GROUP THEORY SYMBOL

GTSymmetryElementQ

GTSymmetryElementQ[symmetry element,cluster]
gives True, if symmetry element leaves cluster invariant, and gives False otherwise.

DetailsDetails

  • A system under consideration is described by a cluster of atoms. Usually the symmetry of cluster is known by construction. Nevertheless it could be necessary sometimes to prove, if cluster is invariant under a certain symmetry element. The argument symmetry element is either a single symmetry element or a list of symmetry elements. The list can be a certain collection of symmetry elements or a whole point group.
  • For a successful application of GTSymmetryElementQ one has to guarantee that the position and orientation of the cluster is in agreement with the definition of the symmetry elements. This should be checked first!
  • The following option can be given:
  • GOVerboseFalseControls the output of additional information
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package:

In[1]:=
Click for copyable input

The NaCl structure will be chosen from the database.

In[2]:=
Click for copyable input

A cluster will be constructed.

In[3]:=
Click for copyable input

The cluster has to show the symmetry of the full cubic point group.

In[4]:=
Click for copyable input
Out[4]=
In[5]:=
Click for copyable input
Out[5]=

One atom is added to the cluster, which obviously does not belong to the NaCl structure

In[6]:=
Click for copyable input
In[7]:=
Click for copyable input
Out[7]=

Because the new atom is placed on the z-axis is sill a symmetry element.

In[8]:=
Click for copyable input
Out[8]=

The symmetry will also be destroyed if an impurity is placed at a lattice site.

In[9]:=
Click for copyable input
Out[9]=
In[10]:=
Click for copyable input
Out[10]=

Options  (1)Options  (1)

Top