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Construction of a generalized gradient approximation by restoring the density-gradient expansion and enforcing a tight Lieb–Oxford bound

J. Chem. Phys. 128, 184109 (2008); doi:10.1063/1.2912068

Published 14 May 2008

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Yan Zhao and Donald G. Truhlar
Department of Chemistry and Supercomputing Institute, University of Minnesota, 207 Pleasant Street, S.E. Minneapolis, Minnesota 55455-0431, USA
Recently, a generalized gradient approximation (GGA) to the density functional, called PBEsol, was optimized (one parameter) against the jellium-surface exchange-correlation energies, and this, in conjunction with changing another parameter to restore the first-principles gradient expansion for exchange, was sufficient to yield accurate lattice constants of solids. Here, we construct a new GGA that has no empirical parameters, that satisfies one more exact constraint than PBEsol, and that performs 20% better for the lattice constants of 18 previously studied solids, although it does not improve on PBEsol for molecular atomization energies (a property that neither functional was designed for). The new GGA is exact through second order, and it is called the second-order generalized gradient approximation (SOGGA). The SOGGA functional also differs from other GGAs in that it enforces a tighter Lieb–Oxford bound. SOGGA and other functionals are compared to a diverse set of lattice constants, bond distances, and energetic quantities for solids and molecules (this includes the first test of the M06-L meta-GGA for solid-state properties). We find that classifying density functionals in terms of the magnitude µ of the second-order coefficient of the density gradient expansion of the exchange functional not only correlates their behavior for predicting lattice constants of solids versus their behavior for predicting small-molecule atomization energies, as pointed out by Perdew and co-workers [Phys. Rev. Lett. 100, 134606 (2008); Perdewibid. 80, 891 (1998)], but also correlates their behavior for cohesive energies of solids, reaction barriers heights, and nonhydrogenic bond distances in small molecules. ©2008 American Institute of Physics
History: Received 26 February 2008; accepted 27 March 2008; published 14 May 2008
Permalink: http://link.aip.org/link/?JCPSA6/128/184109/1
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KEYWORDS and PACS

Keywords
PACS
  • 71.15.Mb
    Density functional theory, local density approximation, gradient and other corrections (condensed matter electronic structure)
  • 61.50.Lt
    Crystal binding; cohesive energy
  • YEAR: 2008

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0021-9606 (print)   1089-7690 (online)
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REFERENCES (48)
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For access to fully linked references, you need to log in. For access to fully linked references, you need to Log in.
  1. P. Hohenberg and W. Kohn, Phys. Rev. 136, 864 (1964);
  2. W. Kohn and L. J. Sham, ibid. 140, 1133 (1965).
  3. W. Kohn, Rev. Mod. Phys. 71, 1253 (1999).
  4. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
  5. A. D. Becke, J. Chem. Phys. 98, 1372 (1993);
    6. 98, 5648 (1993);
    C. Adamo and V. Barone, ibid. 110, 6158 (1999).
  6. Y. Zhao, N. E. Schultz, and D. G. Truhlar, J. Chem. Theory Comput. 2, 364 (2006).
  7. Y. Zhao and D. G. Truhlar, Theor. Chem. Acc. 120, 215 (2008).
    8. See also erratum in Theor. Chem. Acc. 119, 525(2008).
  8. Y. Zhao and D. G. Truhlar, Acc. Chem. Res. 41, 157 (2008).
  9. A. D. Becke, J. Chem. Phys. 104, 1040 (1996).
  10. J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, Phys. Rev. Lett. 91, 146401 (2003).
  11. Y. Zhao and D. G. Truhlar, J. Chem. Phys. 125, 194101 (2006).
  12. M. Gruning, O. Gritsenko, and E. J. Baerends, J. Phys. Chem. A 108, 4459 (2004).
  13. S. K. Ghosh and R. G. Parr, Phys. Rev. A 34, 785 (1986);
    14. A. D. Becke, J. Chem. Phys. 88, 1053 (1988);
    R. M. Koehl, G. K. Odom, and G. E. Scuseria, Mol. Phys. 87, 835 (1996);
    J. P. Perdew, S. Kurth, A. Zupan, and P. Blaha, Phys. Rev. Lett. 82, 2544 (1999).
  14. B. Hammer, L. B. Hansen, and J. K. Norskov, Phys. Rev. B 59, 7413 (1999).
  15. Y. Zhang and W. Yang, Phys. Rev. Lett. 80, 890 (1998).
  16. G. K. H. Madesen, Phys. Rev. B 75, 195108 (2007).
  17. Z. Wu and R. E. Cohen, Phys. Rev. B 73, 235116 (2006);
    18. see also Y. Zhao and D. G. Truhlar (to be published) for discussion of their derivation.
  18. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Phys. Rev. Lett. 100, 136406 (2008).
  19. J. P. Perdew, L. A. Constantin, E. Sagvolden, and K. Burke, Phys. Rev. Lett. 97, 223002 (2006).
  20. J. P. Perdew, A. Ruzsinszky, J. Tao, V. N. Staroverov, G. E. Scuseria, and G. I. Csonka, J. Chem. Phys. 123, 062201 (2005).
  21. E. H. Lieb and S. Oxford, Int. J. Quantum Chem. 19, 427 (1981).
  22. M. M. Odashima and K. Cappelle, J. Chem. Phys. 127, 054106 (2007).
  23. G. I. Csonka, O. A. Vydrov, G. E. Scuseria, A. Ruzsinszky, and J. P. Perdew, J. Chem. Phys. 126, 244107 (2007).
  24. Y. Zhao and D. G. Truhlar, Org. Lett. 9, 1967 (2007).
  25. G. L. Oliver and J. P. Perdew, Phys. Rev. A 20, 397 (1979).
  26. P. R. Antoniewicz and L. Kleinman, Phys. Rev. B 31, 6779 (1985).
  27. S.-K. Ma and K. A. Brueckner, Phys. Rev. 165, 18 (1968).
  28. A. D. Becke, J. Chem. Phys. 84, 4524 (1986).
  29. V. N. Staroverov, G. E. Scuseria, J. Tao, and J. P. Perdew, Phys. Rev. B 69, 075102 (2004).
  30. P. J. Hay and W. R. Wadt, J. Chem. Phys. 82, 299 (1985).
  31. S. Piskunov, E. Heifets, R. I. Eglitis, and G. Borstel, Comput. Mater. Sci. 29, 165 (2004).
  32. B. J. Lynch, Y. Zhao, and D. G. Truhlar, J. Phys. Chem. A 107, 1384 (2003).
  33. B. J. Lynch and D. G. Truhlar, J. Phys. Chem. A 107, 8996 (2003);
    34. 108, 1460(E) (2004).
  34. M. J. Frisch, G. W. Trucks, H. B. Schlegel et al., GAUSSIAN03, Revision D.01, Gaussian, Inc., Pittsburgh, PA, 2004.
  35. D. J. Singh, Planewaves, Pseudopotentials and LAPW Method (Kluwer, Boston, 1994).
  36. S. A. Mabud and A. M. Glazer, J. Appl. Crystallogr. 12, 49 (1979).
  37. Y. Zhao and D. G. Truhlar, J. Phys. Chem. A 109, 5656 (2005);
    38. J. Chem. Theory Comput. 2, 1009 (2006).
  38. R. S. Peace, Acta Crystallogr. 5, 356 (1952).
  39. Y. Baskin and L. Meyer, Phys. Rev. 100, 544 (1955).
  40. J. P. Perdew, in Electronic Structure of Solids '91, edited by P. Ziesche and H. Eschig (Akademie, Berlin, 1991), p. 11.
  41. C. Adamo and V. Barone, J. Chem. Phys. 108, 664 (1998).
  42. A. D. Becke, Phys. Rev. A 38, 3098 (1988).
  43. C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37, 785 (1988).
  44. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 80, 891 (1998).
  45. S. Kurth, J. P. Perdew, and P. Blaha, Int. J. Quantum Chem. 75, 889 (1999).
  46. G. K. H. Madsen, Phys. Rev. B 75, 195108 (2007).
  47. A. Zupan, K. Burke, M. Ernzerhof, and J. P. Perdew, J. Chem. Phys. 106, 10184 (1997).
  48. K. Kuchitsu, Structure of Free Polyatomic Molecules-Basic Data (Springer, Berlin, 1998).
  49. S. J. Chakravorty, S. R. Gwaltney, E. R. Davidson, F. A. Parpia, and C. F. F. Fischer, Phys. Rev. A 47, 3649 (1993).

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