Journal of Chemical Physics
Feedback | Help | Exit
The Journal of Chemical Physics
Search:
   
 
 
 
Previous Article
The merits of the frozen-density embedding scheme to model solvatochromic shifts
We investigate the usefulness of a frozen-density embedding scheme within density-functional theory [J. Phys. Chem. 97, 8050 (1993)] for the calculation of solvatochromic shifts. The frozen-density ca...
Next Article
Experiments and quantum-chemical calculations on Rydberg states of H2CS in the region 5.6–9.5 eV
Absorption spectrum of H2CS in the region 5.6–9.5 eV was recorded with a continuously tunable light source of synchrotron radiation. After we subtracted absorption bands of CS2, our spectrum clea...

Describing static correlation in bond dissociation by Kohn–Sham density functional theory

J. Chem. Phys. 122, 094116 (2005); doi:10.1063/1.1858371

Published 4 March 2005

You are not logged in to this journal. Log in

M. Fuchs
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany and Unité PCPM, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium

Y.-M. Niquet
Unité PCPM, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium and Département de Recherche Fondamentale sur la Matière Condensée, SP2M/LSim, CEA Grenoble, 38054 Grenoble Cedex 9, France

X. Gonze
Unité PCPM, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium

K. Burke
Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, New Jersey 08854
We show that density functional theory within the RPA (random phase approximation for the exchange-correlation energy) provides a correct description of bond dissociation in H2 in a spin-restricted Kohn–Sham formalism, i.e., without artificial symmetry breaking. We present accurate adiabatic connection curves both at equilibrium and beyond the Coulson–Fisher point. The strong curvature at large bond length implies important static (left–right) correlation, justifying modern hybrid functional constructions but also demonstrating their limitations. Although exact at infinite separation and accurate near the equilibrium bond length, the RPA dissociation curve displays unphysical repulsion at larger but finite bond lengths. Going beyond the RPA by including the exact exchange kernel (RPA + X), we find a similar repulsion. We argue that this deficiency is due to the absence of double excitations in adiabatic linear response theory. Further analyzing the H2 dissociation limit we show that the RPA + X is not size consistent, in contrast to the RPA. ©2005 American Institute of Physics
History: Received 19 October 2004; accepted 21 December 2004; published 4 March 2005
Permalink: http://link.aip.org/link/?JCPSA6/122/094116/1
BUY THIS ARTICLE   (US$24)
Download HTML Download Sectioned HTML Download PDF (159 kB) View Cart

KEYWORDS and PACS

Keywords
PACS
  • 31.15.Ew
    Density-functional theory (atoms and molecules)
  • 33.15.Fm
    Molecular bond strengths, dissociation energies
  • 31.25.Nj
    Electron-correlation calculations for diatomic molecules
  • 33.15.Dj
    Interatomic distances and angles in molecules
  • YEAR: 2005

RELATED DATABASES


To view database links for this article,
you need to log in.
To view database links for this article,
you need to log in.

PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
Publisher:
AIP is a member of CrossRef AIP

REFERENCES (81)
View in Separate Window/Tab
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, B864 (1964).
  2. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
  3. W. Koch and M.C. Holthausen, A Chemist's Guide to Density Functional Theory (Wiley-VCH, Weinheim, 2001).
  4. A. D. Becke, J. Chem. Phys. 98, 5648 (1993);
    5. 104, 1040 (1996).
  5. J. P. Perdew, M. Ernzerhof, and K. Burke, J. Chem. Phys. 105, 9982 (1996).
  6. C. Adamo and V. Barone, J. Chem. Phys. 110, 6158 (1999).
  7. J. Dobson, in Topics of Condensed Matter Physics, edited by M. P. Das (Nova, New York, 1994), p. 121;
    8. see also cond-mat/0311371
  8. J. F. Dobson and B. P. Dinte, Phys. Rev. Lett. 76, 1780 (1996).
  9. W. Kohn, Y. Meir, and D. E. Makarov, Phys. Rev. Lett. 80, 4153 (1998).
  10. E. Engel, A. Höck, and R. M. Dreizler, Phys. Rev. A 61, 032502 (2000).
  11. P. García-Gonzáles and R. W. Godby, Phys. Rev. Lett. 88, 056406 (2002).
  12. M. Ernzerhof, K. Burke, and J.P. Perdew, in Recent Developments in Density Functional Theory, edited by J. M. Seminario (Elsevier, Amsterdam, 1997).
  13. T. Bally and G. Nahsari Sastry, J. Phys. Chem. A 101, 7923 (1997).
  14. M. Sodupe, J. Bertran, L. Rodríguez-Santiago, and E. J. Baerends, J. Phys. Chem. A 103, 166 (1999).
  15. M. Ernzerhof, J.P. Perdew, and K. Burke, in Topics in Current Chemistry, edited by R. F. Nalewajski (Springer, Berlin, 1996), Vol. 180, p. 1.
  16. O. V. Gritsenko, P. R. T. Schipper, and E. J. Baerends, J. Chem. Phys. 107, 5007 (1997).
  17. J. P. Perdew, A. Savin, and K. Burke, Phys. Rev. A 51, 4531 (1995).
  18. A. M. Lee and N. C. Handy, J. Chem. Soc., Faraday Trans. 89, 3999 (1993).
  19. C. D. Sherill, M. S. Lee, and M. Head-Gordon, Chem. Phys. Lett. 302, 425 (1999).
  20. M. Filatov and S. Shaik, Chem. Phys. Lett. 332, 409 (2000);
    21. J. Phys. Chem. A 104, 6628 (2000).
  21. R. Pollet, A. Savin, T. Leininger, and H. Stoll, J. Chem. Phys. 116, 1250 (2002).
  22. D. C. Langreth and J. P. Perdew, Solid State Commun. 17, 1425 (1975);
    23. Phys. Rev. B 15, 2884 (1977).
  23. J.P. Perdew and K. Schmidt, in Density Functional Theory and Its Application to Materials, edited by V. Van Doren, C. Van Alsenoy, and P. Geerlings (AIP, Melville, NY, 2001).
  24. S. Kurth and J. P. Perdew, Phys. Rev. B 59, 10461 (1999).
  25. J. F. Dobson and J. Wang, Phys. Rev. Lett. 82, 2123 (1999).
  26. F. Furche, Phys. Rev. B 64, 195120 (2001).
  27. M. Fuchs and X. Gonze, Phys. Rev. B 65, 235109 (2002).
  28. H. Rydberg, M. Dion, N. Jacobson, E. Schröder, P. Hylgaard, S. I. Simak, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 91, 126402 (2003).
  29. M. Dion, H. Rydberg, E. Schröder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004).
  30. Z. Yan, J. P. Perdew, and S. Kurth, Phys. Rev. B 61, 16430 (2000).
  31. J. F. Dobson and J. Wang, Phys. Rev. B 62, 10038 (2000).
  32. J. F. Dobson, J. Wang, and T. Gould, Phys. Rev. B 66, 081108 (2002).
  33. M. Grüning, O. V. Gritsenko, and E. J. Baerends, J. Chem. Phys. 118, 7183 (2003).
  34. J. M. Herbert and J. E. Harriman, Chem. Phys. Lett. 382, 142 (2003).
  35. E. J. Baerends, Phys. Rev. Lett. 87, 133004 (2001).
  36. W. Kolos and C. C. Roothaan, Rev. Mod. Phys. 32, 219 (1960).
  37. Of course, one never works with this decomposition within DFT. The interpretation in terms of covalent and ionic parts is, however, quite natural when PsiKS is analyzed as a many-electron wave function.
  38. C. A. Coulson and I. Fisher, Philos. Mag. 40, 386 (1949).
  39. O. Gunnarsson and B. Lundqvist, Phys. Rev. B 13, 4274 (1976).
  40. R. van Leeuwen, O.V. Gritsenko, and E.J. Baerends, in Topics in Current Chemistry, edited by R. F. Nalewajski (Springer, Berlin, 1996), Vol. 180, p. 107.
  41. C. Filippi, S. B. Healy, P. Kratzer, E. Pehlke, and M. Scheffler, Phys. Rev. Lett. 89, 166102 (2002).
  42. R. Bauernschmitt and R. Ahlrichs, J. Chem. Phys. 104, 9047 (1996).
  43. J. Gräfenstein, E. Kraka, and D. Cremer, Chem. Phys. Lett. 288, 593 (1998).
  44. S. Grimme and M. Waletzke, J. Chem. Phys. 111, 5645 (1999).
  45. P. R. T. Schipper, O. V. Gritsenko, and E. J. Baerends, J. Chem. Phys. 111, 4056 (1999).
  46. A. Görling and M. Levy, Phys. Rev. A 50, 196 (1994);
    47. for a review see also: T. Grabo, T. Kreibich, S. Kurth, and E.K. U. Gross, in Strong Coulomb Correlations in Electronic Structure: Beyond the LDA, edited by V. I. Anisimov (Gordon and Breach, New York, 1999), p. 203.
  47. M. Petersilka, U. J. Gossmann, and E. K. U. Gross, Phys. Rev. Lett. 76, 1212 (1996).
  48. A. Görling and M. Levy, Phys. Rev. B 47, 13105 (1993).
  49. C.-O. Almbladh, U. von Barth, and R. van Leeuwen, Int. J. Mod. Phys. B 13, 535 (1999).
  50. N. E. Dahlen and U. von Barth, J. Chem. Phys. 120, 6826 (2004).
  51. L. J. Holleboom and J. G. Snijders, J. Chem. Phys. 93, 5826 (1990).
  52. F. Aryasetiawan, T. Miyake, and K. Terakura, Phys. Rev. Lett. 88, 166401 (2002);
    53. F. Aryasetiawan, T. Miyake, and K. Terakura, ibid. 90, 189702 (2003).
  53. M. Fuchs, K. Burke, Y.-M. Niquet, and X. Gonze, Phys. Rev. Lett. 90, 189701 (2003).
  54. Y.-M. Niquet, M. Fuchs, and X. Gonze, J. Chem. Phys. 118, 9504 (2003).
  55. Y.-M. Niquet, M. Fuchs, and X. Gonze, Phys. Rev. A 68, 032507 (2003).
  56. J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992).
  57. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3685 (1996).
  58. M. Levy and J. P. Perdew, Phys. Rev. A 32, 2010 (1985).
  59. M. Ernzerhof, Chem. Phys. Lett. 263, 499 (1996).
  60. K. Burke, M. Ernzerhof, and J. P. Perdew, Chem. Phys. Lett. 265, 115 (1997).
  61. R. van Leeuwen, Ph.D. thesis, Vrije Universiteit, 1996.
  62. O. V. Gritensko and E. J. Baerends, Phys. Rev. A 54, 1957 (1996).
  63. We interpolate the (unknown) exact curve in lambda[is-an-element-of][0,1] by DeltaUXC(lambda) = DeltaEX + [DeltaU<sub>XC</sub><sup>[prime]</sup>(0)lambdap(lambda)]/[1 + alphalambdap(lambda)], where alpha= [DeltaU<sub>XC</sub><sup>[prime]</sup>(0)/DeltaUC]–[1/p(1)]. Our interpolation reproduces DeltaEX, DeltaU<sub>XC</sub><sup>[prime]</sup>(0), and DeltaUXC as given in Tables I t2. For R = 1.4  bohr it integrates to DeltaEXC = –2.07  eV, where we have set p(lambda)[equivalent]1. For R = 5  bohr we have chosen p(lambda) = 1 + betalambdae–gammalambda, adjusting beta and gamma to yield DeltaEXC = 0.82  eV and also the strong interaction limit of UXC[H2](lambda) [M. Seidl (private communication)].
  64. A. Puzder, M. Y. Chou, and R. Q. Hood, Phys. Rev. A 64, 022501 (2001).
  65. A. Savin, F. Colonna, and M. Allavena, J. Chem. Phys. 115, 6827 (2001).
  66. F. Colonna, D. Maynau, and A. Savin, Phys. Rev. A 68, 012505 (2003).
  67. R. Q. Hood, M. Y. Chou, A. J. Williamson, G. Rajagopal, and R. J. Needs, Phys. Rev. B 57, 8972 (1998).
  68. R. J. Magyar, W. Terilla, and K. Burke, J. Chem. Phys. 119, 696 (2003).
  69. M. Seidl, J. P. Perdew, and S. Kurth, Phys. Rev. Lett. 84, 5070 (2000).
  70. M. Fuchs and X. Gonze (unpublished).
  71. C. J. Umrigar and X. Gonze, Phys. Rev. A 50, 3827 (1994).
  72. M. Fuchs and X. Gonze (unpublished).
  73. M. Lein, E. K. U. Gross, and J. P. Perdew, Phys. Rev. B 61, 13431 (2000).
  74. M.E. Casida, in Recent Developments and Applications in Density Functional Theory, edited by J. M. Seminario (Elsevier, Amsterdam 1996).
  75. J.C. Slater, Quantum Theory of Molecules and Solids (McGraw-Hill, New York, 1963), Vol. 1, p. 60.
  76. O. V. Gritsenko, S. J. A. van Gisbergen, A. Görling, and E. J. Baerends, J. Chem. Phys. 113, 8478 (2000).
  77. N. T. Maitra, F. Zhang, R. J. Cave, and K. Burke, J. Chem. Phys. 120, 5932 (2004).
  78. X. Gonze, J.-M. Beuken, R. Caracas et al., Comput. Mater. Sci. 25, 478 (2002).
  79. M. Fuchs and M. Scheffler, Comput. Phys. Commun. 107, 67 (1999).
  80. H. Appel, E. K. U. Gross, and K. Burke, Phys. Rev. Lett. 90, 043005 (2003).
  81. R. van Leeuwen (private communication).

CITING ARTICLES
For access to citing articles, you need to log in.
For access to citing articles, you need to Log in.


Copyright © American Institute of Physics