From the density-functional theory to 'density-free' approximation schemes; a one-particle-ensemble formalism

Journal of Physics Condensed Matter

Volumn 8, Issue 35, 1996, Pages 6337-6355

  Farid, Behnam ^a,b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b MAX PLANCK INSTITUT FÜR FESTKÖRPERFORSCHUNG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038624738     PISSN: 09538984     EISSN: None     Source Type: Journal    
DOI: 10.1088/0953-8984/8/35/005     Document Type: Article

References (51)

1. Hohenberg P and Kohn W 1964 Phys Rev 136 B864
2. von Barth U and Hedin L 1972 J. Phys C: Solid State Phys. 5 1629
3. Rajagopal A K and Callaway J 1973 Phys. Rev. B 7 1912
4. Sander L M, Shore H B and Sham L J 1973 Phys. Rev. Lett. 31 533
5. Kalia R K and Vashishta P 1978 Phys Rev B 17 2655
6. Jansen H J F 1991 Phys. Rev. B 43 12 025
7. Kohn W and Sham L J 1965 Phys. Rev. 140 A 1133
8. Thomas L H 1927 Proc. Comb. Phil. Soc. 23 542 Fermi E 1928 Z Phys. 48 73
9. Thomas L H 1927 Proc. Comb. Phil. Soc. 23 542 Fermi E 1928 Z Phys. 48 73
10. Jones R O and Gunnarsson O 1989 Rev. Mod. Phys. 61 689
11. Payne M C, Teter M P, Allan D C, Arias T A and Joannopoulos J D 1992 Rev. Mod. Phys. 64 1045
12. Chacón E, Alvarellos J E and Tarazona P 1985 Phys. Rev. B 32 7868
13. Wang L-W and Teter M P 1992 Phys. Rev. B 45 13 196
14. Perrot F 1994 J. Phys. C: Solid State Phys. 6 431
15. Pearson M, Smarpasu E and Madden P A 1993 J. Phys C: Solid State Phys. 5 3221
16. Smargiassi E and Madden P A 1994 Phys. Rev. B 49 5220
17. Dreizler R M and Gross E K U 1990 Density Functional Theory (Berlin: Springer)
18. This statement, though made frequently, including in this paper, is not unequivocally correect: we shall, however. not go into details in this paper.
19. Wilson E B Jr 1962 J. Chem. Phys. 36 2232
20. Farid B 1996 sybmitted
21. Vosko S H, Wilk L and Nusair M 1980 Can. J. Phys. 58 1200 Vosko S H and Wilk L 1980 Phys. Rev. B 22 3812
22. Vosko S H, Wilk L and Nusair M 1980 Can. J. Phys. 58 1200 Vosko S H and Wilk L 1980 Phys. Rev. B 22 3812
23. Perdew J P and Zunger A 1981 Phys. Rev. B 23 5048
24. Ceperley D M and Alder B J 1980 Phys. Rev. Lett 45 566
25. x dq f̃(q)q sin(q|r - r′|)/|r - r′|.
26. Zaremba E 1990 J. Phys C: Solid State Phys. 2 2479
27. Farid B, Heine V, Engel G E and Robertson I J 1993 Phys. Rev. B 48 11 602
28. XC(q:[n]) see, e.g., figure 12 in [25].
29. eff, contribute to the ground-state total energy.
30. c X - see subsection 4.2 - x can easily be deduced from these.
31. Cohen M L and Heine V 1970 Solid State Physics vol 24, ed H Ehrenreich, F Seitz and D Turnbull (New York; Academic) pp 198-216
32. Penn D R 1962 Phys. Rev. 128 2093
33. Levine Z H and Louie S G 1982 Phys. Rev. B 25 6310 Hybertsen M S and Louie S G 1988 Phys. Rev. B 43 14 142 Zhu X and Louie S G 1991 Phys. Rev. B 43 14 142
34. Levine Z H and Louie S G 1982 Phys. Rev. B 25 6310 Hybertsen M S and Louie S G 1988 Phys. Rev. B 43 14 142 Zhu X and Louie S G 1991 Phys. Rev. B 43 14 142
35. Levine Z H and Louie S G 1982 Phys. Rev. B 25 6310 Hybertsen M S and Louie S G 1988 Phys. Rev. B 43 14 142 Zhu X and Louie S G 1991 Phys. Rev. B 43 14 142
36. Heine V and Weaire D 1970 Solid State Physics vol 24, ed H Ehrenreich, F Seitz and D Turnbull (New York: Academic) pp 249-163 (see in particular p 272)
37. Car R, Tosatti E, Baroni S and Leelaprute S 1981 Phys. Rev. B 24 985
38. (0)] in equation (9).
39. TC, determines the screened potential through which the electrons in the system interact; see, e.g., [25]
40. As one term in this expression is exact and the other a local approximation. we refer to the as a hybrid expression
41. 1/2 is essentiaily complex valued.
42. pw sub-matrix and the diagonal elements are identically vanishing. In this larger matrix we propose the diagonal elements not belonging to the sub-matrix to be those of the uniform electron gas corresponding to the average charge density.
43. Sham L J and Schlüter M 1985 Phys. Rev B 32 3883 Lannoo M, Schlüter M and Sham L J 1985 Phys. Rev. B 32 3890
44. Sham L J and Schlüter M 1985 Phys. Rev B 32 3883 Lannoo M, Schlüter M and Sham L J 1985 Phys. Rev. B 32 3890
45. 0 = 0.0302; it simply coincides with one of the points used by our Gauss - Chebyshev integration tethnique.
46. v[n].
47. v[n].
48. Golub G H and van Loan C F 1983 Matrix Computations (London: North Oxford Academic) ch 9
49. Hubbard J 1959 Phys. Rev. Lett. 3 77
50. Fand B, Engel G E, Daling R and van Haeringen W 1991 Phys. Rev. B 44 13 349
51. s'..