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A Gradient Corrected Two-Point Weighted Density Approximation for Exchange Energies

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

Abstract

A successful symmetric, two-point, nonlocal weighted density approximation for the exchange energy of atoms and molecules can be constructed using a power mean with constant power p when symmetrizing the exchange-correlation hole [Phys. Rev. A 85, 042519 (2012)]. In this work, we consider how this parameter depends on the system’s charge. Exchange energies for all ions with charge from \(-1\) to \(+12\) of the first eighteen atoms of the periodic table are computed and optimized. Appropriate gradient corrections to the current model, based on rational functions, are designed based on the optimal p values we observed for the ionic systems. All of the advantageous features (non-locality, uniform electron gas limit and no self-interaction error) of the original model are preserved.

Notes

Acknowledgements

Support from Compute Canada, NSERC, and the Canada Research Chairs is appreciated.

References

  1. 1.
    R.G. Parr, W. Yang, Density Functional Theory of Atoms and Molecules (Oxford University Press, Oxford, 1989). ISBN 9780195092769Google Scholar
  2. 2.
    P.W. Ayers, W. Yang, in ComputatiOnal Medicinal Chemistry for Drug Discovery, ed. by P. Bultinck, H. de Winter, W. Langenaeker, J.P. Tollenaere (Dekker, New York, 2003), pp. 571–616Google Scholar
  3. 3.
    W. Kohn, A.D. Becke, R.G. Parr, J. Phys. Chem. 100(31), 12974 (1996).  https://doi.org/10.1021/jp960669l
  4. 4.
    A.J. Cohen, P. Mori-Sánchez, W. Yang, Chem. Rev. 112(1), 289 (2012).  https://doi.org/10.1021/cr200107z
  5. 5.
    W. Kohn, Rev. Mod. Phys. 71, 1253 (1999).  https://doi.org/10.1103/RevModPhys.71.1253
  6. 6.
    P.C. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964).  https://doi.org/10.1103/PhysRev.136.B864
  7. 7.
    M. Levy, Proc. Nat. Acad. Sci. 76(12), 6062 (1979)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    S.M. Valone, J. Chem. Phys. 73(9), 4653 (1980).  https://doi.org/10.1063/1.440656
  9. 9.
    E.H. Lieb, Int. J. Quantum Chem. 24(3), 243 (1983).  https://doi.org/10.1002/qua.560240302
  10. 10.
    W. Yang, P.W. Ayers, Q. Wu, Phys. Rev. Lett. 92, 146404 (2004).  https://doi.org/10.1103/PhysRevLett.92.146404
  11. 11.
    P.W. Ayers, Phys. Rev. A 73, 012513 (2006).  https://doi.org/10.1103/PhysRevA.73.012513
  12. 12.
    H. Eschrig, The Fundamentals of Density Functional Theory (Eagle, Leipzig, 2003)zbMATHGoogle Scholar
  13. 13.
    A.J. Cohen, P. Mori-Sánchez, W. Yang, Science 321(5890), 792 (2008).  https://doi.org/10.1126/science.1158722
  14. 14.
    J.P. Perdew, A. Ruzsinszky, J. Tao, V.N. Staroverov, G.E. Scuseria, G.I. Csonka, J. Chem. Phys. 123(6), 062201 (2005).  https://doi.org/10.1063/1.1904565
  15. 15.
    M. Ernzerhof, J.P. Perdew, K. Burke, in Density Functional Theory I: Functionals and Effective Potentials, ed. by R.F. Nalewajski (Springer, Berlin, Heidelberg, 1996), pp. 1–30.  https://doi.org/10.1007/3-540-61091-X_1. ISBN 978-3-540-49945-9
  16. 16.
    J.P. Perdew, A. Ruzsinszky, L.A. Constantin, J. Sun, G.I. Csonka, J. Chem. Theory Comput. 5(4), 902 (2009).  https://doi.org/10.1021/ct800531s
  17. 17.
    W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965).  https://doi.org/10.1103/PhysRev.140.A1133
  18. 18.
    S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58(8), 1200 (1980).  https://doi.org/10.1139/p80-159
  19. 19.
    J.P. Perdew, Y. Wang, Phys. Rev. B 45, 13244 (1992).  https://doi.org/10.1103/PhysRevB.45.13244
  20. 20.
    J.P. Perdew, W. Yue, Phys. Rev. B 33, 8800 (1986).  https://doi.org/10.1103/PhysRevB.33.8800
  21. 21.
    A.D. Becke, Phys. Rev. A 38, 3098 (1988).  https://doi.org/10.1103/PhysRevA.38.3098
  22. 22.
    J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996), [Erratum Phys. Rev. Lett. 78, 1396 (1997)].  https://doi.org/10.1103/PhysRevLett.77.3865
  23. 23.
    N.C. Handy, A.J. Cohen, Mol. Phys. 99(5), 403 (2001).  https://doi.org/10.1080/00268970010018431
  24. 24.
    A. Savin, in Recent Developments of Modern Density Functional Theory, ed. by J.M. Seminario (Elsevier, New York, 1996), p. 327CrossRefGoogle Scholar
  25. 25.
    P.W. Ayers, M. Levy, J. Chem. Phys. 140(18), 18A537 (2014).  https://doi.org/10.1063/1.4871732
  26. 26.
    M. Levy, J.S.M. Anderson, F.H. Zadeh, P.W. Ayers, J. Chem. Phys. 140(18), 18A538 (2014).  https://doi.org/10.1063/1.4871734
  27. 27.
    P. Mori-Sánchez, A.J. Cohen, W. Yang, Phys. Rev. Lett. 102, 066403 (2009).  https://doi.org/10.1103/PhysRevLett.102.066403
  28. 28.
    A. Ruzsinszky, J.P. Perdew, G.I. Csonka, J. Chem. Phys. 134(11), 114110 (2011).  https://doi.org/10.1063/1.3569483
  29. 29.
    A. Ruzsinszky, J.P. Perdew, G.I. Csonka, J. Chem. Theory Comput. 6(1), 127 (2010).  https://doi.org/10.1021/ct900518k
  30. 30.
    A. Puzder, M. Dion, D.C. Langreth, J. Chem. Phys. 124(16), 164105 (2006).  https://doi.org/10.1063/1.2189229
  31. 31.
    T. Thonhauser, A. Puzder, D.C. Langreth, J. Chem. Phys. 124(16), 164106 (2006).  https://doi.org/10.1063/1.2189230
  32. 32.
    M. Dion, H. Rydberg, E. Schröder, D.C. Langreth, B.I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004).  https://doi.org/10.1103/PhysRevLett.92.246401
  33. 33.
    O.A. Vydrov, T. Van Voorhis, J. Chem. Phys. 133(24), 244103 (2010).  https://doi.org/10.1063/1.3521275
  34. 34.
    O.A. Vydrov, T. Van Voorhis, J. Chem. Phys. 130(10), 104105 (2009).  https://doi.org/10.1063/1.3079684
  35. 35.
    O.A. Vydrov, T. Van Voorhis, Phys. Rev. Lett. 103, 063004 (2009).  https://doi.org/10.1103/PhysRevLett.103.063004
  36. 36.
    O.A. Vydrov, Q. Wu, T. Van Voorhis, J. Chem. Phys. 129(1), 014106 (2008).  https://doi.org/10.1063/1.2948400
  37. 37.
    B.I. Lundqvist, Y. Andersson, H. Shao, S. Chan, D.C. Langreth, Int. J. Quantum Chem. 56(4), 247 (1995).  https://doi.org/10.1002/qua.560560410
  38. 38.
    R. Cuevas-Saavedra, D. Chakraborty, S. Rabi, C. Cárdenas, P.W. Ayers, J. Chem. Theory Comput. 8(11), 4081 (2012).  https://doi.org/10.1021/ct300325t
  39. 39.
    R. Cuevas-Saavedra, D. Chakraborty, P.W. Ayers, Phys. Rev. A 85, 042519 (2012).  https://doi.org/10.1103/PhysRevA.85.042519
  40. 40.
    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
  41. 41.
    R. Cuevas-Saavedra, D.C. Thompson, P.W. Ayers, Int. J. Quantum Chem. 116(11), 852 (2016).  https://doi.org/10.1002/qua.25081
  42. 42.
    R. Cuevas-Saavedra, P.W. Ayers, J. Phys. Chem. Solids 73(5), 670 (2012).  https://doi.org/10.1016/j.jpcs.2012.01.004
  43. 43.
    R. Cuevas-Saavedra, P.W. Ayers, Chem. Phys. Lett. 539, 163 (2012).  https://doi.org/10.1016/j.cplett.2012.04.037
  44. 44.
    H. Antaya, Y. Zhou, M. Ernzerhof, Phys. Rev. A 90, 032513 (2014).  https://doi.org/10.1103/PhysRevA.90.032513
  45. 45.
    C.E. Patrick, K.S. Thygesen, J. Chem. Phys. 143(10), 102802 (2015).  https://doi.org/10.1063/1.4919236
  46. 46.
    Y. Zhou, H. Bahmann, M. Ernzerhof, J. Chem. Phys. 143(12), 124103 (2015).  https://doi.org/10.1063/1.4931160
  47. 47.
    J.P. Přecechtělová, H. Bahmann, M. Kaupp, M. Ernzerhof, J. Chem. Phys. 143(14), 144102 (2015).  https://doi.org/10.1063/1.4932074
  48. 48.
    O.V. Gritsenko, B. Ensing, P.R.T. Schipper, E.J. Baerends, J. Phys. Chem. A 104(37), 8558 (2000).  https://doi.org/10.1021/jp001061m
  49. 49.
    Y. Zhang, W. Yang, J. Chem. Phys. 109(7), 2604 (1998).  https://doi.org/10.1063/1.476859
  50. 50.
    A. Savin, Chem. Phys. 356(1), 91 (2009), Moving Frontiers in Quantum Chemistry.  https://doi.org/10.1016/j.chemphys.2008.10.023
  51. 51.
    O. Gunnarsson, B.I. Lundqvist, Phys. Rev. B 13, 4274 (1976).  https://doi.org/10.1103/PhysRevB.13.4274
  52. 52.
    D.C. Langreth, J.P. Perdew, Phys. Rev. B 15, 2884 (1977).  https://doi.org/10.1103/PhysRevB.15.2884
  53. 53.
    M.S. Becker, Phys. Rev. 185, 168 (1969).  https://doi.org/10.1103/PhysRev.185.168
  54. 54.
    N.H. March, Phys. Chem. Liq. 46(5), 465 (2008).  https://doi.org/10.1080/00319100802239503
  55. 55.
    C. Amovilli, N.H. March, Phys. Rev. B 76, 195104 (2007).  https://doi.org/10.1103/PhysRevB.76.195104
  56. 56.
    R. Cuevas-Saavedra, P.W. Ayers, Int. J. Mod. Phys. B 24(25n26), 5115 (2010).  https://doi.org/10.1142/S0217979210057250
  57. 57.
    R. Cuevas-Saavedra, P.W. Ayers, Exchange-Correlation Functionals from the Identical-Particle Ornstein-Zernike Equation:. Basic Formulation and Numerical Algorithms (World Scientific, Singapore, 2012), vol. 25, pp. 237–249.  https://doi.org/10.1142/9789814340793_0019. ISBN 9789814340793
  58. 58.
    P. Gori-Giorgi, F. Sacchetti, G.B. Bachelet, Phys. Rev. B 61, 7353 (2000), [66, 159901(E) (2002)].  https://doi.org/10.1103/PhysRevB.61.7353
  59. 59.
    P. Gori-Giorgi, J.P. Perdew, Phys. Rev. B 66, 165118 (2002).  https://doi.org/10.1103/PhysRevB.66.165118
  60. 60.
    D. Chakraborty, R. Cuevas-Saavedra, P.W. Ayers, in Many-Body Approaches at Different Scales: A Tribute to Norman H. March on the Occasion of His 90th Birthday, ed. by G.G.N. Angilella, C. Amovilli (Springer, New York, 2018), chap. 17, p. 199. (This volume.).  https://doi.org/10.1007/978-3-319-72374-7_17
  61. 61.
    J.P.A. Charlesworth, Phys. Rev. B 53, 12666 (1996).  https://doi.org/10.1103/PhysRevB.53.12666
  62. 62.
    P. García-González, J.E. Alvarellos, E. Chacón, P. Tarazona, Phys. Rev. B 62, 16063 (2000).  https://doi.org/10.1103/PhysRevB.62.16063

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

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

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