Skip to main content
SpringerLink
Log in

Implementation of Orbital Functionals in the Context of Time-Dependent Density-Functional Theory

  • Condensed Matter
  • Published:
Brazilian Journal of Physics Aims and scope Submit manuscript

Abstract

The computational implementation of orbital functionals has become one of the great modern challenges for density-functional theory (DFT). In static cases, the exact procedure of implementing orbital functionals is the so-called optimized effective potential method (OEP). In situations involving temporal variations, in the context of the time-dependent density-functional theory (TDDFT), TDOEP becomes the correct approach. However, both OEP and TDOEP are known by their severe computational costs, and for this reason they are used in a very restricted set of situations. Therefore, the development of approximations is important. In this work, using one-dimensional model systems, we investigate strategies for the implementation of time-dependent orbital functionals, in order to circumvent or avoid the use of TDOEP. We have found that a local scaling approximation to the TDOEP yields encouraging results aiming the numerical implementation of orbital functionals within the TDDFT context.

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
Fig. 8

Similar content being viewed by others

References

  1. P. Hohenberg, W. Kohn, Inhomogeneous electron gas. Phys. Rev. 136, 864–871 (1964)

    Article  ADS  MathSciNet  Google Scholar 

  2. W. Kohn, L. Sham, Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138 (1965)

    Article  ADS  MathSciNet  Google Scholar 

  3. W. Kohn, Nobel lecture: electronic structure of matter-wave functions and density functionals. Rev. Mod. Phys. 71(5), 1253–1266 (1999)

    Article  ADS  Google Scholar 

  4. A. Mattsson, In pursuit of the “divine” functional. Science. 298(5594), 759 (2002)

    Article  Google Scholar 

  5. J. Perdew, A. Ruzsinszky, J. Tao, V. Staroverov, G. Scuseria, G. Csonka, Prescription for the design and selection of density functional approximations: more constraint satisfaction with fewer fits. J. Chem. Phys. 123, 062201 (2005)

    Article  ADS  Google Scholar 

  6. K. Capelle, A bird’s-eye view of density-functional theory. Brazilian J. Phys. 36(4A), 1318–1343 (2006)

    Article  ADS  Google Scholar 

  7. A.J. Cohen, P. Mori-Sánchez, W. Yang, Challenges for density functional theory. Chem. Rev. 112, 289–320 (2012)

    Article  Google Scholar 

  8. E. Runge, E.K.U. Gross, Density-functional theory for time-dependent systems. Phys. Rev. Lett. 52(12), 997–1000 (1984)

    Article  ADS  Google Scholar 

  9. N.T. Maitra, Perspective: fundamental aspects of time-dependent density functional theory. J. Chem. Phys. 144(22), 220901 (2016)

    Article  ADS  Google Scholar 

  10. K. Burke, J. Werschnik, E.K.U. Gross, Time-dependent density functional theory: past, present, and future. J. Chem. Phys. 123(6), 062206 (2005)

    Article  ADS  Google Scholar 

  11. S. Kümmel, L. Kronik, Orbital-dependent density functionals: theory and applications. Rev. Modern Phys. 80(1), 3–60 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  12. S. Kümmel, J. Perdew, Optimized effective potential made simple: orbital functionals, orbital shifts, and the exact Kohn-Sham exchange potential. Phys. Rev. B. 68(3), 35103 (2003)

    Article  ADS  Google Scholar 

  13. C. Ullrich, U. Gossmann, E.K.U. Gross, Time-dependent optimized effective potential. Phys. Rev. Lett. 74(6), 872–875 (1995)

    Article  ADS  Google Scholar 

  14. J. Krieger, Y. Li, G. Iafrate, Systematic approximations to the optimized effective potential: application to orbital-density-functional theory. Phys. Rev. A. 46(9), 5453–5458 (1992)

    Article  ADS  Google Scholar 

  15. C. Ullrich, P.-G. Reinhard, E. Suraud, Simplified implementation of interaction correction in sodium clusters. Phys. Rev. A. 62(5), 53202 (2000)

    Article  ADS  Google Scholar 

  16. M. Cafiero, C. Gonzalez, Approximate self-consistent potentials for density-functional-theory exchange-correlation functionals. Phys. Rev. A. 71(4), 42505 (2005)

    Article  ADS  Google Scholar 

  17. M. Lima, et al., Simple implementation of complex functionals: scaled self-consistency. J. Chem. Phys. 126(14), 144107 (2007)

    Article  ADS  Google Scholar 

  18. T.E. Baker, E.M. Stoudenmire, L.O. Wagner, K. Burke, S.R. White, One dimensional mimicking of electronic structure: the case for exponentials. Phys. Rev. B. 91, 235141 (2015)

    Article  ADS  Google Scholar 

  19. L.O. Wagner, E.M. Stoudenmire, K. Burke, S.R. WHITE, Reference electronic structure calculations in one dimension. Phys. Chem. Chem. Phys. 14, 8581–8590 (2012)

    Article  Google Scholar 

  20. M.E. Bento, D. Vieira, Implementation strategies for orbital-dependent density functionals. Braz. J. Phys. 46, 636 (2016)

    Article  ADS  Google Scholar 

  21. J.W.O. Silva, D. Vieira, Construction of exchange-correlation potentials for strongly interacting one-dimensional systems. Braz. J. Phys. 47, 393 (2017)

    Article  ADS  Google Scholar 

  22. M.B.P. Querne, D. Vieira, Finite temperatures by means of zero kelvin Kohn-Sham formalism of density-functional theory. Braz. J. Phys. 49, 615 (2019)

    Article  ADS  Google Scholar 

  23. A. Benítez, C.R. Proetto, Kohn-sham potential for a strongly correlated finite system with fractional occupancy. Phys. Rev. A. 94, 052506 (2016)

    Article  ADS  Google Scholar 

  24. D. Vieira, Strong correlations in density-functional theory: a model of spin-charge and spin-orbital separations. J. Chem. Theory Comput. 10, 3641 (2014)

    Article  Google Scholar 

  25. D. Vieira, Spin-independent V-representability of Wigner crystal oscillations in one-dimensional Hubbard chains: the role of spin-charge separation. Phys. Rev. B. 86, 075132 (2012)

    Article  ADS  Google Scholar 

  26. D.G. Tempel, T.J. Martínez, N.T. Maitra, Revisiting molecular dissociation in density functional theory: a simple model. J. Chem. Theory Comput. 5, 770 (2009)

    Article  Google Scholar 

  27. J.P. Perdew, A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B. 23, 5048 (1981)

    Article  ADS  Google Scholar 

  28. M. Thiele, E.K.U. Gross, S. Kümmel, Adiabatic approximation in nonperturbative time-dependent density-functional theory. Phys. Rev. Lett. 100(15), 153004 (2008)

    Article  ADS  Google Scholar 

  29. R. van Leeuwen, Mapping from densities to potentials in time-dependent density-functional theory. Phys. Rev. Lett. 82(19), 3863 (1999)

    Article  ADS  Google Scholar 

  30. C. Ullrich, Time-dependent density-functional theory: concepts and applications. Oxford Graduate Texts (2012)

  31. M. Mundt, S. Kümmel, R. van Leeuwen, P.-G. Reinhard, Violation of the zero-force theorem in the time-dependent Krieger-Li-Iafrate approximation. Phys. Rev. A. 75, 050501 (2007)

    Article  ADS  Google Scholar 

  32. H.O. Wijewardane, C. Ullrich, Real-time electron dynamics with exact-exchange time-dependent density-functional theory. Phys. Rev. Lett. 100(5), 56404 (2008)

    Article  ADS  Google Scholar 

  33. D. Vieira, K. Capelle, C. Ullrich, Physical signatures of discontinuities of the time-dependent exchange-correlation potential. Phys. Chem. Chem. Phys. 11, 4647 (2009)

    Article  Google Scholar 

  34. P. Elliott, A. Cangi, S. Pittali, E.K.U. Gross, K. Burke, Almost exact exchange at almost no computational cost in electronic structure. Phys. Rev. A. 92, 022513 (2015)

    Article  ADS  Google Scholar 

  35. P. Mori-Sánchez, A. Cohen, W. Yang, Localization and delocalization errors in density functional theory and implications for band-gap prediction. Phys. Rev. Lett. 100(14), 146401 (2008)

    Article  ADS  Google Scholar 

  36. A. Cohen, Mori-SÁnchez P., W. Yang, Insights into current limitations of density functional theory. Science. 321(5890), 792 (2008)

    Article  ADS  Google Scholar 

  37. N. Helbig, et al., Density functional theory beyond the linear regime: validating an adiabatic local density approximation. Phys. Rev. A. 83, 032503 (2011)

    Article  ADS  Google Scholar 

Download references

Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. The authors also received financial support from the Fundação de Amparo à Pesquisa e Inovação do Estado de Santa Catarina (FAPESC).

Author information

Author notes

  1. Flávia P. de Farias Guarezi

    Present address: Escola de Educação Básica Dr. Tufi Dippe, Joinville, SC, Brazil

Authors and Affiliations

  1. Departamento de Física, Universidade do Estado de Santa Catarina, Joinville, SC, Brazil

    Flávia P. de Farias Guarezi & Daniel Vieira

Authors
  1. Flávia P. de Farias Guarezi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Daniel Vieira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Vieira.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guarezi, F.P.d.F., Vieira, D. Implementation of Orbital Functionals in the Context of Time-Dependent Density-Functional Theory. Braz J Phys 50, 699–710 (2020). https://doi.org/10.1007/s13538-020-00795-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13538-020-00795-2

Keywords

Search

Navigation