Skip to main content

Advertisement

SpringerLink
Log in

Partitioning the DFT exchange-correlation energy in line with the interacting quantum atoms approach

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

Abstract

The interacting quantum atoms (IQA) energy partition has given important insights about different systems and processes in theoretical chemistry. Given its intrinsic dependence on first- and second-order density matrices, IQA is only cleanly defined within wavefunction methods. This means that, despite the importance of density functional theory (DFT) in electronic structure methods, a neat IQA–DFT implementation is not straightforward. This work addresses this issue through a new implementation of IQA within the Kohn–Sham formalism of DFT in conjunction with hybrid and non-hybrid functionals that contributes further to that already presented (Maxwell et al. in Phys Chem Chem Phys, 2016. doi:10.1039/C5CP07021J). For this purpose, we use additive exchange-correlation (xc) energies, defined within the IQA approach, to scale the one- and two-atom terms of the Kohn–Sham xc energy. This leads to an exact partition of the xc DFT energy of a molecule into intra-atomic and inter-atomic contributions. The suggested method is illustrated with several molecules together with some of the most popular local and hybrid DFT functionals. Overall, we anticipate that the approach put forward in this work will prove useful in getting further insights of phenomena in chemistry which are properly described with DFT .

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

Notes

  1. The McWeeny normalization criterion, \(\int _{\infty } \int _{\infty } \rho _2(\varvec{r}_1,\varvec{r}_2) {\mathrm{d}}\varvec{r}_1 {\mathrm{d}}\varvec{r}_2=N(N-1)\), has been used in Eq. 3.

References

  1. Stone AJ (2013) The theory of intermolecular forces. Oxford University Press, Oxford

    Book  Google Scholar 

  2. Hayes IC, Stone AJ (1984) Mol Phys 53:83

    Article  CAS  Google Scholar 

  3. Hayes IC, Stone AJ (1984) Mol Phys 53:69

    Article  CAS  Google Scholar 

  4. London F (1937) Trans Faraday Soc 33:8

    Article  CAS  Google Scholar 

  5. Longuet-Higgins HC (1965) Discuss Faraday Soc 40:7

    Article  Google Scholar 

  6. Jeziorski B, Moszynski R, Szalewicz K (1994) Chem Rev 94:1887

    Article  CAS  Google Scholar 

  7. Misquitta AJ, Podeszwa R, Jeziorski B, Szalewicz K (2005) J Chem Phys 123:214103

    Article  Google Scholar 

  8. Hobza P, Müller-Dethlefs K (2010) Non-covalent interactions: theory and experiment. Cambridge University Press, Cambridge

    Google Scholar 

  9. Hesselmann A, Jansen G, Schütz M (2006) J Chem Phys 122:014103

    Article  Google Scholar 

  10. Morokuma K (1971) J Chem Phys 55:1236

    Article  CAS  Google Scholar 

  11. Kitaura K, Morokuma K (1976) Int J Quantum Chem 10:325

    Article  CAS  Google Scholar 

  12. Bickelhaupt FM, Evert Jan Baerends EJ (2007) Rev Comput Chem 15:1

    Article  Google Scholar 

  13. Ziegler T, Rauk A (1977) Theor Chem Acc 46:1

    Article  CAS  Google Scholar 

  14. Su P, Li H (2009) J Chem Phys 131:014102

    Article  Google Scholar 

  15. Glendening ED, Streitwieser J (1994) J Chem Phys 100:2900

    Article  CAS  Google Scholar 

  16. Weinhold F (1997) J Mol Struct 399:191

    Google Scholar 

  17. Reed AR, Weinhold F (1983) J Chem Phys 78:4066

    Article  CAS  Google Scholar 

  18. Reed AR, Weinhold F, Curtiss LA, Pochatko DJ (1986) J Chem Phys 84:5687

    Article  CAS  Google Scholar 

  19. Reed AR, Curtiss LA, Weinhold F (1988) Chem Rev 88:899

    Article  CAS  Google Scholar 

  20. Blanco MA, Martín Pendás A, Francisco E (2005) J Chem Theory Comput 1:1096

    Article  CAS  Google Scholar 

  21. Francisco E, Martín Pendás A, Blanco MA (2006) J Chem Theory Comput 2:90

    Article  CAS  Google Scholar 

  22. Tognetti V, Joubert L (2014) Phys Chem Chem Phys 16:14539

    Article  CAS  Google Scholar 

  23. Maxwell P, Martín Pendás A, Popelier PLA (2016) Phys Chem Chem Phys. doi:10.1039/C5CP07021J

    Google Scholar 

  24. Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. Oxford University Press, New York

    Google Scholar 

  25. Becke A (1993) J Chem Phys 98:5648

    Article  CAS  Google Scholar 

  26. Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994) J Phys Chem 98:11623

    Article  CAS  Google Scholar 

  27. McWeeny R (1992) Methods of molecular quantum mechanics, 2nd edn. Academic Press, London

    Google Scholar 

  28. Löwdin PO (1955) Phys Rev 97:1474

    Article  Google Scholar 

  29. Martín Pendás A, Francisco E (2015) Promolden. A qtaim/iqa code (unpublished). A QTAIM/IQA code (Unpublished)

  30. Schmidt MW, Baldridge KK, Boatz JA, Elbert ST, Gordon MS, Jensen JH, Koseki S, Matsunaga N, Nguyen KA, Su SJ, Windus TL, Dupuis M, Montgomery JA (1993) J Comput Chem 14:1347

    Article  CAS  Google Scholar 

  31. Dirac PAM (1930) Proc Camb Philos Soc 26:376

    Article  CAS  Google Scholar 

  32. Vosko SH, Wilk L, Nusair M (1980) Can J Phys 58:1980

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  35. Lebedev VI, Laikov DN (1999) Dokl Math 59:477

    Google Scholar 

  36. Francisco E, Martín Pendás A (2015) Imolint (Unpublished)

  37. Bader RFW (1990) Atoms in molecules. Oxford University Press, Oxford

    Google Scholar 

  38. Martín Pendás A, Blanco MA, Francisco E (2004) J Chem Phys 120:4581

    Article  Google Scholar 

  39. Marques MAL, Oliveira MJT, Burnus T (2012) Comput Phys Commun 183:2272

    Article  CAS  Google Scholar 

  40. Rodríguez JI, Ayers PA, Götz W, Castillo-Alvarado FL (2009) J Chem Phys 131:021101

    Article  Google Scholar 

Download references

Acknowledgments

The authors thank the Spanish MINECO, Grant CTQ2012-31174, for financial support. T. R-R gratefully acknowledges computer time from DGTIC/UNAM (project SC16-1-IG-99) and funding from CONACyT-México and DGAPA/UNAM, Grants 253776 and IN209715 respectively. Additionally, T. R.-R. is also thankful to David Vázquez Cuevas, Gladys Cortés Romero and Magdalena Aguilar Araiza for technical support.

Author information

Authors and Affiliations

  1. Departamento de Química Física y Analítica, Facultad de Química, Universidad de Oviedo, 33006, Oviedo, Spain

    E. Francisco, J. L. Casals-Sainz & A. Martín Pendás

  2. Instituto de Química, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, Delegación Coyoacán, C.P. 04510, Ciudad de México, México

    Tomás Rocha-Rinza

Authors
  1. E. Francisco
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. L. Casals-Sainz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tomás Rocha-Rinza
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Martín Pendás
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Martín Pendás.

Additional information

Published as part of the special collection of articles “Festschrift in honour of A. Vela”.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Francisco, E., Casals-Sainz, J.L., Rocha-Rinza, T. et al. Partitioning the DFT exchange-correlation energy in line with the interacting quantum atoms approach. Theor Chem Acc 135, 170 (2016). https://doi.org/10.1007/s00214-016-1921-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00214-016-1921-x

Keywords

Search

Navigation