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Measured Electron Density Distributions in Crystals as a Basis for Band Structure Calculations

  • John Avery
  • Peter Sommer Larsen
  • Michael Grodzicki

Abstract

General methods are outlined for constructing Fourier coefficients of the Coulomb and Slater potentials in crystals from X-ray diffraction measurements of the charge density supplemented with atomic Hartree-Fock data. Corrections for temperature effects are discussed. Asymptotic expressions for the Fourier coefficients are also given, as well as an expression for the Coulomb contribution to the binding energy.

Keywords

Fourier Coefficient Acta Cryst Band Structure Calculation Electronic Charge Density Charge Neutrality Condition 
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.

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References

  1. 1.
    P. Becker, Editor, “Electron and Magnetization Densities in Crystals”, Plenum, New York (1980).Google Scholar
  2. 2.
    E.N. Maslen, Acta Cryst. B24, 1172 (1968).Google Scholar
  3. 3.
    P. Coppens and A. Vos, Acta Cryst. B27, 146 (1971).Google Scholar
  4. 4.
    F.L. Hirshfeld, Acta Cryst. A32, 239 (1976).Google Scholar
  5. 5.
    R.F. Stewart, J.Chem.Phys. 53, 205 (1970).CrossRefGoogle Scholar
  6. 6.
    P. Coppens and E.D. Stephens, Advances in Quantum Chemistry 10, Academic Press, New York (1977).Google Scholar
  7. 7.
    P.J.E. Aldred and M. Hart, Proc.Roy.Soc., (London) A 332, 223 (1973).Google Scholar
  8. 8.
    P. Becker, Phys.Scr. 15, 119 (1977).CrossRefGoogle Scholar
  9. 9.
    J. Avery, Int.J.Quantum Chem. 16, 1265 (1979).CrossRefGoogle Scholar
  10. 10.
    J. Avery and E. Berg, Int.J.Quantum Chem. 16, 1279 (1979).CrossRefGoogle Scholar
  11. 11.
    J. Avery, Int.J.Quantum Chem. Symp. 13, 403 (1979).Google Scholar
  12. 12.
    J. Avery and P.-J. Ørmen, Int.J.Quantum Chem. 18, 953 (1980).CrossRefGoogle Scholar
  13. 13.
    J. Avery and P.-J. Ørmen, Int.J.Quantum Chem. Symp. 14, 629 (1980).Google Scholar
  14. 14.
    J. Avery, P.-J. Ørmen and I. Chatterjee, Int.J.Quantum Chem. 21, 515 (1982).CrossRefGoogle Scholar
  15. 15.
    J. Avery and P.-J. Ørmen, Int.J.Quantum Chem. Symp. 15, 477 (1981).Google Scholar
  16. 16.
    J. Avery and P.-J. Ørmen, Acta Cryst. A35, 849 (1979).Google Scholar
  17. 17.
    J.C. Slater, Phys.Rev. 81, 385 (1951).CrossRefGoogle Scholar
  18. 18.
    E.J. Baerends, D.E. Ellis and P. Ros, Theor.Chim. Acta 27, 339 (1972).CrossRefGoogle Scholar
  19. 19.
    O. Gunnarson and P. Johansen, Int.J.Quantum Chem. 10, 307 (1976).CrossRefGoogle Scholar
  20. 20.
    E. Clementi, “Tables of Atomic Functions”, Supplement to IBM J. Res.Dev. 9, 2 (1965).CrossRefGoogle Scholar
  21. 21.
    D.T. Cromer and J.B. Mann, Acta Cryst. A24, 321 (1968).Google Scholar
  22. 22.
    C. Scheringer, Acta Cryst. A34, 905 (1978).Google Scholar
  23. 23.
    J.C. Slater, “Quantum Theory of Molecules and Solids, Vol. 4, The Self-Consistent Field for Molecules and Solids”, McGraw-Hill (1974).Google Scholar
  24. 24.
    R.F. Stewart, Acta Cryst. A31, S218 (1975).Google Scholar
  25. R.F. Stewart, Acta Cryst. A32, 182 (1976).Google Scholar
  26. R.F. Stewart, Acta Cryst. A32, 565 (1976).Google Scholar
  27. R.F. Stewart, Acta Cryst. A33, 33 (1977).Google Scholar
  28. R.F. Stewart, Acta Cryst. A34, S27 (1978).Google Scholar
  29. 25.
    R.F. Stewart, Bul.Amer.Phys.Soc. 23, 305 (1977).Google Scholar
  30. 26.
    R.F. Stewart, Chem.Phys.Letters, 65, 335 (1979).CrossRefGoogle Scholar
  31. 27.
    R.F. Stewart, J. Bentley and B. Goodman, J.Chem.Phys. 63, 3031 (1975).CrossRefGoogle Scholar
  32. 28.
    L.J. Massa and W.L. Clinton, Trans.Amer.Cryst.Assn. 8, 149 (1972).Google Scholar
  33. 29.
    W.L. Clinton and L.J. Massa, Phy s.Rev. Letters 29, 1363 (1972).CrossRefGoogle Scholar
  34. 30.
    C.A. Frishberg and L.J. Massa, Int.J.Quantum Chem. 18, 801 (1978).CrossRefGoogle Scholar
  35. 31.
    C. Frishberg and L.J. Massa, Phys.Rev. B24, 7018 (1981).Google Scholar
  36. 32.
    C. Frishberg and L.J. Massa, Acta Cryst. A38, 93 (1982).Google Scholar
  37. 33.
    B.T.M. Willis and A.W. Pryor, “Thermal Vibrations in Crystallography”, Cambridge University Press (1975).Google Scholar

Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • John Avery
    • 1
  • Peter Sommer Larsen
    • 1
  • Michael Grodzicki
    • 2
  1. 1.Department of Physical Chemistry, H. C. Ørsted InstituteUniversity of CopenhagenDenmark
  2. 2.Institute for Theoretical PhysicsUniversity of HamburgHamburg 36Germany

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