Interatomic potentials in solids

  • N. H. March
Section B: Potentials
First Online:
Part of the Lecture Notes in Physics book series (LNP, volume 166)

Abstract

The following points have been stressed in this brief survey:
  1. (i)

    The ground-state energy E is very naturally considered as E[ϱ(r{{ℓ}}], p being the electron density and {ie113-1} the totality of nuclear sites.

     
  2. (ii)

    Whereas the wave equation gives a delocalized ϱ(r{{ℓ}}) inevitably (and only determines localized distributions uniquely in a special case like NaCl), physical and chemical intuition can go into choice of localized densities, which will then often allow decomposition into pair, and many body terms.

     
  3. (iii)

    Even for small displacements from equilibrium, however, as in for example lattice vibrations, such localized electron distributions must deform as the nuclei move.

     
  4. (iv)

    For the classical ionic model, the localized picture corresponds to the Heitler-London crystal wave function of cations and anions, which leads in turn to a superposition property of first-order density matrices. The additivity property of polarizabilities follows as a consequence.

     
  5. (v)

    Bonds afford a valuable description of electron density and hence force fields in group IV semiconductors, partially ionic 3–5 compounds, and metals with directional charge distribution (e.g. Be (30-32) Fe, Cr).

     
  6. (vi)

    For small displacements, an exact formal theory exists. But this requires the concept of a tensor charge density; this has not yet been made quantitative though.

     
  7. (vii)

    Some progress is possible for large displacements, but presently only through limited cohesive energy inversion at a first-principle level. Otherwise, modelling or phenomenology is still essential in this important area. This latter problem will be taken up in several later chapters in the book.

     

Keywords

Force Field Cohesive Energy Bond Charge Valence Force Field Free Electron Metal 
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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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • N. H. March
    • 1
  1. 1.Theoretical Chemistry DepartmentOxford

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