Advertisement

Occupation probabilities as variables in electronic structure theory: cooper pairing, OP-NSOFT-Cs,t, and the homogeneous electron liquid

  • Ralph Gebauer
  • Morrel H. Cohen
  • Roberto Car
Regular Article
  • 39 Downloads
Part of the following topical collections:
  1. Topical issue: Special issue in honor of Hardy Gross

Abstract

The energy functional of a novel electronic structure theory, OP-NSOFT, has as variables the natural spin orbitals (NSO) of the trial function and their joint occupation probabilities in the search for the ground state energy. When occupancy is restricted to the spin-paired NSOs of DOCI, the resulting theory, OP-NSOFT-0, scales as M3, with M the size of the one-electron basis set. Accurate results were obtained for small molecules, particularly near dissociation where single reference theories like DFT are inaccurate. The homogeneous electron liquid (HEL) could serve as a test bed of OP-NSOFT for condensed systems, but OP-NSOFT-0 reduces to the Hartree–Fock approximation for the HEL. Cooper pairing is introduced instead, both singlet pairing, OP-NOFT-Cs, and fully polarized triplet pairing, OP-NSOFT-Ct. The former yields 1/3 of the diffusion-Monte-Carlo correlation energy, the latter 1/2 to 1/3 with decreasing electron density for rs values between 1 and 10. Both yield the discontinuity in the single-particle occupation number required by the Luttinger theorem. Two-state joint occupation probabilities illustrate the importance of electron–electron small-angle scattering in establishing electron correlation in the unpolarized HEL.

References

  1. 1.
    P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964) ADSCrossRefGoogle Scholar
  2. 2.
    W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965) ADSCrossRefGoogle Scholar
  3. 3.
    T.L. Gilbert, Phys. Rev. B 12, 2111 (1975) ADSCrossRefGoogle Scholar
  4. 4.
    M. Piris, Phys. Rev. Lett. 119, 063002 (2017) ADSCrossRefGoogle Scholar
  5. 5.
    R. van Meer, O.V. Gritsenko, E.J. Baerends, J. Chem. Phys. 148, 104102 (2018) ADSCrossRefGoogle Scholar
  6. 6.
    K. Pernal, K.J.H. Giesbertz, Top. Curr. Chem. 368, 125 (2016) CrossRefGoogle Scholar
  7. 7.
    J.M. Herbert, J.E. Harriman, Chem. Phys. Lett. 382, 142 (2003) ADSCrossRefGoogle Scholar
  8. 8.
    M. Piris, Int. J. Quantum Chem. 113, 620 (2013) CrossRefGoogle Scholar
  9. 9.
    M. Piris, J.M. Ugalde, Int. J. Quantum Chem. 114, 1169 (2014) CrossRefGoogle Scholar
  10. 10.
    A.J. Coleman, Rev. Mod. Phys. 35, 668 (1963) ADSCrossRefGoogle Scholar
  11. 11.
    C. Garrod, J.K. Percus, J. Math. Phys. 5, 1756 (1964) ADSCrossRefGoogle Scholar
  12. 12.
    J. Percus, Comput. Theor. Chem. 1003, 2 (2013) CrossRefGoogle Scholar
  13. 13.
    Z. Zhao, B.J. Braams, M. Fukuda, M.L. Overton, J.K. Percus, J. Chem. Phys. 120, 2095 2004 ADSCrossRefGoogle Scholar
  14. 14.
    M. Nakata, H. Nakatusuji, M. Ehara, J. Chem. Phys. 114, 8282 (2001) ADSCrossRefGoogle Scholar
  15. 15.
    G. Gidofalvi, D.A. Mazziotti, J. Chem. Phys. 129, 134108 (2008) ADSCrossRefGoogle Scholar
  16. 16.
    R. Gebauer, M.H. Cohen, R. Car, Proc. Nat. Acad. Sci. 113, 46 (2016); referred to as I. There, the acronym used was OP-NOFT for occupation-probability-based natural-orbital functional theory, which here has been replaced by OP-NSOFT occupation-probability-based natural-spin-orbital functional theory as more accurate CrossRefGoogle Scholar
  17. 17.
    P.O. Löwdin, Phys. Rev. 97, 1474 (1955) ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    D.A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008) ADSCrossRefGoogle Scholar
  19. 19.
    M. Piris, J.M. Matxain, X. Lopez, J. Chem. Phys. 139, 234109 (2013) ADSCrossRefGoogle Scholar
  20. 20.
    D.M. Ceperly, B.J. Alder, Phys. Rev. Lett. 45, 566 (1980) ADSCrossRefGoogle Scholar
  21. 21.
    G. Ortiz, P. Ballone, Phys. Rev. B 50, 1391 (1994) ADSCrossRefGoogle Scholar
  22. 22.
    G. Ortiz, P. Ballone, Erratum Phys. Rev. B 56, 9970 (1997) ADSCrossRefGoogle Scholar
  23. 23.
    N.N. Lathiotakis, N. Helbig, E.K.U. Gross, Phys. Rev. B 75 195120 (2007) ADSCrossRefGoogle Scholar
  24. 24.
    J. Bardeen, L.N. Cooper, J.R. Schrieffer, Phys. Rev. 106, 162 (1957) ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    A.J. Leggett, Phys. Rev. Lett. 29, 1227 (1972) ADSCrossRefGoogle Scholar
  26. 26.
    K. Pernal, J. Cioslowski, J. Chem. Phys. 120, 5987 (2004) ADSCrossRefGoogle Scholar
  27. 27.
    P.W. Ayers, S. Liu, Phys. Rev. A 75, 022514 (2007) ADSCrossRefGoogle Scholar
  28. 28.
    P.W. Ayers, E.R. Davidson, Adv. Chem. Phys. 134, 443 (2007) Google Scholar
  29. 29.
    B. Lukman, J. Koller, B. Borstnik, A. Azman, Mol. Phys. 18, 857 (1970) ADSCrossRefGoogle Scholar
  30. 30.
    W.B. England, J. Phys. Chem. 86, 1204 (1982) CrossRefGoogle Scholar
  31. 31.
    W.B. England, Int. J. Quantum Chem. 23, 905 (1983) CrossRefGoogle Scholar
  32. 32.
    M. Piris, R. Cruz, Int. J. Quantum Chem. 53, 353 (1995) CrossRefGoogle Scholar
  33. 33.
    M. Piris, L.A. Montero, N. Cruz, J. Chem. Phys. 107, 180 (1997) ADSCrossRefGoogle Scholar
  34. 34.
    V.N. Staroverov, G.E. Scuseria, J. Chem. Phys. 117, 2489 (2002) ADSCrossRefGoogle Scholar
  35. 35.
    V.N. Staroverov, G.E. Scuseria, J. Chem. Phys. 117, 11107 (2002) ADSCrossRefGoogle Scholar
  36. 36.
    G. Csanyi, T.A. Arias, Phys. Rev. B 61 7348 (2000) ADSCrossRefGoogle Scholar
  37. 37.
    M. Piris, P. Otto, J. Chem. Phys. 112, 8187 (2000) ADSCrossRefGoogle Scholar
  38. 38.
    J.M. Blatt, Prog. Theor. Phys. 23, 447 (1960) ADSCrossRefGoogle Scholar
  39. 39.
    A.J. Coleman, J. Math. Phys. 6, 1425 (1965) ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    S. Bratoz, P.h. Durand, J. Chem. Phys. 43, 2670 (1965) ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    J.M. Luttinger, Phys. Rev. 119, 1153 (1960) ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    F. Bloch, Z. Phys. 57, 545 (1929) ADSCrossRefGoogle Scholar
  43. 43.
    F.H. Zong, C. Lin, D.M. Ceperley, Phys. Rev. E 66, 036703 (2002) ADSCrossRefGoogle Scholar
  44. 44.
    D. Ceperley, Phys. Rev. B 18, 3126 (1978) ADSCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • Ralph Gebauer
    • 1
  • Morrel H. Cohen
    • 2
    • 3
  • Roberto Car
    • 3
    • 4
  1. 1.The Abdus Salam International Centre for Theoretical PhysicsTriesteItaly
  2. 2.Department of Physics and AstronomyRutgers UniversityPiscatawayUSA
  3. 3.Department of ChemistryPrinceton UniversityPrincetonUSA
  4. 4.Department of PhysicsPrinceton UniversityPrincetonUSA

Personalised recommendations