [24]
    Cioslowski, J., Liu, G., Rychlewski, J., Cancek, W., Komasa, J. 1999J. Chem. Phys.1113401Google Scholar
  25. [25]
    Koga, T. 1990J. Chem. Phys.935856Google Scholar
  26. [26]
    Tsuneda, T., Suzumura, T., Hirao, K. 1999J. Chem. Phys.11010664Google Scholar
  27. [27]
    Schipper, P.R.T., Gritsenko, O.V., Baerends, E.J. 1998Phys. Rev. A571729Google Scholar
  28. [28]
    Koga, T., Matsuyama, H. 1999Int. J. Quant. Chem.74455Google Scholar
  29. [29]
    Ugalde, J.M., Sarasola, C. 1994Phys. Rev. A493081Google Scholar
  30. [30]
    Koga, T., Matsuyama, H. 1997J. Chem. Phys.10710062Google Scholar
  31. [31]
    Mercero, J.M., Fowler, J.E., Sarasola, C., Ugalde, J.M. 1999Phys. Rev. A594255Google Scholar
  32. [32]
    Ludeña, E.V., López-Boada, R., Karasiev, V., Pino, R., Valderrama, E., Maldonado, J., Colle, R., Hinze , J. 1999Adv. Quant. Chem.3347Google Scholar
  33. [33]
    Ludeña, E.V., López-Boada, R., Karasiev, V., Valderrama, E., Maldonado , J. 1999J. Comp. Chem.20155Google Scholar
  34. [34]
    Cioslowski, J. 1988Phys. Rev. Lett.602141Google Scholar
  35. [35]
    Kryachko, E.S., Ludeña , E.V. 1991J. Chem. Phys.959054Google Scholar
  36. [36]
    Gross, E.K.U., Petersilka, M., Grabo, T., Series, ACS 1996Density Funct. Methods Chem.62942Google Scholar
  37. [37]
    Görling, A., Ernzerhof, M. 1995Phys. Rev. A514501Google Scholar
  38. [38]
    McWeeny, R. 1959Proc. R. Soc. Lond. A253242Google Scholar
  39. [39]
    McWeeny, R. 1960Rev. Mod. Phys.32335Google Scholar
  40. [40]
    Valderrama, E., Ludeña, E.V., Hinze , J. 1999J. Chem. Phys.1102343Google Scholar
  41. [41]
    Linderberg, J., Shull, H. 1960J. Mol. Spectr.51Google Scholar
  42. [42]
    Jitrik, O., Bunge, C.F. 1997Phys. Rev. A562614Google Scholar
  43. [43]
    Davidson, E.R., Hagstrom, S.A., Chakravorty, S.J., Umar, V.M., Froese-Fischer, C. 1991Phys. Rev. A447071Google Scholar
  44. [44]
    Chakravorty, S.J., Gwaltney, S.R., Davidson, E.R., Parpia, F.A., Froese-Fischer, C. 1993Phys. Rev. A473649Google Scholar
  45. [45]
    Ludeña, E.V., Lopez-Boada, R., Maldonado, J., Koga, T., Kryachko , E.S. 1993Phys. Rev. A481937Google Scholar
  46. [46]
    Thakkar, A.J., Moore, N.J. 1981Int. J. Quant. Chem. Symp.15393Google Scholar
  47. [47]
    Thakkar, A.J., Tripathi, A.N., Jr, V.H. Smith 1984Int. J. Quant. Chem.26157Google Scholar
  48. [48]
    Fradera, X., Sarasola, C., Ugalde, J.M., Boyd, R.J. 1999Chem. Phys. Lett.304393Google Scholar
  49. [49]
    Valderrama, E., Mercero, J.M., Ugalde, J.M. 2001J. Phys. B34275Google Scholar
  50. [50]
    Koga, T., Matsuyama, H. 1997J. Phys. B305631Google Scholar
  51. [51]
    Koga, T. 1998J. Chem. Phys.1082515Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Kimika FakultateaEuskal Herriko UnibertsitateaEuskadiSpain

Personalised recommendations