Skip to main content
SpringerLink
Log in

Ab initio dynamic correlation effects in density functional theories: a density based study for argon

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

Abstract

In an attempt to get more insight into the links between the coverage of dynamic electron correlation effects defined in traditional wave function theories (WFT) by density functional theories (DFT) we have performed comprehensive studies for the Ar atom, for which the dynamic correlation effects play the dominant role. A density-based approach directly hinged on difference radial density (DRD) distributions defined with respect the Hartree-Fock radial density has been employed for analyzing the impact of dynamic correlation effects on the density. The DRD-distributions calculated by ab initio methods have been compared with their DFT counterparts generated for representatives of several generations of broadly used exchange-correlation functionals and for the recently developed orbital-dependent OEP2 exchange-correlation functional (Bartlett et al. in J Chem Phys 122:034104, 2005). For the local, generalized-gradient, and hybrid functionals it has been found that the dynamic WFT correlation effects on the density are to a significant extent accounted for by densities resulting from exchange-only calculations. It has been shown that the removal of self-interaction errors does not change this result. It has been demonstrated that the VWN5 and LYP correlation functionals do not represent any substantial dynamical correlation effects on the electron density, whereas these effects are well represented by the orbital-dependent OEP2 correlation functional. Critical comparison of the results of the present investigations with various published results obtained for more complex many-electron systems has been made. Attention has been paid to bringing into sharper relief the differences between the conclusions reached when using energy- or density-based criteria.

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
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Baerends EJ (2000) Perspective on Self-consistent equations including exchange and correlation effects. Theor Chem Acc 103:265–269

    CAS  Google Scholar 

  2. Bartlett RJ, Grabowski I, Hirata S, Ivanov S (2005) The exchange-correlation potential in ab initio density functional theory. J Chem Phys 122:034104

    Article  CAS  Google Scholar 

  3. Becke AD (1988) Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 38:3098–3100

    Article  CAS  Google Scholar 

  4. Becke AD (1993) Density–functional thermochemistry, III. The role of exact exchange. J Chem Phys 98:5648–5652

    Article  CAS  Google Scholar 

  5. Becke AD (1996) Density-functional thermochemistry, IV. A new dynamical correlation functional and implications for exact-exchange mixing. J Chem Phys 104:1040–1046

    Article  CAS  Google Scholar 

  6. Bylaska EJ, de Jong WA, Govind N, Kowalski K, Straatsma TP, Valiev M, Wang D, Apra E, Windus TL, Hammond J, Nichols P, Hirata S, Hackler MT, Zhao Y, Fan PD, Harrison RJ, Dupuis M, Smith DMA, Nieplocha J, Tipparaju V, Krishnan M, Wu Q, Voorhis TV, Auer AA, Nooijen M, Brown E, Cisneros GIF, Fruchtl H, Garza J, Hirao K, Kendall R, Nichols JA, Tsemekhman K, Wolinski K, Anchell J, Bernholdt D, Borowski P, Clark T, Clerc D, Dachsel H, Deegan M, Dyall K, Elwood D, Glendening E, Gutowski MAH, Jaffe J, Johnson B, Ju J, Kobayashi R, Kutteh R, Lin Z, Littlefield R, Long X, Meng B, Nakajima T, Niu S, Pollack L, Rosing M, Sandrone G, Stave M, Taylor H, Thomas G, van Lenthe J, Wong A, Zhang Z (2007) A computational chemistry package for parallel computers, vol version 5.1. Pacific Northwest National Laboratory, Richland

    Google Scholar 

  7. Cremer D (2001) Density functional theory: coverage of dynamic and non-dynamic electron correlation effects. Mol Phys 99:1899–1940

    Article  CAS  Google Scholar 

  8. de Proft F, Geerlings P (1994) The effect of electron correlation on the shell structure of atoms. Chem Phys Lett 220:405–410

    Article  Google Scholar 

  9. Dunning TH Jr (1989) Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J Chem Phys 90:1007–1023

    Article  CAS  Google Scholar 

  10. Engel E, Vosko SH (1993) Accurate optimized-potential-model solution for spherical spin-polarized atoms: Evidence for limitations of the exchange-only local spin-density and generalized-gradient approximations. Phys Rev A 47: 2800–2811

    Article  CAS  Google Scholar 

  11. Fertig H, Kohn W (2000) Symmetry of the electron density in Hartree, Hartree-Fock, and density functionals theories. Phys Rev A 62:052511

    Article  Google Scholar 

  12. Filatov M, Cremer D (2005) Calculation of spin-densities within the context of density functional theory. the crucial role of the correlation functional. J Chem Phys 123:124101

    Article  CAS  Google Scholar 

  13. Filippi C, Umrigar CJ, Gonze X (1996) Separation of the exchange-correlation potential into exchange plus correlation: An optimized effective potential approach. Phys Rev A 54:4810–4814

    Article  CAS  Google Scholar 

  14. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Montgomery JA Jr, Kudin TKN, Burant JC, Millam JM, Iyengar SS, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson GA, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasgawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Klene M, Li X, Knox JE, Hratchian HP, Cross JB, Adamo C, Jarmillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski J, Ayala PY, Morokuma K, Voth GA, Salvador P, Dannenberg J, Zakrzewski VG, Dapprich S, Daniels AD, Strain MC, Farkas O, Malick DK, Rabuck AD, Raghavachari K, Foresman JB, Ortiz JV, Cui Q, Baboul AG, Clifford S, Cioslowski J, Stefanov BB, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin RL, Fox DJ, Keith T, Al-Laham MA, Peng CY, Nanayakkara A, Challacombe M, Gill PMW, Johnson B, Chen W, Wong MW, Gonzalez C, Pople JA (2003) Gaussian 03, revision A.1. Gaussian, Inc., Pittsburgh

    Google Scholar 

  15. Görling A (1999) New KS method for molecules based on an exchange charge density generating the exact local KS exchange potential. Phys Rev Lett 83:5459–5462

    Article  Google Scholar 

  16. Grabowski I, Hirata S, Ivanov S, Bartlett RJ (2002) Ab initio density functional theory: OEP-MBPT(2). A new orbital-dependent correlation functional. J Chem Phys 116:4415–4425

    Article  CAS  Google Scholar 

  17. Gräfenstein J, Kraka E, Cremer D (2004) Effect of the self-interaction error for three electron bonds: on the development of new exchange correlation functionals. Phys Chem Chem Phys. 6:1096–1112

    Article  CAS  Google Scholar 

  18. Gritsenko OV, Ensing B, Schipper PRT, Baerends EJ (2000) Comparison of the accurate Kohn-Sham solution with generalized gradient approximations (GGAs) for the S N 2 reaction F − + CH 3 F → FCH 3 + F −: A qualitative rule to predict success of failure of GGAs. J Phys Chem A 104:8558–8565

    Article  CAS  Google Scholar 

  19. Gritsenko OV, Schipper PRT, Baerends EJ (1997) Exchange and correlation energy in density functional theory: Comparison of accurate density functional theory quantities with traditional Hartree-Fock based ones and generalized gradient approximations for the molecules Li 2, N 2, F 2. J Chem Phys 107:5700–5015

    Article  Google Scholar 

  20. Gutlé C, Heully JL, Krieger J, Savin A (2002) Coupled-cluster calculations using local potentials. Phys Rev A 66:012504

    Article  CAS  Google Scholar 

  21. Handy NC, Cohen AJ (2001) Left-right correlation energy. Mol Phys 99:403–412

    Article  CAS  Google Scholar 

  22. Handy NC, Cohen AJ (2002) A dynamical correlation functional. J Chem Phys 116:5411–5418

    Article  CAS  Google Scholar 

  23. Handy NC, Pople JA, Head-Gordon M, Raghavachari K, Trucks GW (1989) Size-consistent Brueckner theory limited to double substitutions. Chem Phys Lett 164:185–192

    Article  CAS  Google Scholar 

  24. Harrison JG (1983) An improved self-interaction-corrected local spin density functional for atoms. J Chem Phys 78:4562–4566

    Article  CAS  Google Scholar 

  25. He Y, Gräfenstein J, Kraka E, Cremer D (2000) What correlation effect are covered by density functional theory? Mol Phys 98:1639–1658

    Article  CAS  Google Scholar 

  26. Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:B864–B871

    Article  Google Scholar 

  27. Ivanov S, Hirata S, Bartlett RJ (1999) Exact exchange treatment for molecules in finite-basis-set Kohn-Sham theory. Phys Rev Lett 83:5455–5458

    Article  CAS  Google Scholar 

  28. Jankowski K, Malinowski P, Polasik M (1980) Second-order correlation energies for F−, Na+1, Mg+2, and Ar+8: Z-dependence of irreducible pair energies. Phys Rev A 22:51–60

    Article  CAS  Google Scholar 

  29. Jankowski K, Nowakowski K, Grabowski I, Wasilewski J (2009) Coverage of dynamic correlation effects by dft functionals: Density-based anlysis for neon. J Chem Phys 130:164102

    Article  CAS  Google Scholar 

  30. Johnson BG, Gill PMW, Pople JA (1993) The performance of a family of density functional methods. J Chem Phys 98:5612–5626

    Article  CAS  Google Scholar 

  31. Karasiev V, Ludena EV (2002) Asymptotically adjusted self-consistent multiplicative parameter exchange-energy method: Application to diatomic molecules. Phys Rev A 65:032515

    Article  CAS  Google Scholar 

  32. Kohn W, Sham LJ (1965) Self–consistent equations including exchange and correlation effects. Phys Rev 140:A1133–A1138

    Article  Google Scholar 

  33. Kohout M, Savin A (1996) Atomic shell structure and electron numbers. Int J Quantum Chem 60:875–882

    Article  CAS  Google Scholar 

  34. Krieger JB, Li Y, Iafrate GJ (1992) Construction and application of an accurate local spin-polarized Kohn-Sham potential with integer discontinuity: exchange-only theory. Phys Rev A 45:101–126

    Article  CAS  Google Scholar 

  35. Krieger JB, Li Y, Iafrate GJ (1993) Self-consistent calculations of atomic properties using self-interaction-free exchange-only kohn-sham potentials. Phys Rev A 47:165–181

    Article  Google Scholar 

  36. Krijn MPCM, Feil D (1988) Accuracy of various approximations to exchange and correlation for the electron density distribution in atoms and small molecules. Chem Phys Lett 150:45–54

    Article  CAS  Google Scholar 

  37. Kümmel S, Perdew JP (2003) Optimized effective potential made simple: Orbital functionals, orbital shifts, and the exact kohn–sham exchange potential. Phys Rev B 68:035103

    Article  CAS  Google Scholar 

  38. Kutzelnigg W (2006) Density functional theory (DFT) and ab-initio quantum chemistry (AIQC). Story of a difficult partnership. In: Lecture series on computer and computational sciences, vol 6. Brill, Leiden, pp 23–62

  39. Lee C, Yang W, Parr RG (1988) Development of the Colle–Salvetti correlation–energy formula into a functional of the electron density. Phys Rev B 37:785–789

    Article  CAS  Google Scholar 

  40. Meyer H, Müller T, Schweig A (1996) Electron correlation effects in position and momentum space: the atoms li through ar. J Mol Struct 360:55–65

    CAS  Google Scholar 

  41. Meyer H, Schweig A, Zittlau W (1982) Effect of triply and quadruply excited configurations on molecular one-electron densities in configuration interaction calculations. Chem Phys Lett 92:637–641

    Article  CAS  Google Scholar 

  42. Misquitta AJ, Podeszwa R, Jeziorski B, Szalewicz K (2005) Intramolecular potentials based on symmetry-adapted perturbation theory with dispersion energies from time-dependent density-functional calculations. J Chem Phys 123:214103

    Article  CAS  Google Scholar 

  43. Møller C, Plesset MS (1934) Note on an approximate treatment for many-electron systems. Phys Rev 36:618–622

    Article  Google Scholar 

  44. Nesbet RK (1958) Brueckner’s theory and the method of superposition of configurations. Phys Rev 109:1632–1638

    Article  CAS  Google Scholar 

  45. Neumann R, Nobes RH, Handy NC (1996) Exchange functionals and potentials. Mol Phys 87:1–36

    Article  CAS  Google Scholar 

  46. Nowakowski K (2009) Dissertation (in Polish). Nicholas Copernicus University, Toruń, Poland

  47. Ortiz-Henarejos E, San-Fabián E (1997) Differences between ab initio and density functional electron densities. Int J Quantum Chem 61:245–252

    Article  CAS  Google Scholar 

  48. Paldus J (2003) In: Wilson S (ed) Handbook of molecular physics and quantum chemistry. Wiley, Chichester, pp 272–313

  49. Pedroza AC (1986) Nonlocal density functionals: comparison with exact results for finite systems. Phys Rev A 33:804–813

    Article  CAS  Google Scholar 

  50. Perdew JP, Ernzerhof M (1998) In: Dobson JF, Vignale G, Das MP (eds) Electronic density functional theory: recent progress, and new directions. Plenum Press, New York, p 31

  51. Perdew JP, Tao ARJ, Staroverov VN, Scuseria GE, Csonka GI (2005) Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits. J Chem Phys 123:062201

    Article  CAS  Google Scholar 

  52. Perdew JP, Zunger A (1981) Self-interaction corrections in density-functional approximations for many-electron systems. Phys Rev B 23:5048–5079

    Article  CAS  Google Scholar 

  53. Polo V, Gräfenstein J, Kraka E, Cremer D (2003) Long-range and short-range Coulomb correlation effects as simulted by Hartree-Fock, local density approximation, and generalized gradient approximation exchange functionals. Theor Chem Acc 109:22–35

    CAS  Google Scholar 

  54. Roos BO, Taylor PR, Siegbahn PEM (1980) A complete active space SCF method (CASSCF) using a density amtrix formulated super-CI approach. Chem Phys 48:157–173

    Article  CAS  Google Scholar 

  55. Seidl M, Perdew JP, Kurth S (2000) Simulation of all-order density-functional perturbation theory, using the second order and the strong-correlation limit. Phys Rev Lett 84:5070–5073

    Article  CAS  Google Scholar 

  56. Sen KD, Slamet M, Sahni V (1993) Atomic shell structure in Hartree-Fock theory. Chem Phys Lett 205:313–316

    Article  CAS  Google Scholar 

  57. Stanton JF, Gauss J, Watts JD, Nooijen M, Oliphant N, Perera SA, Szalay P, Lauderdale WJ, Kucharski S, Gwaltney S, Beck S, Balková A, Bernholdt DE, Baeck KK, Rozyczko P, Sekino H, Hober C, Bartlett RJ (2007) Integral packages included are VMOL (J. Almlöf and P.R. Taylor); VPROPS (P. Taylor) ABACUS; (T. Helgaker, H.J. Aa. Jensen, P. Jörgensen, J. Olsen, and P.R. Taylor): ACES II. Quantum Theory Project, Gainesville, Florida

  58. Talman JD, Shadwick WF (1976) Optimized effective atomic central potential. Phys Rev A 14:36–40

    Article  CAS  Google Scholar 

  59. Valderrama EG, Ugalde JM (2005) Electron correlation studies by means of local-scaling transformations and electron pair density functions. J Math Chem 37:211–231

    Article  CAS  Google Scholar 

  60. van Heusden CM, Kobayashi R, Amos RD, Handy NC (1993) Electron densities from the Brueckner doubles method. Theor Chim Acta 86:25–39

    Article  Google Scholar 

  61. Vosko SH, Wilk L, Nusair M (1980) Accurate spin–dependent electron liquid correlation energies for local spin density calculations: a critical analysis. Can J Phys 58:1200–1211

    Article  CAS  Google Scholar 

  62. Wang J, Eriksson LA, Johnson BG, Boyd RJ (1996) Electron densities of homonuclear diatomic molecules as calculated from density functional theory. J Phys Chem 100:5274–5280

    Article  CAS  Google Scholar 

  63. Wang J, Eriksson LA, Johnson BG, Boyd RJ (1996) Electron densities of homonuclear diatomic molecules as calculated from density functional theory. J Chem Phys 100:5274–5280

    Article  CAS  Google Scholar 

  64. Widmark PO, Malmqvist PA, Roos BO (1990) Density matrix averaged atomic natural orbital (ano) basis sets for correlated molecular wave functions. i. first row atoms. Theor Chim Acc (Theor Chim Acta) 77:291–306

    Article  CAS  Google Scholar 

Download references

Acknowledgments

Dedicated to Professor Sandor Suhai on the ocassion of his 65th birthday and published as part of the Suhai Festschrift issue. This work has been supported during the years 2006–2009 by the Polish Ministry of Higher Education as the research projects No. N204 126 31/2930 and NN204 074 633. We also thank Andrew Teale for the generation of accurate CCSD electron densities.

Author information

Authors and Affiliations

  1. Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University, 87-100, Toruń, Poland

    Karol Jankowski, Krzysztof Nowakowski, Ireneusz Grabowski & Jan Wasilewski

Authors
  1. Karol Jankowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Krzysztof Nowakowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ireneusz Grabowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jan Wasilewski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Karol Jankowski.

Additional information

Dedicated to Professor Sandor Suhai on the occasion of his 65th birthday and published as part of the Suhai Festschrift Issue.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jankowski, K., Nowakowski, K., Grabowski, I. et al. Ab initio dynamic correlation effects in density functional theories: a density based study for argon. Theor Chem Acc 125, 433–444 (2010). https://doi.org/10.1007/s00214-009-0638-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00214-009-0638-5

Keywords

Search

Navigation