Advertisement

Static correlated functionals for reduced density matrix functional theory

  • Carlos L. Benavides-RiverosEmail author
  • Miguel A. L. Marques
Regular Article
First Online:
Part of the following topical collections:
  1. Topical issue: Special issue in honor of Hardy Gross

Abstract

Based on recent progress on fermionic exchange symmetry we propose a way to develop new functionals for reduced density matrix functional theory. For some settings with an odd number of electrons, by assuming saturation of the inequalities stemming from the generalized Pauli principle, the many-body wave-function can be written explicitly in terms of the natural occupation numbers and the natural orbitals. This leads to an expression for the two-particle reduced density matrix and therefore for the correlation energy functional. This functional is tested for a three-electron Hubbard model where it shows excellent performance both in the weak and strong correlation regimes.

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

References

  1. 1.
    T.L. Gilbert, Phys. Rev. B 12, 2111 (1975) ADSCrossRefGoogle Scholar
  2. 2.
    K. Pernal, K.J.H. Giesbertz, Top. Curr. Chem. 368, 125 (2016) CrossRefGoogle Scholar
  3. 3.
    A.J. Coleman, Rev. Mod. Phys. 35, 668 (1963) ADSCrossRefGoogle Scholar
  4. 4.
    A. Klyachko, J. Phys. 36, 72 (2006) Google Scholar
  5. 5.
    M. Altunbulak A. Klyachko, Commun. Math. Phys. 282, 287 (2008) ADSCrossRefGoogle Scholar
  6. 6.
    C. Schilling, D. Gross, M. Christandl, Phys. Rev. Lett. 110, 040404 (2013) ADSCrossRefGoogle Scholar
  7. 7.
    C.L. Benavides-Riveros, J.M. Gracia-Bondia, M. Springborg, Phys. Rev. A 88, 022508 (2013) ADSCrossRefGoogle Scholar
  8. 8.
    R. Chakraborty, D.A. Mazziotti, Phys. Rev. A 89, 042505 (2014) ADSCrossRefGoogle Scholar
  9. 9.
    R. Chakraborty, D.A. Mazziotti, Phys. Rev. A 91, 010101 (2015) ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    C.L. Benavides-Riveros, M. Springborg, Phys. Rev. A 92, 012512 (2015) ADSCrossRefGoogle Scholar
  11. 11.
    C. Schilling, Phys. Rev. A 91, 022105 (2015) ADSCrossRefGoogle Scholar
  12. 12.
    C.L. Benavides-Riveros, N.N. Lathiotakis, M.A.L. Marques, Phys. Chem. Chem. Phys. 19, 12655 (2017) CrossRefGoogle Scholar
  13. 13.
    R. Chakraborty, D.A. Mazziotti, J. Chem. Phys. 148, 054106 (2018) ADSCrossRefGoogle Scholar
  14. 14.
    A.M.K. Müller, Phys. Lett. A 105, 446 (1984) ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    R.L. Frank, E.H. Lieb, R. Seiringer, H. Siedentop, Phys. Rev. A 76, 052517 (2007) ADSCrossRefGoogle Scholar
  16. 16.
    P. Blanchard, J.M. Gracia-Bondía, J.C. Várilly, Int. J. Quant. Chem. 112, 1134 (2012) CrossRefGoogle Scholar
  17. 17.
    M.A. Buijse, E.J. Baerends, Mol. Phys. 100, 401 (2002) ADSCrossRefGoogle Scholar
  18. 18.
    O. Gritsenko, K. Pernal, E.J. Baerends, J. Chem. Phys. 122, 204102 (2005) ADSCrossRefGoogle Scholar
  19. 19.
    S. Goedecker, C.J. Umrigar, Phys. Rev. Lett. 81, 866 (1998) ADSCrossRefGoogle Scholar
  20. 20.
    N.N. Lathiotakis, S. Sharma, J.K. Dewhurst, F.G. Eich, M.A.L. Marques, E.K.U. Gross, Phys. Rev. A 79, 040501 (2009) ADSCrossRefGoogle Scholar
  21. 21.
    J. Cioslowski, K. Pernal, J. Chem. Phys. 111, 3396 (1999) ADSCrossRefGoogle Scholar
  22. 22.
    G. Csányi, S. Goedecker, T.A. Arias, Phys. Rev. A 65, 032510 (2002) ADSCrossRefGoogle Scholar
  23. 23.
    M. Piris, in Natural Orbital Functional Theory (John Wiley &Sons, New Jersey, 2007), pp. 385–427 Google Scholar
  24. 24.
    M. Piris, Phys. Rev. Lett. 119, 063002 (2017) ADSCrossRefGoogle Scholar
  25. 25.
    N.N. Lathiotakis, M.A.L. Marques, J. Chem. Phys. 128, 184103 (2008) ADSCrossRefGoogle Scholar
  26. 26.
    P.J. Stephens, F.J. Devlin, C.F. Chabalowski, M.J. Frisch, J. Phys. Chem. 98, 11623 (1994) CrossRefGoogle Scholar
  27. 27.
    S. Sharma, J.K. Dewhurst, S. Shallcross, E.K.U. Gross, Phys. Rev. Lett. 110, 116403 (2013) ADSCrossRefGoogle Scholar
  28. 28.
    K. Pernal, New J. Phys. 17, 111001 (2015) ADSCrossRefGoogle Scholar
  29. 29.
    S.M. Valone, J. Chem. Phys. 73, 1344 (1980) ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    I. Mayer, I. Pápai, I. Bakó, Á. Nagy, J. Chem. Theory Comput. 13, 3961 (2017) CrossRefGoogle Scholar
  31. 31.
    I. Theophilou, N.N. Lathiotakis, M. Marques, N. Helbig, J. Chem. Phys. 142, 154108 (2015) ADSCrossRefGoogle Scholar
  32. 32.
    A.E. DePrince III, J. Chem. Phys. 145, 164109 (2016) Google Scholar
  33. 33.
    A. Sawicki, A. Huckleberry, M. Kuś, Commun. Math. Phys. 305, 441 (2011) ADSCrossRefGoogle Scholar
  34. 34.
    T. Maciażek, A. Sawicki, J. Phys. A 51, 07LT01 (2018) CrossRefGoogle Scholar
  35. 35.
    C.L. Benavides-Riveros, Chem. Modell. 14, 71 (2018) CrossRefGoogle Scholar
  36. 36.
    R.E. Borland, K. Dennis, J. Phys. B 5, 7 (1972) ADSCrossRefGoogle Scholar
  37. 37.
    C. Schilling, C.L. Benavides-Riveros, P. Vrana, Phys. Rev. A 96, 052312 (2017) ADSCrossRefGoogle Scholar
  38. 38.
    C. Schilling, Phys. Rev. B 92, 155149 2015 ADSCrossRefGoogle Scholar
  39. 39.
    C.L. Benavides-Riveros, C. Schilling, Z. Phys. Chem. 230, 703 (2016) CrossRefGoogle Scholar
  40. 40.
    F. Tennie, V. Vedral, C. Schilling, Phys. Rev. A 94, 012120 (2016) ADSCrossRefGoogle Scholar
  41. 41.
    C. Schilling, M. Altunbulak, S. Knecht, A. Lopes, J.D. Whitfield, M. Christandl, D. Gross, M. Reiher, Phys. Rev. A 97, 052503 (2018) ADSCrossRefGoogle Scholar
  42. 42.
    K. Pernal, Comput. Theor. Chem. 1003, 127 (2013) CrossRefGoogle Scholar
  43. 43.
    M. Piris, J.M. Matxain, X. Lopez, J. Chem. Phys. 139, 234109 (2013) ADSCrossRefGoogle Scholar
  44. 44.
    P. Löwdin, H. Shull, Phys. Rev. 101, 1730 (1956) ADSCrossRefGoogle Scholar
  45. 45.
    R. Gebauer, M.H. Cohen, R. Car, Proc. Natl. Acad. Sci. U.S.A. 113, 12913 (2016) ADSCrossRefGoogle Scholar
  46. 46.
    T. Baldsiefen, A. Cangi, F.G. Eich, E.K.U. Gross, Phys. Rev. A 96, 062508 (2017) ADSCrossRefGoogle Scholar
  47. 47.
    C.L. Benavides-Riveros, J.M. Gracia-Bondía, Phys. Rev. A 87, 022118 (2013) ADSCrossRefGoogle Scholar
  48. 48.
    E. Kamil, R. Schade, T. Pruschke, P.E. Blöchl, Phys. Rev. B 93, 085141 (2016) ADSCrossRefGoogle Scholar
  49. 49.
    C.L. Benavides-Riveros, N.N. Lathiotakis, C. Schilling, M.A.L. Marques, Phys. Rev. A 95, 032507 (2017) ADSCrossRefGoogle Scholar
  50. 50.
    C.L. Benavides-Riveros, M.A.L. Marques, 2018, in preparation Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Carlos L. Benavides-Riveros
    • 1
    Email author
  • Miguel A. L. Marques
    • 1
  1. 1.Institut für Physik, Martin-Luther-Universität Halle-WittenbergHalle (Saale)Germany

Personalised recommendations

Cite article

Buy options