GroupTheory`
GroupTheory`

GTTbSymbol2C

GTTbSymbol2C[l<,l>,m,shell]

gives a symbol according to the nomenclature of the two-center approximation.

Details and Options

  • To describe the interaction of two atoms at sides and with orbital symmetry and the corresponding energy integrals are decomposed in two-center form.
  • The nomenclature of the two-center approximation was introduce by Slater and Koster.
  • The first angular momentum is smaller than to avoid appearance of parameters which differ only by a sign.
  • Furthermore holds.
  • If symbols for the on-site energies are generated.
  • The following option can be given:
  • GOTbBasis 0Supresses superscripts with element names
  • See: J. C. Slater, G. F. Koster,Simplified LCAO method for the periodic potential problem, Phys. Ref. 94, 1498-1524 (1954)
  • A.V. Podolskiy, P. Vogl,Compact expression for the angular dependence of tight-binding Hamiltonian matrix elements, Phys. Rev. B 69, 233101 (2004)
  • W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 9.4

Examples

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Basic Examples  (1)

First load the package.

Symbols for interaction of two wave functions.

Symbols for interaction of two wave functions. Here the atoms belong to the next nearest neighbor shell.

If an * orbital is involved, has to be used.

GTTbSymbol2C generates also on-site parameters.

Options  (1)

GOTbBasis  (1)

If different types of atoms appear we have to distinguish the tight-binding parameters accordingly. GaAs will be described by a basis set of s,p,s* orbitals for Ga and As, for example.

Note, the element names in the superscript are ordered lexicographically. the angular momenta are ordered accordingly.