GroupTheory`
GroupTheory`
GTTbNumberOfIntegrals
GTTbINumberOfIntegrals[character table, subgroup character tables,irreducible representations] gives the number of independent Integrals in a three-center tight-binding Hamiltonian for a certain shell.
Details and Options
- The following options can be given:
-
GOVerbose False Controls output of additional information GONames {} controls names of IReps - The point group of the crystal is
. The crystal is considered as a series of shells of atoms of constant distance from a central atom. The shells 
are characterized by the shell vectors 
. The groups 
contain the elements of 
that transform the shell vectors into the vectors 
. The information about the character tables of 
and 
is used to calculated the number of independent integrals in a three-center tight-binding Hamiltonian. - See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chpter 9.4.2
- See also: R.F. Egorov, B.I. Reser, and V.P. Shirkovskii, Consistent treatment of Symmetry in the Tight Binding Approximation, phys.stat.sol. 26, 391 (1968)
Examples
open allclose allBasic Examples (1)
The character table of the group is calculated. The notation of Mulliken is used.
qv contains the vectors 
of shell 
which are the minimum set to recalculate all vectors of the coordination sphere by point group operations. In case of the simple cubic lattice it is one vector per coordination sphere.
The groups 
of the vectors 
, i.e. all operations of the point group, leaving the vectors constant, are generated.
The character tables of the groups.
The number of independent integrals are calculated for each shell.
