GroupTheory`
GroupTheory`

GTVibDisplacementRep

GTVibDisplacementRep[molecular data]

gives the displacement representation of a molecule, defined by molecular data.

Details and Options

  • The matrix Γ(T) represents a 3Nx3N dimensional representation matrix related to the transformation T ∈ 0. N is the number of atoms in the molecule. The displacement representation itself can be found from the direct product of the permutation matrices and the rotation matrices for the group element T.
  • The following options can be given:
  • GOFast GOFastValueSkips the input validation
    GOVerbose TrueControls the output of additional information
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 13.1.1

Examples

open allclose all

Basic Examples  (1)

First load the package:

Set the directory to read data sets.

Read the data of ammonia from the database.

Specify the parameters of the structure.

The group contains 6 elements. Thus, the displacement representation contains 6 matrices. The dimension of the matrices of the displacement representation is 4x3=12, because ammonia contains 4 atoms and the dimension of the transformation matrices is 3.

The matrices and the matrix plots demonstrate the principle of the displacement representation. The permutations of the atoms under the symmetry element define the positions where the corresponding rotation matrix is placed. It can be seen, that under the N atom does not change its place.

Options  (2)

GOFast  (1)

GOVerbose  (1)

Additional information about the construction of the displacement representation are provided. it is active only if GOFast->True i set.