The program SUBGROUPS
Given a space group and a supercell, this program calculates all the posible space groups compatible with the supercell.
The output of the program can be chosen to be the list of subgroups or a graph showing the subgroup-tree. In both cases the groups are grouped into conjugacy classes. More information about the conjugacy classes and the subgroups can be obtained: members of the conjugacy classes, transformation matrix to a standard or reference (default) setting of every group, lists of general positions, etc...
Alternative input data and optional filters for the output.
The program allows different input data sets and different conditions to be fulfilled by the subgroups given in the output. These are the alternative input/output conditions (ordered as in the main page of the program):
- The space group can be given in a non standard setting, introducing a set of generators of the group.
- Possible limitations of the subgroup list. By default, the program calculates all the subgroups compatible with the input data, being the last subgroup (the subgroup with the lowest symmetry) P1( #1). It is also possible to limit the bottom of the subgroup-tree (or the list of subgroups) giving one of these options:
- Lowest space group to be considered. The number of the group at the bottom of the list/graph should be given. The output (as a list or as a graph) shows all the subgroups of the given group which are also supergroups of the chosen "lowest space group".
- Lowest point group to be considered. The number of the point group at the bottom of the list/graph should be given. The output (as a list or as a graph) shows all the subgroups of the given group which have as point group the given "lowest point group" or a supergroup of this lowest point group.
- Only subgroups of a given crystal system. The output (as a list or as a graph) shows all the subgroups of the given group which belong to the chosen crystal system or which are supergroups of a group of the chosen crystal system.
- Only maximal subgroups. It gives only the maximal subgroups of the given groups which fulfill all the conditions of the input.
- Further limitations considering physical properties of the point groups. The list/graph of the output can be restricted to those space groups whose point group is:
- Centrosymmetric or non-centrosymmetric.
- Polar or non-polar.
- Instead of a supercell, a modulation wave-vector can be given, clicking on Alternatively give the modulation wave vector(s). Once this option has been chosen, the menu offers several possibilities:
- Show the independent vectors of the star. Clicking on this sentence the program will show all the independent wave-vectors of the star of the previously introduced modulation wave-vector (in those stars where -k belongs to the star it is not shown.) One the complete list is shown, the user can select some vectors of the star or the whole star as modulation wave-vectors.
- The option More wave-vectors needed allows to introduce as modulation wave-vectors vectors which belong to different stars. This option can be combined with the previous one.
- Checking the box Choose the whole star of the modulation vector(s) the whole set of vectors of the star(s) of the given wave-vectors (with respect to the point group of the given space group) are considered as modulation wave-vectors.
- Selecting the box Include the subgroups compatible with intermediate cells. the output shows all the subgroups compatible with intermediate unit cells (all intermediate unit cells between the unit cell of the given group and the supercell or the supercell determined by the introduced modulation wave-vectors.)
- Optional when a (or a set of) modulation wave-vector(s) are given. Wyckoff positions of the atoms. The list or graph of subgroups can be further refined when the atoms occupy special positions in the unit cell. Clicking on Wyckoff, the wyckoff positions of the atoms can be given.
- Active irreducible representations (irreps). Clicking on Representations, the program shows the list or irreps corresponding to the given propagation wave-vectors. The user can check some of those irreps. The program will show only those subgroups that come these irreps as active irreps. When the option Wyckoff positions of the atoms has been previously used, the clickable irreps are only those compatible with the given wyckoff positions.
Alternative output.
If the option Representations has been chosen, the default output gives the subgroups compatible with all the chosen representations. Once this first output is shown, it is possible to get the subgroups compatible with at least one chosen irrep.
