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Hartree-Fock Crystal-Orbital Theory of Periodic Polymers

  • János J. Ladik

Abstract

We consider a three-dimensional periodic polymer or molecular crystal containing m orbitals in the elementary cell of one or more atoms. For the sake of simplicity the number of elementary cells in the direction of each crystal axis is taken equal to an odd number: N 1 = N 2 = N 3 = 2N + 1. We assume further that there is an interaction between orbitals belonging to different elementary cells. In that case we can describe, in the one-electron approximation, the delocalized crystal orbitals of the polymer with the aid of the linear-combination-of-atomic-orbitals (LCAO) approximation in the form
$$\phi _{h}^{p}(r)=\sum\limits_{q}{\sum\limits_{g=1}^{m}{C{{(p)}_{h;q,g}}\chi _{g}^{q}}}$$
(1.1)
where p = (p 1, p 2, p 3) and q = (q 1, q 2, q 3); integers p j and q j (j = 1, 2, 3) run over − N,..., 0,..., N and Σ q is a shorthand notation for \(\sum _{{{q}_{1}}=-N}^{N}\sum _{{{q}_{2}}=-N}^{N}\sum _{{{q}_{3}}=-N}^{N}\). Further, χ g = χ g (rR q r g a ) is the gth atomic orbital (AO) (corresponding to the atom with position vector r g a ) in the cell characterized by the vector R q = q 1 a 1 + q 2 a 2 + q 3 a 3 (q j = − N,..., 0,..., N), where a l, a 2, and a 3 are the three basis vectors of the crystal.

Keywords

Elementary Cell Atomic Orbital Translational Symmetry Spin Formalism Slater Determinant 
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

© Plenum Press, New York 1988

Authors and Affiliations

  • János J. Ladik
    • 1
  1. 1.University of Erlangen-NurembergErlangen-WaterlooFederal Republic of Germany

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