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Kinetic Energy Density Functionals from Models for the One-Electron Reduced Density Matrix

  • D. Chakraborty
  • R. Cuevas-Saavedra
  • P. W. Ayers
Chapter

Abstract

Orbital-free kinetic energy functionals can be constructed by writing the one-electron reduced density matrix as an approximate functional of the ground-state electron density. In order to utilize this strategy, one needs to impose appropriate N-representability constraints upon the model 1-electron reduced density matrix. We present several constraints of this sort here, the most powerful of which is based upon the March-Santamaria identity for the local kinetic energy.

Notes

Acknowledgements

Support from Sharcnet, NSERC, and the Canada Research Chairs is appreciated. RCS acknowledges financial support from CONACYT, ITESM and DGRI-SEP.

References

  1. 1.
    W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965).  https://doi.org/10.1103/PhysRev.140.A1133
  2. 2.
    F.R. Manby, P.J. Knowles, A.W. Lloyd, Chem. Phys. Lett. 335(5), 409 (2001).  https://doi.org/10.1016/S0009-2614(01)00075-6
  3. 3.
    P.W. Ayers, S. Liu, Phys. Rev. A 75, 022514 (2007).  https://doi.org/10.1103/PhysRevA.75.022514
  4. 4.
    E.S. Kryachko, E.V. Ludea, Phys. Rev. A 43, 2179 (1991).  https://doi.org/10.1103/PhysRevA.43.2179
  5. 5.
    E.V. Ludeña, J. Mol. Struct. Theochem 709(1), 25 (2004), A Collection of Papers Presented at the 29th International Congress of Theoretical Chemists of Latin Expression, Marrakech, Morocco, 8–12 September 2003.  https://doi.org/10.1016/j.theochem.2004.03.047
  6. 6.
    E.V. Ludeña, F. Illas, A. Ramirez-Solis, Int. J. Mod. Phys. B 22(25–26), 4642 (2008).  https://doi.org/10.1142/S0217979208050395
  7. 7.
    V.V. Karasiev, R.S. Jones, S.B. Trickey, F.E. Harris, in New developments in quantum chemistry, ed. by J.L. Paz, A.J. Hernandez (Transworld Research Network, Kerala, India, 2009)Google Scholar
  8. 8.
    J.D. Chai, J.D. Weeks, Phys. Rev. B 75, 205122 (2007).  https://doi.org/10.1103/PhysRevB.75.205122
  9. 9.
    T.A. Wesolowski, Int. J. Chem. (CHIMIA) 58(5), 311 (2004).  https://doi.org/10.2533/000942904777677885
  10. 10.
    Y.A. Wang, E.A. Carter, S.D. Schwartz, in Theoretical methods in condensed phase chemistry, ed. by S.D. Schwartz (Kluwer, Dordrecht, 2000), pp. 117–184. ISBN 9780306469497Google Scholar
  11. 11.
    P. García-González, J.E. Alvarellos, E. Chacón, Phys. Rev. B 53, 9509 (1996).  https://doi.org/10.1103/PhysRevB.53.9509
  12. 12.
    J.M. Dieterich, W.C. Witt, E.A. Carter, J. Comp. Chem. 38(17), 1552 (2017).  https://doi.org/10.1002/jcc.24806
  13. 13.
    H.J. Chen, A.H. Zhou, Numer. Math. Theory Meth. Appl. 1, 1 (2008)Google Scholar
  14. 14.
    D. García-Aldea, J.E. Alvarellos, in Advances in computational methods in sciences and engineering, Lecture series on computer and computational sciences, vol. 4A–4B, ed. by T. Simos, G. Maroulis (Koninklijke Brill NV, Leiden, 2005), pp. 1462–1466. Selected Papers from the International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2005). ISBN 9789067644419Google Scholar
  15. 15.
    S.S. Iyengar, M. Ernzerhof, S.N. Maximoff, G.E. Scuseria, Phys. Rev. A 63, 052508 (2001).  https://doi.org/10.1103/PhysRevA.63.052508
  16. 16.
    G.C. Kin-Lic, N.C. Handy, J. Chem. Phys. 112(13), 5639 (2000).  https://doi.org/10.1063/1.481139
  17. 17.
    A.J. Thakkar, Phys. Rev. A 46, 6920 (1992).  https://doi.org/10.1103/PhysRevA.46.6920
  18. 18.
    D. García-Aldea, J.E. Alvarellos, J. Chem. Phys. 127(14), 144109 (2007).  https://doi.org/10.1063/1.2774974
  19. 19.
    K. Finzel, Int. J. Quantum Chem. 115(23), 1629 (2015).  https://doi.org/10.1002/qua.24986
  20. 20.
    K. Finzel, J. Chem. Phys. 144(3), 034108 (2016).  https://doi.org/10.1063/1.4940035
  21. 21.
    K. Finzel, Theor. Chem. Acc. 135(4), 87 (2016).  https://doi.org/10.1007/s00214-016-1850-8
  22. 22.
    K. Finzel, Int. J. Quantum Chem. 116(16), 1261 (2016).  https://doi.org/10.1002/qua.25169
  23. 23.
    K. Finzel, J. Davidsson, I.A. Abrikosov, Int. J. Quantum Chem. 116(18), 1337 (2016).  https://doi.org/10.1002/qua.25181
  24. 24.
    K. Finzel, P.W. Ayers, Theor. Chem. Acc. 135(12), 255 (2016).  https://doi.org/10.1007/s00214-016-2013-7
  25. 25.
    K. Finzel, Int. J. Quantum Chem. 117(5), 25329 (2017), e25329.  https://doi.org/10.1002/qua.25329
  26. 26.
    K. Finzel, P.W. Ayers, Int. J. Quantum Chem. 117(10), 25364 (2017), e25364.  https://doi.org/10.1002/qua.25364
  27. 27.
    A. Genova, M. Pavanello, (2017), Preprint arXiv:1704.08943 [cond-mat.mtrl-sci]
  28. 28.
    Y.A. Wang, N. Govind, E.A. Carter, Phys. Rev. B 58, 13465 (1998).  https://doi.org/10.1103/PhysRevB.58.13465
  29. 29.
    Y.A. Wang, N. Govind, E.A. Carter, Phys. Rev. B 60, 16350 (1999).  https://doi.org/10.1103/PhysRevB.60.16350
  30. 30.
    B. Zhou, V.L. Ligneres, E.A. Carter, J. Chem. Phys. 122(4), 044103 (2005).  https://doi.org/10.1063/1.1834563
  31. 31.
    L.W. Wang, M.P. Teter, Phys. Rev. B 45, 13196 (1992).  https://doi.org/10.1103/PhysRevB.45.13196
  32. 32.
    E. Smargiassi, P.A. Madden, Phys. Rev. B 49, 5220 (1994).  https://doi.org/10.1103/PhysRevB.49.5220
  33. 33.
    F. Perrot, J. Phys.: Condens. Matt. 6(2), 431 (1994).  https://doi.org/10.1088/0953-8984/6/2/014
  34. 34.
    D. García-Aldea, J.E. Alvarellos, Phys. Rev. A 77, 022502 (2008).  https://doi.org/10.1103/PhysRevA.77.022502
  35. 35.
    D. García-Aldea, J.E. Alvarellos, Phys. Rev. A 76, 052504 (2007).  https://doi.org/10.1103/PhysRevA.76.052504
  36. 36.
    P. García-González, J.E. Alvarellos, E. Chacón, Phys. Rev. A 54, 1897 (1996).  https://doi.org/10.1103/PhysRevA.54.1897
  37. 37.
    C. Huang, E.A. Carter, Phys. Rev. B 81, 045206 (2010).  https://doi.org/10.1103/PhysRevB.81.045206
  38. 38.
    I.V. Ovchinnikov, L.A. Bartell, D. Neuhauser, J. Chem. Phys. 126(13), 134101 (2007).  https://doi.org/10.1063/1.2716667
  39. 39.
    C. Herring, Phys. Rev. A 34, 2614 (1986).  https://doi.org/10.1103/PhysRevA.34.2614
  40. 40.
    E. Chacón, J.E. Alvarellos, P. Tarazona, Phys. Rev. B 32, 7868 (1985).  https://doi.org/10.1103/PhysRevB.32.7868
  41. 41.
    D. García-Aldea, J.E. Alvarellos, J. Chem. Phys. 129(7), 074103 (2008).  https://doi.org/10.1063/1.2968612
  42. 42.
    T. Verstraelen, P.W. Ayers, V. Van Speybroeck, M. Waroquier, J. Chem. Phys. 138(7), 074108 (2013).  https://doi.org/10.1063/1.4791569
  43. 43.
    D. Chakraborty, R. Cuevas-Saavedra, P.W. Ayers, Theor. Chem. Acc. 136(9), 113 (2017).  https://doi.org/10.1007/s00214-017-2149-0
  44. 44.
    M. Levy, Proc. Nat. Acad. Sci. 76(12), 6062 (1979)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    M. Levy, J.P. Perdew, in Density Functional Methods In Physics, ed. by R.M. Dreizler, J. da Providência (Springer US, Boston, MA, 1985), pp. 11–30. ISBN 978-1-4757-0818-9.  https://doi.org/10.1007/978-1-4757-0818-9_2
  46. 46.
    M. Levy, Theor. Comp. Chem. 4, 3 (1996), Recent Developments and Applications of Modern Density Functional Theory.  https://doi.org/10.1016/S1380-7323(96)80083-5
  47. 47.
    Q. Wu, W. Yang, J. Chem. Phys. 118(6), 2498 (2003).  https://doi.org/10.1063/1.1535422
  48. 48.
    Q. Zhao, R.G. Parr, J. Chem. Phys. 98(1), 543 (1993).  https://doi.org/10.1063/1.465093
  49. 49.
    Q. Zhao, R.C. Morrison, R.G. Parr, Phys. Rev. A 50, 2138 (1994).  https://doi.org/10.1103/PhysRevA.50.2138
  50. 50.
    P.W. Ayers, R. Cuevas-Saavedra, D. Chakraborty, Phys. Lett. A 376(6), 839 (2012).  https://doi.org/10.1016/j.physleta.2012.01.028
  51. 51.
    X.P. Li, R.W. Nunes, D. Vanderbilt, Phys. Rev. B 47, 10891 (1993).  https://doi.org/10.1103/PhysRevB.47.10891
  52. 52.
    E. Hernández, M.J. Gillan, C.M. Goringe, Phys. Rev. B 53, 7147 (1996).  https://doi.org/10.1103/PhysRevB.53.7147
  53. 53.
    M. Challacombe, J. Chem. Phys. 110(5), 2332 (1999).  https://doi.org/10.1063/1.477969
  54. 54.
    W. Kohn, Phys. Rev. Lett. 76, 3168 (1996).  https://doi.org/10.1103/PhysRevLett.76.3168
  55. 55.
    R. Baer, M. Head-Gordon, Phys. Rev. Lett. 79, 3962 (1997).  https://doi.org/10.1103/PhysRevLett.79.3962
  56. 56.
    E. Prodan, W. Kohn, Proc. Natl. Acad. Sci. (USA) 102(33), 11635 (2005).  https://doi.org/10.1073/pnas.0505436102
  57. 57.
    G. Sperber, Int. J. Quantum Chem. 5(2), 189 (1971).  https://doi.org/10.1002/qua.560050206
  58. 58.
    P. de Silva, J. Korchowiec, T.A. Wesolowski, J. Chem. Phys. 140(16), 164301 (2014).  https://doi.org/10.1063/1.4871501
  59. 59.
    R.C. Morrison, P.W. Ayers, J. Chem. Phys. 103(15), 6556 (1995).  https://doi.org/10.1063/1.470382
  60. 60.
    R.C. Morrison, C.M. Dixon, J.R. Mizell, Int. J. Quantum Chem. 52(S28), 309 (1994).  https://doi.org/10.1002/qua.560520832
  61. 61.
    W.P. Wang, R.G. Parr, Phys. Rev. A 16, 891 (1977).  https://doi.org/10.1103/PhysRevA.16.891
  62. 62.
    P. García-González, J.E. Alvarellos, E. Chacón, Phys. Rev. A 57, 4192 (1998).  https://doi.org/10.1103/PhysRevA.57.4192
  63. 63.
    P. García-González, J.E. Alvarellos, E. Chacón, Phys. Rev. B 57, 4857 (1998).  https://doi.org/10.1103/PhysRevB.57.4857
  64. 64.
    E. Chacón, P. Tarazona, Phys. Rev. B 37, 4013 (1988).  https://doi.org/10.1103/PhysRevB.37.4013
  65. 65.
    R. Cuevas-Saavedra, D. Chakraborty, P.W. Ayers, Phys. Rev. A 85, 042519 (2012).  https://doi.org/10.1103/PhysRevA.85.042519
  66. 66.
    J.A. Alonso, L.A. Girifalco, Solid State Commun. 24(2), 135 (1977).  https://doi.org/10.1016/0038-1098(77)90591-9
  67. 67.
    J.A. Alonso, L.A. Girifalco, Phys. Rev. B 17, 3735 (1978).  https://doi.org/10.1103/PhysRevB.17.3735
  68. 68.
    O. Gunnarsson, M. Jonson, B.I. Lundqvist, Solid State Commun. 24(11), 765 (1977).  https://doi.org/10.1016/0038-1098(77)91185-1
  69. 69.
    R. Cuevas-Saavedra, P.W. Ayers, Chem. Phys. Lett. 539, 163 (2012).  https://doi.org/10.1016/j.cplett.2012.04.037
  70. 70.
    N.H. March, R. Santamaria, Int. J. Quantum Chem. 39(4), 585 (1991).  https://doi.org/10.1002/qua.560390405
  71. 71.
    D. Chakraborty, P.W. Ayers, J. Math. Chem. 49(8), 1822 (2011).  https://doi.org/10.1007/s10910-011-9861-0
  72. 72.
    P.W. Ayers, J. Math. Phys. 46(6), 062107 (2005).  https://doi.org/10.1063/1.1922071
  73. 73.
    L. Cohen, J. Chem. Phys. 70(2), 788 (1979).  https://doi.org/10.1063/1.437511
  74. 74.
    P.W. Ayers, R.G. Parr, A. Nagy, Int. J. Quantum Chem. 90(1), 309 (2002).  https://doi.org/10.1002/qua.989
  75. 75.
    A.A. Kugler, Phys. Rev. A 41, 3489 (1990).  https://doi.org/10.1103/PhysRevA.41.3489
  76. 76.
    A. Nagy, Phys. Rev. A 47, 2715 (1993).  https://doi.org/10.1103/PhysRevA.47.2715
  77. 77.
    R.G. Parr, S. Liu, A.A. Kugler, A. Nagy, Phys. Rev. A 52, 969 (1995).  https://doi.org/10.1103/PhysRevA.52.969
  78. 78.
    A. Nagy, S. Liu, R.G. Parr, Phys. Rev. A 59, 3349 (1999).  https://doi.org/10.1103/PhysRevA.59.3349
  79. 79.
    A. Nagy, Int. J. Quantum Chem. 106(5), 1043 (2006).  https://doi.org/10.1002/qua.20872
  80. 80.
    P.W. Ayers, Phys. Rev. A 74, 042502 (2006).  https://doi.org/10.1103/PhysRevA.74.042502
  81. 81.
    D. Chakraborty, P.W. Ayers, J. Math. Chem. 49(8), 1810 (2011).  https://doi.org/10.1007/s10910-011-9860-1
  82. 82.
    P.W. Ayers, J. Math. Chem. 44(2), 311 (2008).  https://doi.org/10.1007/s10910-007-9261-7
  83. 83.
    S. Liu, Phys. Rev. A 54, 1328 (1996).  https://doi.org/10.1103/PhysRevA.54.1328
  84. 84.
    M. Chan, R. Cuevas-Saavedra, D. Chakraborty, P.W. Ayers, Computation 5(4), 42 (2017).  https://doi.org/10.3390/computation5040042

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Authors and Affiliations

  • D. Chakraborty
    • 1
  • R. Cuevas-Saavedra
    • 1
  • P. W. Ayers
    • 1
  1. 1.Department of Chemistry and Chemical BiologyMcMaster UniversityHamiltonCanada

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