Simple model for the spherically and system-averaged pair density: Results for two-electron atoms

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 71, Issue 3, 2005, Pages

  Gori Giorgi, Paola ^a   Savin, Andreas ^a  

^a LABORATOIRE DE CHIMIE THÉORIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRON-ELECTRON REPULSION; ELECTRONIC PAIR DENSITY; KOHN-SHAM (KS) FORMALISM; NONUNIFORM SYSTEMS;

APPROXIMATION THEORY; COMPUTATIONAL METHODS; ELECTRON GAS; KINETIC ENERGY; MATRIX ALGEBRA; OPTIMIZATION; PROBABILITY DENSITY FUNCTION;

CARRIER CONCENTRATION;

EID: 18444417418     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.71.032513     Document Type: Article

References (71)

1. W. Kohn, Rev. Mod. Phys. 71, 1253 (1999).
2. A. E. Mattsson, Science 298, 759 (2002).
3. A Primer in Density Functional Theory, edited by C. Fiolhais, F. Nogueira, and M. Marques (Springer-Verlag, Berlin, 2003).
4. W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
5. J. P. Perdew and K. Schmidt, in Density Functional Theory and Its Applications to Materials, edited by V. VanDoren et al. (AIP, New York, 2001), and references therein.
6. A. Savin, F. Colonna, and R. Pollet, Int. J. Quantum Chem. 93, 166 (2003), and references therein.
7. V. Sahni, Quantal Density Functional Theory (Springer-Verlag, Berlin, 2004).
8. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996);
9. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 78, 1396 (1997);
10. A. D. Becke, Phys. Rev. A 38, 3098 (1988);
11. J. Chem. Phys. 84, 4524 (1986);
12. C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37, 785 (1988);
13. J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, ibid. 46, 6671 (1992);
14. J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, Phys. Rev. B 48, 4978 (1993).
15. J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, Phys. Rev. Lett. 91, 146401 (2003).
16. J. P. Perdew, A. Ruzsinszky, J. Tao, V. N. Staroverov, G. E. Scuseria, and G. I. Csonka, J. Chem. Phys. (to be published).
17. M. Seidl, J. P. Perdew, and S. Kurth, Phys. Rev. Lett. 84, 5070 (2000).
18. See, e.g., S. Kümmel and J. P. Perdew, Phys. Rev. B 68, 035103 (2003);
19. W. Yang and Q. Wu, Phys. Rev. Lett. 89, 143002 (2002);
20. R. J. Magyar, A. Fleszar, and E. K. U. Gross, Phys. Rev. B 69, 045111 (2004);
21. M. Grüning, O. V. Gritsenko, and E. J. Baerends, J. Chem. Phys. 118, 7183 (2003).
22. C. A. Coulson and A. H. Neilson, Proc. Phys. Soc. London 78, 831 (1961).
23. J. Cioslowski, B. B. Stefanov, A. Tan, and C. J. Umrigar, J. Chem. Phys. 103, 6093 (1995).
24. J. Cioslowski and G. Liu, J. Chem. Phys. 109, 8225 (1998).
25. E. Valderrama, J. M. Ugalde, and R. J. Boyd, in Many-electron Densities and Reduced Density Matrices, edited by J. Cioslowski (Kluwer Academic/Plenum Publishers, New York, 2000).
26. E. R. Davidson, Reduced Density Matrices in Quantum Chemistry (Academic Press, New York, 1976).
27. A. J. Coleman and V. I. Yukalov, Reduced Density Matrices: Coulson's Challenge (Springer-Verlag, New York, 2000).
28. See, e.g., G. Mazzone, F. Sacchetti, and V. Contini, Phys. Rev. B 28, 1772 (1983);
29. C. Petrillo and F. Sacchetti, ibid. 51, 4755 (1995).
30. A. K. Rajagopal, J. C. Kimball, and M. Banerjee, Phys. Rev. B 18, 2339 (1978);
31. X.-Y. Pan and V. Sahni, J. Chem. Phys. 119, 7083 (2003).
32. The difference in kinetic energy can be obtained from the adiabatic connection formula that can be viewed as a generalization of the above argument, and is treated in Sec. V.
33. A. W. Overhauser, Can. J. Phys. 73, 683 (1995).
34. P. Gori-Giorgi and J. P. Perdew, Phys. Rev. B 64, 155102 (2001).
35. B. Davoudi, M. Polini, R. Asgari, and M. P. Tosi, Phys. Rev. B 66, 075110 (2002).
36. M. Corona, P. Gori-Giorgi, and J. P. Perdew, Phys. Rev. B 69, 045108 (2004);
37. I. Nagy, R. Diez Muino, J. I. Juaristi, and P. M. Echenique, ibid. 69, 233105 (2004).
38. P. Ziesche, Phys. Lett. A 195, 213 (1994);
39. M. Levy and P. Ziesche, J. Chem. Phys. 115, 9110 (2001).
40. A. Gonis, T. G. Schulthess, J. van Ek, and P. E. A. Turchi, Phys. Rev. Lett. 77, 2981 (1996);
41. A. Gonis, T. G. Schulthess, P. E. A. Turchi, and J. van Ek, Phys. Rev. B 56, 9335 (1997).
42. A. Nagy, Phys. Rev. A 66, 022505 (2002).
43. F. Furche, Phys. Rev. A 70, 022514 (2004).
44. J. M. Soler, Phys. Rev. B 69, 195101 (2004).
45. M. Levy, Proc. Natl. Acad. Sci. U.S.A. 76, 6062 (1979).
46. E. Lieb, Int. J. Quantum Chem. 24, 243 (1983).
47. J. Harris and R. Jones, J. Phys. F: Met. Phys. 4, 1170 (1974);
48. D. C. Langreth and J. P. Perdew, Solid State Commun. 17, 1425 (1975);
49. O. Gunnarsson and B. I. Lundqvist, Phys. Rev. B 13, 4274 (1976).
50. W. Yang, J. Chem. Phys. 109, 10107 (1998).
51. A. Savin, in Recent Developments and Applications of Modern Density Functional Theory, edited by J. M. Seminario (Elsevier, Amsterdam, 1996);
52. T. Leininger, H. Stell, H.-J. Werner, and A. Savin, Chem. Phys. Lett. 275, 151 (1997);
53. R. Pollet, A. Savin, T. Leininger, and H. Stell, J. Chem. Phys. 116, 1250 (2002).
54. R. Pollet, F. Colonna, T. Leininger, H. Stall, H.-J. Werner, and A. Savin, Int. J. Quantum Chem. 91, 84 (2003);
55. J. Toulouse (private communication).
56. J. Toulouse, F. Colonna, and A. Savin, Phys. Rev. A 70, 062505 (2004).
57. B. Davoudi, R. Asgari, M. Polini, and M. P. Tosi, Phys. Rev. B 68, 155112 (2003);
58. R. Asgari, B. Davoudi, and M. P. Tosi, Solid State Commun. 131, 301 (2004).
59. R. Asgari, B. Davoudi, M. Polini, and M. P. Tosi (unpublished).
60. D. E. Freund, B. D. Huxtable, and J. D. Morgan III, Phys. Rev. A 29, 980 (1984).
61. 12). See also C. J. Umrigar and X. Gonze, Phys. Rev. A 50, 3827 (1994), and Ref. [14].
62. P. Ziesche, Phys. Rev. B 67, 233102 (2003);
63. P. Ziesche, K. Pernal, and F. Tasnádi, Phys. Status Solidi B B239, 185 (2003).
64. F. Colonna and A. Savin, J. Chem. Phys. 110, 2828 (1999).
65. Q. Zhao, R. C. Morrison, and R. G. Parr, Phys. Rev. A 50, 2138 (1994);
66. R. van Leeuwen and E. J. Baerends ibid. 49, 2421 (1994).
67. J. P. Perdew, A. Savin, and K. Burke, Phys. Rev. A 51, 4531 (1995);
68. K. Burke, J. P. Perdew, and M. Ernzerhof, J. Chem. Phys. 109, 3760 (1998);
69. E. Valderrama and J. M. Ugalde, Int. J. Quantum Chem. 86, 40 (2002).
70. X. Fradera, M. Duran, E. Valderrama, and J. M. Ugalde, Phys. Rev. A 62, 034502 (2000).
71. P. Gori-Giorgi and J. P. Perdew, Phys. Rev. B 66, 165118 (2002).