Warming Up Density Functional Theory

  • Justin C. Smith
  • Francisca Sagredo
  • Kieron Burke
Chapter

Abstract

Density functional theory (DFT) has become the most popular approach to electronic structure across disciplines, especially in material and chemical sciences. In 2016, at least 30,000 papers used DFT to make useful predictions or give insight into an enormous diversity of scientific problems, ranging from battery development to solar cell efficiency and far beyond. The success of this field has been driven by usefully accurate approximations based on known exact conditions and careful testing and validation. In the last decade, applications of DFT in a new area, warm dense matter, have exploded. DFT is revolutionizing simulations of warm dense matter including applications in controlled fusion, planetary interiors, and other areas of high energy density physics. Over the past decade or so, molecular dynamics calculations driven by modern density functional theory have played a crucial role in bringing chemical realism to these applications, often (but not always) in excellent agreement with experiment. This chapter summarizes recent work from our group on density functional theory at nonzero temperatures, which we call thermal DFT. We explain the relevance of this work in the context of warm dense matter, and the importance of quantum chemistry to this regime. We illustrate many basic concepts on a simple model system, the asymmetric Hubbard dimer.

Keywords

Thermal density functional theory Ensemble density functional theory Warm dense matter Exact conditions Thermal linear response 

Notes

Acknowledgements

The authors acknowledge support from the US Department of Energy (DOE), Office of Science, Basic Energy Sciences under Award No. DE-FG02-08ER46496. J.C.S. acknowledges support through the NSF Graduate Research fellowship program under Award No. DGE-1321846.

References

  1. 1.
    T.R. Mattsson, M.P. Desjarlais, Phys. Rev. Lett. 97, 017801 (2006), https://doi.org/10.1103/PhysRevLett.97.017801
  2. 2.
    U.D. of Energy, Basic research needs for high energy density laboratory physics: Report of the workshop on high energy density laboratory physics research needs. Technical report, Office of Science and National Nuclear Security Administration (2009)Google Scholar
  3. 3.
    W. Lorenzen, B. Holst, R. Redmer, Phys. Rev. Lett. 102, 115701 (2009), https://doi.org/10.1103/PhysRevLett.102.115701
  4. 4.
    M.D. Knudson, M.P. Desjarlais, A. Becker, R.W. Lemke, K.R. Cochrane, M.E. Savage, D.E. Bliss, T.R. Mattsson, R. Redmer, Science 348(6242), 1455 (2015)CrossRefGoogle Scholar
  5. 5.
    M.D. Knudson, M.P. Desjarlais, Phys. Rev. Lett. 103, 225501 (2009), https://doi.org/10.1103/PhysRevLett.103.225501
  6. 6.
    M.D. Knudson, M.P. Desjarlais, A. Pribram-Jones, Phys. Rev. B 91, 224105 (2015)CrossRefGoogle Scholar
  7. 7.
    B. Holst, R. Redmer, M.P. Desjarlais, Phys. Rev. B 77, 184201 (2008)CrossRefGoogle Scholar
  8. 8.
    A. Kietzmann, R. Redmer, M.P. Desjarlais, T.R. Mattsson, Phys. Rev. Lett. 101, 070401 (2008)CrossRefGoogle Scholar
  9. 9.
    S. Root, R.J. Magyar, J.H. Carpenter, D.L. Hanson, T.R. Mattsson, Phys. Rev. Lett. 105(8), 085501 (2010), https://doi.org/10.1103/PhysRevLett.105.085501
  10. 10.
    R.F. Smith, J.H. Eggert, R. Jeanloz, T.S. Duffy, D.G. Braun, J.R. Patterson, R.E. Rudd, J. Biener, A.E. Lazicki, A.V. Hamza, J. Wang, T. Braun, L.X. Benedict, P.M. Celliers, G.W. Collins, Nature 511(7509), 330 (2014), https://doi.org/10.1038/nature13526
  11. 11.
    F. Graziani, M.P. Desjarlais, R. Redmer, S.B. Trickey (eds.), Frontiers and Challenges in Warm Dense Matter, Lecture Notes in Computational Science and Engineering, vol. 96 (Springer International Publishing, 2014)Google Scholar
  12. 12.
    S. Ichimaru, Statistical Plasma Physics. Frontiers in Physics (Westview, Boulder, CO, 2004), http://cds.cern.ch/record/1106845
  13. 13.
    C.K. Birdsall, A.B. Langdon, Plasma physics via computer simulation (CRC Press, 2004)Google Scholar
  14. 14.
    T. Sjostrom, J. Dufty, Phys. Rev. B 88, 115123 (2013), https://doi.org/10.1103/PhysRevB.88.115123
  15. 15.
    V.V. Karasiev, T. Sjostrom, J. Dufty, S.B. Trickey, Phys. Rev. Lett. 112, 076403 (2014), https://doi.org/10.1103/PhysRevLett.112.076403
  16. 16.
    K. Burke, J. Chem. Phys. 136(15), 150901 (2012), http://link.aip.org/link/?JCP/136/150901/1
  17. 17.
    W. Kohn, L.J. Sham, Phys. Rev. 140(4A), A1133 (1965), https://doi.org/10.1103/PhysRev.140.A1133
  18. 18.
    R. Car, M. Parrinello, Phys. Rev. Lett. 55(22), 2471 (1985), https://doi.org/10.1103/PhysRevLett.55.2471
  19. 19.
    N.D. Mermin, Phys. Rev. 137, A: 1441 (1965)Google Scholar
  20. 20.
    B. Militzer, D.M. Ceperley, Phys. Rev. Lett. 85, 1890 (2000), https://doi.org/10.1103/PhysRevLett.85.1890
  21. 21.
    V.S. Filinov, M. Bonitz, W. Ebeling, V.E. Fortov, Plasma Physics and Controlled Fusion 43(6), 743 (2001), http://stacks.iop.org/0741-3335/43/i=6/a=301
  22. 22.
    B. Militzer, Phys. Rev. B 79, 155105 (2009), https://doi.org/10.1103/PhysRevB.79.155105
  23. 23.
    T. Schoof, M. Bonitz, A. Filinov, D. Hochstuhl, J. Dufty, Contributions to Plasma Physics 51(8), 687 (2011), https://doi.org/10.1002/ctpp.201100012
  24. 24.
    K.P. Driver, B. Militzer, Phys. Rev. Lett. 108, 115502 (2012), https://doi.org/10.1103/PhysRevLett.108.115502
  25. 25.
    T. Schoof, S. Groth, J. Vorberger, M. Bonitz, Phys. Rev. Lett. 115, 130402 (2015), https://doi.org/10.1103/PhysRevLett.115.130402
  26. 26.
    T. Dornheim, S. Groth, T. Sjostrom, F.D. Malone, W.M.C. Foulkes, M. Bonitz, Phys. Rev. Lett. 117, 156403 (2016), https://doi.org/10.1103/PhysRevLett.117.156403
  27. 27.
    J.M. McMahon, M.A. Morales, C. Pierleoni, D.M. Ceperley, Rev. Mod. Phys. 84, 1607 (2012), https://doi.org/10.1103/RevModPhys.84.1607
  28. 28.
    J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996), http://link.aps.org/doi/10.1103/PhysRevLett.77.3865
  29. 29.
    C. Toher, A. Filippetti, S. Sanvito, K. Burke, Phys. Rev. Lett. 95, 146402 (2005)CrossRefGoogle Scholar
  30. 30.
    S.Y. Quek, L. Venkataraman, H.J. Choi, S.G. Louie, M.S. Hybertsen, J.B. Neaton, Nano Letters 7(11), 3477 (2007), https://doi.org/10.1021/nl072058i. PMID: 17900162
  31. 31.
    M. Koentopp, C. Chang, K. Burke, R. Car, J. Phys. Condens. Matter 20(8), 083203 (2008), http://stacks.iop.org/0953-8984/20/i=8/a=083203
  32. 32.
    P. Hohenberg, W. Kohn, Phys. Rev. 136(3B), B864 (1964), https://doi.org/10.1103/PhysRev.136.B864
  33. 33.
    E.H. Lieb, Rev. Mod. Phys. 53, 603 (1981), https://doi.org/10.1103/RevModPhys.53.603
  34. 34.
    M.A. Marques, M.J. Oliveira, T. Burnus, Comput. Phys. Commun. 183(10), 2272 (2012), https://doi.org/10.1016/j.cpc.2012.05.007
  35. 35.
    J.P. Perdew, Y. Wang, Phys. Rev. B 45(23), 13244 (1992), https://doi.org/10.1103/PhysRevB.45.13244
  36. 36.
    J.P. Perdew, A. Ruzsinszky, L.A. Constantin, J. Sun, G.I. Csonka, J. Chem. Theor. Comput. 5(4), 902 (2009), https://doi.org/10.1021/Ct800531s
  37. 37.
    L.O. Wagner, E.M. Stoudenmire, K. Burke, S.R. White, Phys. Rev. Lett. 111, 093003 (2013), https://doi.org/10.1103/PhysRevLett.111.093003
  38. 38.
    D.J. Carrascal, J. Ferrer, J.C. Smith, K. Burke, J. Phys.C ondens. Matter 27(39), 393001 (2015), http://stacks.iop.org/0953-8984/27/i=39/a=393001
  39. 39.
    N.T. Maitra, The Journal of Chemical Physics 144(22), 220901 (2016), https://doi.org/10.1063/1.4953039
  40. 40.
    N.T. Maitra, F. Zhang, R.J. Cave, K. Burke, J. Chem. Phys. 120(13), 5932 (2004), http://link.aip.org/link/?JCP/120/5932/1
  41. 41.
    A. Dreuw, J.L. Weisman, M. Head-Gordon, J. Chem. Phys. 119(6) (2003)Google Scholar
  42. 42.
    D.J. Tozer, J. Chem. Phys. 119(24) (2003)Google Scholar
  43. 43.
    B.G. Levine, C. Ko, J. Quenneville, T.J. Martnez, Mol. Phys. 104(5–7), 1039 (2006), https://doi.org/10.1080/00268970500417762
  44. 44.
    M. van Faassen, P.L. de Boeij, R. van Leeuwen, J.A. Berger, J.G. Snijders, Phys. Rev. Lett. 88, 186401 (2002)CrossRefGoogle Scholar
  45. 45.
    A. Theophilou, J. Phys. C 12, 5419 (1979)CrossRefGoogle Scholar
  46. 46.
    E.K.U. Gross, L.N. Oliveira, W. Kohn, Phys. Rev. A 37, 2809 (1988), https://doi.org/10.1103/PhysRevA.37.2809
  47. 47.
    E.K.U. Gross, M. Petersilka, T. Grabo, Chem. Appl. Density-Funct. Theor. 629, 42 (1996)CrossRefGoogle Scholar
  48. 48.
    A. Pribram-Jones, Z.H. Yang, J.R. Trail, K. Burke, R.J. Needs, C.A. Ullrich, J. Chem. Phys. 140, 18A541 (2014)CrossRefGoogle Scholar
  49. 49.
    Z.h. Yang, J.R. Trail, A. Pribram-Jones, K. Burke, R.J. Needs, C.A. Ullrich, Phys. Rev. A 90, 042501 (2014), https://doi.org/10.1103/PhysRevA.90.042501
  50. 50.
    B. Senjean, E.D.H. rd, M.M. Alam, S. Knecht, E. Fromager. Mol. Phys. 114(7–8), 968 (2016), https://doi.org/10.1080/00268976.2015.1119902
  51. 51.
    L.M.K. Deur, E. Fromager, Submitted (2016)Google Scholar
  52. 52.
    M.M. Alam, S. Knecht, E. Fromager, Phys. Rev. A 94, 012511 (2016), https://doi.org/10.1103/PhysRevA.94.012511
  53. 53.
    K. Burke, J. Werschnik, E.K.U. Gross, J. Chem. Phys. 123(6), 062206 (2005), https://doi.org/10.1063/1.1904586
  54. 54.
    M. Levy, J. Perdew, Phys. Rev. A 32, 2010 (1985), https://doi.org/10.1103/PhysRevA.32.2010
  55. 55.
    E.H. Lieb, S. Oxford, Int. J. Quantum Chem. 19(3), 427 (1981), http://dx.doi.org/10.1002/qua.560190306
  56. 56.
    J. Sun, A. Ruzsinszky, J.P. Perdew, Phys. Rev. Lett. 115, 036402 (2015), https://doi.org/10.1103/PhysRevLett.115.036402
  57. 57.
    S. Pittalis, C.R. Proetto, A. Floris, A. Sanna, C. Bersier, K. Burke, E.K.U. Gross, Phys. Rev. Lett. 107, 163001 (2011), https://doi.org/10.1103/PhysRevLett.107.163001
  58. 58.
    A. Pribram-Jones, S. Pittalis, E. Gross, K. Burke, in Frontiers and Challenges in Warm Dense Matter, Lecture Notes in Computational Science and Engineering, vol. 96, ed. by F. Graziani, M.P. Desjarlais, R. Redmer, S.B. Trickey (Springer International Publishing, 2014), pp. 25–60, https://doi.org/10.1007/978-3-319-04912-0_2
  59. 59.
    A. Pribram-Jones, K. Burke, Phys. Rev. B 93, 205140 (2016), https://doi.org/10.1103/PhysRevB.93.205140
  60. 60.
    D. Langreth, J. Perdew, Solid State Commun. 17, 1425 (1975)CrossRefGoogle Scholar
  61. 61.
    W.T.D. Frydel, K. Burke, J. Chem. Phys. 112, 5292 (2000)CrossRefGoogle Scholar
  62. 62.
    J.P. Perdew, M. Ernzerhof, K. Burke, J. Chem. Phys. 105(22), 9982 (1996), http://link.aip.org/link/?JCP/105/9982/1
  63. 63.
    K. Burke, J.C. Smith, P.E. Grabowski, A. Pribram-Jones, Phys. Rev. B 93, 195132 (2016), https://doi.org/10.1103/PhysRevB.93.195132
  64. 64.
    S. Ichimaru, Rev. Mod. Phys. 54, 1017 (1982)CrossRefGoogle Scholar
  65. 65.
    J.W. Dufty, S.B. Trickey, Phys. Rev. B 84, 125118 (2011), https://doi.org/10.1103/PhysRevB.84.125118
  66. 66.
    J.W. Dufty, S. Trickey, Mol. Phys. 114(7–8), 988 (2016)CrossRefGoogle Scholar
  67. 67.
    P.R.T. Schipper, O.V. Gritsenko, E.J. Baerends, Theoretical chemistry accounts: theory, computation, and modeling (Theoretica Chimica Acta) 98, 16 (1997), https://doi.org/10.1007/s002140050273
  68. 68.
    P. Ziesche, S. Kurth, J.P. Perdew, Computational Materials Science 11(2), 122 (1998), https://doi.org/10.1016/S0927-0256(97)00206-1
  69. 69.
    J.P.S. Kurth, P. Blaha, Int. J. Quantum Chem. 75, 889 (1999)CrossRefGoogle Scholar
  70. 70.
    A. Tkatchenko, M. Scheffler, Phys. Rev. Lett. 102, 073005 (2009)CrossRefGoogle Scholar
  71. 71.
    D. Ceperley, M. Kalos, K. Binder, Monte Carlo Methods in Statistical Physics (Springer, Berlin, 1979)Google Scholar
  72. 72.
    M.P. Nightingale, C.J. Umrigar, Quantum Monte Carlo methods in physics and chemistry. 525 (Springer Science & Business Media, 1998)Google Scholar
  73. 73.
    S.R. White, Phys. Rev. Lett. 69(19), 2863 (1992), http://link.aps.org/doi/10.1103/PhysRevLett.69.2863
  74. 74.
    N. Schuch, F. Verstraete, Nat. Phys. 5, 732 (2009), https://doi.org/10.1038/nphys1370
  75. 75.
    C.J. Umrigar, X. Gonze, Phys. Rev. A 50(5), 3827 (1994)CrossRefGoogle Scholar
  76. 76.
    C. Filippi, C.J. Umrigar, M. Taut, The Journal of Chemical Physics 100(2), 1290 (1994), https://doi.org/10.1063/1.466658
  77. 77.
    C.J. Huang, C.J. Umrigar, Phys. Rev. A 56, 290 (1997), https://doi.org/10.1103/PhysRevA.56.290
  78. 78.
    N. Lima, M. Silva, L. Oliveira, K. Capelle, Phys. Rev. Lett. 90(14), 146402 (2003)CrossRefGoogle Scholar
  79. 79.
    J.C. Smith, A. Pribram-Jones, K. Burke, Phys. Rev. B 93, 245131 (2016), https://doi.org/10.1103/PhysRevB.93.245131
  80. 80.
    G. Stefanucci, R. Van Leeuwen, Nonequilibrium Many-Body Theory of Quantum Systems: A Modern Introduction (Cambridge University Press, 2013)Google Scholar
  81. 81.
    E. Runge, E.K.U. Gross, Phys. Rev. Lett. 52(12), 997 (1984), https://doi.org/10.1103/PhysRevLett.52.997
  82. 82.
    K. Burke, J. Werschnik, E.K.U. Gross, J. Chem. Phys. 123(6), 062206 (2005), http://link.aip.org/link/?JCP/123/062206/1
  83. 83.
    D. Gericke, M. Schlanges, W. Kraeft, Physics Letters A 222(4), 241 (1996), https://doi.org/10.1016/0375-9601(96)00654-8
  84. 84.
    V. Rizzi, T.N. Todorov, J.J. Kohanoff, A.A. Correa, Phys. Rev. B 93, 024306 (2016).  https://doi.org/10.1103/PhysRevB.93.024306
  85. 85.
    d A. Pribram-Jones, P.E. Grabowski, K. Burke, Phys. Rev. Lett. 116, 233001 (2016), https://doi.org/10.1103/PhysRevLett.116.233001
  86. 86.
    E. Gross, W. Kohn, Phys. Rev. Lett. 55, 2850 (1985)CrossRefGoogle Scholar
  87. 87.
    L. Kadanoff, G. Baym, D. Pines, Quantum Statistical Mechanics. Advanced Books Classics Series (Addison-Wesley, 1994)Google Scholar
  88. 88.
    L. Schimka, J. Harl, A. Stroppa, A. Grüneis, M. Marsman, F. Mittendorfer, G. Kresse, Nat. Mater. 9(9), 741 (2010)CrossRefGoogle Scholar
  89. 89.
    S.X. Hu, L.A. Collins, T.R. Boehly, J.D. Kress, V.N. Goncharov, S. Skupsky, Phys. Rev. E 89, 043105 (2014), https://doi.org/10.1103/PhysRevE.89.043105
  90. 90.
    B. Bennett, J. Johnson, G. Kerley, G. Rood, Recent developments in the sesame equation-of-state library. Technical report, Los Alamos Scientific Lab., N. Mex. (USA) (1978)Google Scholar
  91. 91.
    Y.T. Lee, R. More, Phys. Fluids (1958–1988) 27(5), 1273 (1984)Google Scholar
  92. 92.
    B. Wilson, V. Sonnad, P. Sterne, W. Isaacs, J. Quant. Spectrosc. Radiat. Transfer 99(1), 658 (2006)CrossRefGoogle Scholar
  93. 93.
    Y. Miguel, T. Guillot, L. Fayon, arXiv preprint arXiv:1609.05460 (2016)
  94. 94.
    D. Clery, Science 353(6298), 438 (2016), https://doi.org/10.1126/science.353.6298.438
  95. 95.
    H.F. Wilson, B. Militzer, Phys. Rev. Lett. 108, 111101 (2012), https://doi.org/10.1103/PhysRevLett.108.111101
  96. 96.
    S. Root, L. Shulenburger, R.W. Lemke, D.H. Dolan, T.R. Mattsson, M.P. Desjarlais, Phys. Rev. Lett. 115, 198501 (2015), https://doi.org/10.1103/PhysRevLett.115.198501
  97. 97.
    H.F. Wilson, M.L. Wong, B. Militzer, Phys. Rev. Lett. 110, 151102 (2013), https://doi.org/10.1103/PhysRevLett.110.151102
  98. 98.
    P. Sperling, E.J. Gamboa, H.J. Lee, H.K. Chung, E. Galtier, Y. Omarbakiyeva, H. Reinholz, G. Röpke, U. Zastrau, J. Hastings, L.B. Fletcher, S.H. Glenzer, Phys. Rev. Lett. 115, 115001 (2015), https://doi.org/10.1103/PhysRevLett.115.115001
  99. 99.
    P. Davis, T. Döppner, J. Rygg, C. Fortmann, L. Divol, A. Pak, L. Fletcher, A. Becker, B. Holst, P. Sperling, et al., Nat. Commun. 7 (2016)Google Scholar
  100. 100.
    D. Kraus, A. Ravasio, M. Gauthier, D. Gericke, J. Vorberger, S. Frydrych, J. Helfrich, L. Fletcher, G. Schaumann, B. Nagler, et al., Nat. Commun. 7 (2016)Google Scholar
  101. 101.
    A.D. Baczewski, L. Shulenburger, M.P. Desjarlais, S.B. Hansen, R.J. Magyar, Phys. Rev. Lett. 116, 115004 (2016), https://doi.org/10.1103/PhysRevLett.116.115004
  102. 102.
    L.A. Curtiss, K. Raghavachari, P.C. Redfern, J.A. Pople, J. Chem. Phys. 106(3) (1997)Google Scholar
  103. 103.
    K.R.L.A. Curtiss, P.C. Redfern, J. Pople, J. Chem. Phys. 109, 42 (1998)CrossRefGoogle Scholar
  104. 104.
    J. Paier, R. Hirschl, M. Marsman, G. Kresse, The Journal of chemical physics 122(23), 234102 (2005), https://doi.org/10.1063/1.1926272
  105. 105.
    T.J. Lenosky, S.R. Bickham, J.D. Kress, L.A. Collins, Phys. Rev. B 61, 1 (2000), https://doi.org/10.1103/PhysRevB.61.1
  106. 106.
    M. Ernzerhof, G.E. Scuseria, J. Chem. Phys. 110, 5029 (1999), http://link.aip.org/link/JCPSA6/v110/i11/p5029/s1
  107. 107.
    G. Kresse, J. Furthmüller, Phys. Rev. B 54(16), 11169 (1996), https://doi.org/10.1103/PhysRevB.54.11169
  108. 108.
    F. Furche, Phys. Rev. B 64, 195120 (2001)CrossRefGoogle Scholar
  109. 109.
    F. Furche, J. Chem. Phys. 129(11), 114105 (2008)CrossRefGoogle Scholar
  110. 110.
    H. Eshuis, J. Yarkony, F. Furche, The Journal of Chemical Physics 132(23), 234114 (2010), https://doi.org/10.1063/1.3442749
  111. 111.
    H. Eshuis, J. Bates, F. Furche, Theoretical Chemistry Accounts 131(1), 1 (2012), https://doi.org/10.1007/s00214-011-1084-8
  112. 112.
    F. Furche, Ann. Rev. Phys. Chem. 68(1) (2016)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Justin C. Smith
    • 1
  • Francisca Sagredo
    • 2
  • Kieron Burke
    • 2
  1. 1.Department of Physics and AstronomyUniversity of CaliforniaIrvineUSA
  2. 2.Department of ChemistryUniversity of CaliforniaIrvineUSA

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