Advertisement

Basic Concepts in Dielectric Response and Pseudopotentials

  • J. T. Devreese
  • F. Brosens

Abstract

A system of M electrons in a potential V 0 (which might be due to the ions and to external perturbations), is described by the hamiltonian:
$$H = \sum\limits_j^M {\frac{{p_j^2}}{{2m}} + \sum\limits_j^{\scriptstyle M \hfill \atop \scriptstyle \hfill} {{V^0}\left( {\overrightarrow r j} \right) + \frac{{{e^2}}}{e}\sum\limits_j^M {\sum\limits_{i \ne j}^M {\frac{1}{{|{{\overrightarrow r }_i} - {{\overrightarrow r }_j}|}}} } } } $$
(1.1)
Due to the Coulomb repulsion between the electrons, this hamiltonian is obviously nota sum of single particle hamiltonians H j . In principle, this means that the total wave function depends on the positions of all the electrons, the coordinates of which are all correlated.

Keywords

Dielectric Function Random Phase Approximation Core State Schrodinger Equation Dynamical Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

Chapter 1

  1. 1.
    J. B. Mann, Atomic structure calculations, 1: Hartree-Fock Energy Results for Elements Hydrogen to Lawrencium (Clearinghouse for Technical Information, Springfield, Va.), 1967Google Scholar
  2. C. F. Fischer, Atomic Data 4, 451 (1972)CrossRefGoogle Scholar
  3. 2.
    See e.g. D. W. Langer, R. N. Euwema, K. Era and T. Koda, Phys. Rev. B2, 4005 (1970)CrossRefGoogle Scholar
  4. 3.
    P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964)CrossRefGoogle Scholar
  5. 4.
    W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965)CrossRefGoogle Scholar
  6. 5.
    E. P. Wigner and F. Seitz, Phys. Rev. 43, 804 (1933)CrossRefGoogle Scholar
  7. 6.
    M. Gell’mann and K. Brueckner, Phys. Rev. 108, 364, (1957)CrossRefGoogle Scholar
  8. 7.
    E. P. Wigner, Trans. Faraday Soc. 34, 678 (1938)CrossRefGoogle Scholar
  9. 8.
    G. D. Mahan, Many-particle Physics, Plenum, 1981Google Scholar
  10. 9.
    In the next sections, we closely follow D. C. Wallace, Thermodynamics of Crystals, J. Wiley, New York, 1972, chapter 5.Google Scholar
  11. 10.
    H. Ehrenreich and M. H. Cohen, Phys. Rev. 115, 786 (1959)CrossRefGoogle Scholar
  12. 11.
    G. Niklasson, Phys. Rev. B10, 3052 (1974)CrossRefGoogle Scholar
  13. 12.
    P. E. Van Camp, V. E. Van Doren and J. T. Devreese, Phys. Rev. Lett. 42, 1224 (1979)CrossRefGoogle Scholar

Chapter 2

  1. 1.
    J. Lindhard, Kong. Danske Vid. Selsk., Mat.-fys. Medd. 24, No. 8 (1954)Google Scholar
  2. D. Bohm and D, Pines, Phys. Rev. 92, 609 (1953)CrossRefGoogle Scholar
  3. D. Pines and P. Nozières, The Theory of Quantum Liquids, Vol. 1, (Benjamin, New York), 1966Google Scholar
  4. 2.
    D. M. Miliotis, Phys. Rev. B3, 701 (1971)CrossRefGoogle Scholar
  5. P. Zacharias, J. Phys. F5, 645 (1975)CrossRefGoogle Scholar
  6. H. J. Höhberger, A. Otto and E. Petri, Solid State Commun. 18, 175 (1975)CrossRefGoogle Scholar
  7. P. M. Platzman and P. Eisenberger, Phys. Rev. Lett. 33, 152 (1974)CrossRefGoogle Scholar
  8. P. E. Batson, C. H. Chen and J. Silcox, Phys. Rev. Lett. 37, 937 (1976)CrossRefGoogle Scholar
  9. P. C. Gibbons, S. E. Schnatterly, J. J. Ritsko and J. R. Fields, Phys. Rev. B13, 2451 (1976)CrossRefGoogle Scholar
  10. S. E. Schnatterly in Solid State Physics 34, eds. H. Ehrenreich, F. Seitz and D. Turnbull ( Academic Press, New York ), 1979Google Scholar
  11. 3.
    A. J. Glick and R. A. Ferrell, Ann. of Phys. 11, 359 (1960)CrossRefGoogle Scholar
  12. 4.
    J. Hubbard, Proc. Roy. Soc. A240, 539 (1957)CrossRefGoogle Scholar
  13. D. J. W. Geldart and S. H. Vosko, Can. J. Phys. 44, 2137 (1966)CrossRefGoogle Scholar
  14. L. Kleinman, Phys. Rev. 180, 585 (1967)CrossRefGoogle Scholar
  15. K. S. Singwi, M. P. Tosi, R. H. Land and A. Sjölander, Phys. Rev. 176, 589 (1968)CrossRefGoogle Scholar
  16. M. P. Tosi, Il Nouvo Cimento, 1, 160 (1968)Google Scholar
  17. D. Langreth, Phys. Rev. 181, 753 (1969)CrossRefGoogle Scholar
  18. L. Hedin and S. Lundqvist, in Solid State Physics 23, eds. H. Ehrenreich, F. Seitz and D. Turnbull ( Academic Press, New York ), 1969Google Scholar
  19. K. S. Singwi, A. Sjölander, M. P. Tosi and R. H. Land, Solid State Comm. 7, 1503 (1969)CrossRefGoogle Scholar
  20. K. S. Singwi, A. Sjölander, M. P. Tosi and R. H. Land, Phys. Rev. B1, 1044 (1970)Google Scholar
  21. D. J. W. Geldart and R. Taylor, Can. J. Phys. 48, 155; 167 (1970)CrossRefGoogle Scholar
  22. A. W. Overhauser, Phys. Rev. B3, 1888 (1971)CrossRefGoogle Scholar
  23. P. Vashishta and K. S. Singwi, Phys. Rev. Be, 875 (1972)Google Scholar
  24. L. J. Sham, Phys. Rev. B7, 4357 (1973)CrossRefGoogle Scholar
  25. K. N. Pathak and P. Vashishta, Phys. Rev. B7, 3649 (1973)CrossRefGoogle Scholar
  26. 5.
    R. Dekeyser, Physica (Utrecht) 38, 189 (1968)CrossRefGoogle Scholar
  27. 6.
    J. C. Kimball, Phys. Rev. A7, 1648 (1973)CrossRefGoogle Scholar
  28. 7.
    G. Niklasson, Phys. Rev. B10, 3052 (1974)CrossRefGoogle Scholar
  29. 8.
    A. A. Kugler, J. Stat. Phys. 12, 35 (1975)CrossRefGoogle Scholar
  30. 9.
    F. Brosens, L. F. Lemmens and J. T. Devreese, Phys. Stat. Sol., 74, 45 (1976)CrossRefGoogle Scholar
  31. F. Brosens, J. T. Devreese and L. F. Lemmens, Phys. Stat. Sol., 80, 99 (1977)CrossRefGoogle Scholar
  32. 10.
    H. Mori, Progr. Theor. Phys. 33, 423 (1965)CrossRefGoogle Scholar
  33. 11.
    G. Mukhopadhyay and A. Sjölander, Phys. Rev. B17, 3580 (1978)Google Scholar
  34. F. Yoshida, S. Takeno and H. Yasuhara, Progr. Theor. Phys. 64, 40 (1980)CrossRefGoogle Scholar
  35. H. De Raedt and B. De Raedt, Phys. Rev. B18, 2039 (1978)CrossRefGoogle Scholar
  36. 12.
    J. T. Devreese, F. Brosens and L. F. Lemmens, Phys. Rev. B21, 1394 (1980)CrossRefGoogle Scholar
  37. F. Brosens, J. T. Devreese and L. F. Lemmens, Phys. Rev. B21, 1363 (1980)CrossRefGoogle Scholar
  38. J. T. Devreese and F. Brosens, in Proceedings of the 1981 NATO Advanced Study Institute on Electron Correlations in Solids, Molecules and Atoms, eds. J. T. Devreese and F. Brosens ( Plenum Press, New York ), 1983Google Scholar
  39. 13.
    W. E. Brittin and W. E. Chappell, Rev. Mod. Phys. 34, 620 (1962)CrossRefGoogle Scholar
  40. 14.
    G. Niklasson, Phys. Rev. B10, 3052 (1974)CrossRefGoogle Scholar
  41. G. Niklasson, in Proceedings of the 1981 NATO Advanced Study Institute on Electron Correlations in Solids, Molecules and Atoms, eds. J. T. Devreese and F. Brosens ( Plenum, New York ), 1983Google Scholar
  42. 15.
    S. Schnatterly, in Proceedings of the 1981 NATO Advanced Study Institute on Electron Correlations in Solids, Molecules and Atoms,eds.Google Scholar
  43. J. T. Devreese and F. Brosens ( Plenum, New York ), 1983Google Scholar
  44. 16.
    D. N. Tripathy and S. S. Mandai, Phys. Rev. B16, 231 (1979)Google Scholar
  45. 17.
    F. Toigo and T. O. Woodruff, Phys. Rev. B2, 3958 (1970)CrossRefGoogle Scholar
  46. 18.
    B. K. Rao, D. N. Tripathy and S. S. Mandai, J. Phys. F9, L51 (1979)CrossRefGoogle Scholar
  47. L. F. Lemmens, F. Brosens and J. T. Devreese, Phys. Rev. B20, 5398 (1979)CrossRefGoogle Scholar
  48. F. Brosens, J. T. Devreese and L. F. Lemmens, J. Phys. F10, L27 (1980)CrossRefGoogle Scholar
  49. A. Holas and K. S. Singwi, J. Phys. F11, L285 (1981)CrossRefGoogle Scholar
  50. 19.
    D. J. W. Geldart and R. Taylor, Can. J. Phys. 48, 155; 167 (1970)CrossRefGoogle Scholar
  51. 20.
    A. Holas, P. K. Aravind and K. S. Singwi, Phys. Rev. B20, 4912 (1979)CrossRefGoogle Scholar
  52. 21.
    F. Brosens and J. T. Devreese, Phys. Rev. B29, 543 (1984)CrossRefGoogle Scholar
  53. 22.
    N. E. Brener and J. L. Fry, Phys. Rev. B19, 1720 (1979)CrossRefGoogle Scholar
  54. 23.
    L. Hedin and S. Lundqvist, in Solid State Physics 23, eds. H. Ehrenreich, F. Seitz and D. Turnbull ( Academic Press, New York ), 1969Google Scholar
  55. 24.
    H. Nachtegaele, F. Brosens and J. T. Devreese, Phys. Rev. 28, 6064 (1983)CrossRefGoogle Scholar
  56. 25.
    K. Utsumi and S. Ichimaru, Phys. Rev. B23, 3291 1981CrossRefGoogle Scholar
  57. S. Ichimaru and K. Utsumi, Phys. Rev. B24, 7385 (1981)CrossRefGoogle Scholar
  58. 26.
    L. Lantto, P. Pietiläinen and A. Kallio, Phys. Rev. B28, 5568 (1982)Google Scholar
  59. 27.
    D. Ceperley, Phys. Rev. B18, 3126 (1978)CrossRefGoogle Scholar
  60. D. M. Ceperley and B. J. Adler, Phys. Rev. Lett. 45, 566 (1980)CrossRefGoogle Scholar

Chapter 3

  1. 1.
    A. O. E. Animalu and V. Heine, Phil. Mag. 12, 1249 (1965)CrossRefGoogle Scholar
  2. 2.
    L. Szasz and G. McGinn, J. Chem. Phys. 47, 3495 (1967)CrossRefGoogle Scholar
  3. 3.
    A. Zunger and M. L. Cohen, Phys. Rev. B18, 5449 (1978)CrossRefGoogle Scholar
  4. 4.
    A. U. Hazi and S. A. Rice, J. Chem. Phys. 48, 495 (1968)CrossRefGoogle Scholar
  5. 5.
    J. C. Barthelat and P. Durand, Chem. Phys. Lett. 18, 63 (1972)CrossRefGoogle Scholar
  6. 6.
    M. A. Ratner, S. Topiol and J. W. Moskowitz, Chem. Phys. 20, 1 (1976)Google Scholar
  7. 7.
    A. Redondo, W. A. Goddard and T.C. McGill, Phys. Rev. B15, 5038 (1977)CrossRefGoogle Scholar
  8. 8.
    K. M. Ho, M. L. Cohen and M. Schlüter, Chem. Phys. Lett. 48, 608 (1977)CrossRefGoogle Scholar
  9. 9.
    W. A. Harrison, in Pseudopotentials in the Theory of Metals, ( Benjamin, New York, 1966 )Google Scholar
  10. 10.
    V. Heine, M. L. Cohen and V. Heine, and D. Weaire, in Solid State Physics 24, Eds. H. Ehrenreich, F. Seitz and D. Turnbull (Academic, New York, 1970 )Google Scholar
  11. 11.
    M. Schlüter, J. R. Chelikowsky, S. G. Louie and M. L. Cohen, Phys. Rev. B12, 4200 (1975)CrossRefGoogle Scholar
  12. 12.
    J. A. Appelbaum and D. Hamann, Rev. Mod. Phys. 48, 479 (1976)CrossRefGoogle Scholar
  13. 13.
    S. G. Louie, K. M. Ho, J. R. Chelikowsky and M. L. Cohen, Phys. Rev. 15, 5627 (1977)CrossRefGoogle Scholar
  14. 14.
    G. P. Kerker, K. M. Ho and M. L. Cohen, Phys. Rev. B18, 5473 (1978)CrossRefGoogle Scholar
  15. 15.
    W. A. Harrison, in Pseudopotentials in the Theory of Metals, ( Benjamin, New York, 1966 )Google Scholar
  16. 16.
    V. Heine, M. L. Cohen and V. Heine. Weaire, in Solid State Physics 24, Eds. H. Ehrenreich, F. Seitz and D. Turnbull ( Academic, New York, 1970 )Google Scholar
  17. 17.
    D. Stroud and N. W. Ashcroft, J. Phys. F 1, 113 (1971)CrossRefGoogle Scholar
  18. 18.
    P. B. Allen and M. L. Cohen, Phys. Rev. 187, 525 (1969)CrossRefGoogle Scholar
  19. 19.
    J. C. Phillips and L. Kleinman, Phys. Rev. 116, 287 (1975)CrossRefGoogle Scholar
  20. 20.
    C. Herring, Phys. Rev. 57, 1169 (1940)CrossRefGoogle Scholar
  21. 21.
    B. J. Austin, V. Heine and L. J. Sham, Phys. Rev 127, 276 (1982)CrossRefGoogle Scholar
  22. 22.
    V. Heine, in The Physics of Metals. I. Electrons, J. M. Ziman, ed. Cambridge University Press, New York, 1969, p. 7Google Scholar
  23. 23.
    W. A. Harrison, Phys. Rev. 131, 2433 (1963)CrossRefGoogle Scholar
  24. 24.
    N. W. Ashcroft, Physics Letters 23, 48 (1966)CrossRefGoogle Scholar
  25. 25.
    N. W. Ashcroft, J. Phys. Cl, 232 (1968)Google Scholar
  26. 26.
    I. V. Abarenkov and V. Heine, Phil. Mag. 12, 529 (1965)CrossRefGoogle Scholar
  27. 27.
    A. O. E. Animalu and V. Heine, Phil. Mag. 12, 1249 (1965)CrossRefGoogle Scholar
  28. A. O. E. Animalu, Proc. Roy. Soc. A 294, 376 (1966)CrossRefGoogle Scholar
  29. 28.
    W. A. Harrison, Electronic Structure and the Properties of Solids, ed. W. H. Freeman, San Francisco, 1980Google Scholar
  30. 29.
    R. Kahn and W. A. Goddard III, J. Chem. Phys. 56, 2685 (1972)CrossRefGoogle Scholar
  31. C. F. Melius and W. A. Goddard III, Phys. Rev A10, 1528 (1974)Google Scholar
  32. S. Topioi, A. Zunger and M. A. Ratner, Chem. Phys. Lett. 49, 367 (1977)CrossRefGoogle Scholar
  33. 30.
    D. R. Hamann, M. Schlüter and C. Chiang, Phys. Rev. Lett. 43, 1494 (1979)CrossRefGoogle Scholar
  34. 31.
    G. B. Bachelet, D. R. Hamann and M. Schlüter, Phys. Rev. B28, 4199 (1982)Google Scholar
  35. 32.
    R.W. Shaw and W. A. Harrison, Phys. Rev. 183, 604 (1967)CrossRefGoogle Scholar

Chapter 4

  1. 1.
    W. A. Harrison, Pseudopotentials in the Theory of Metals, Benjamin, New York, 1966Google Scholar
  2. 2.
    V. Heine, in Solid State Physics 24, eds. H. Ehrenreich, F. Seitz and D. Turnbull ( Academic, New York ), 1970Google Scholar
  3. 3.
    D. C. Wallace, Thermodynamics in Crystals, Ed, J. Wiley, New York, 1972Google Scholar

Chapter 5

  1. 1.
    The general outline of this section follows Harrison, Ref. 1 of the previous chapter.Google Scholar
  2. 2.
    R. Stedman and G. Nilsson, Phys. Rev. 145, 492 (1966)CrossRefGoogle Scholar
  3. 3.
    For this derivation we closely follow D. C. Wallace, Thermodynamics of Crystals, J. Wiley, New York, 1972Google Scholar
  4. 4.
    R. W. Shaw and W. A. Harrison, Phys. Rev. 183, 604 (1967)CrossRefGoogle Scholar
  5. 5.
    C. M. Bertoli, V. Bortolani, C. Calandra and F. Nizzoli, Phys. Rev. Lett. 31, 1466 (1973)CrossRefGoogle Scholar

Chapter 6

  1. 1.
    W. A. Harrison, Electronic Structure and the Properties of Solids, W. H. Freeman, San Francisco, 1980, p. 393Google Scholar
  2. 2.
    See e.g. P. K. Lam and M. L. Cohen, Phys. Rev. 25, 6139 (1982)CrossRefGoogle Scholar
  3. 3.
    P. E. Van Camp, V. E. Van Doren and J. T. Devreese, Phys. Rev. Lett. 42, 1224 (1979)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • J. T. Devreese
    • 1
    • 2
    • 3
  • F. Brosens
    • 1
    • 4
  1. 1.Department of PhysicsUniversitaire Instelling AntwerpenAntwerpen-WilrijkBelgium
  2. 2.Institute of Applied MathematicsR. U. C. A.AntwerpenBelgium
  3. 3.University of TechnologyEindhovenThe Netherlands
  4. 4.National Fund for Scientific ResearchBelgium

Personalised recommendations