Last Modified 17 December 1999

How to generate k-points using the "static" tight-binding program

While we have provided a selection of pre-defined k-points for several crystals structures, it is always possible that you may want to generate your own k-points:

• Our mesh points may not be dense enough
• You would like to try another type of mesh
• We haven't found k-points for your lattice

The static program has a way to generate new k-points under these conditions. The only catch is that you must know the space group of your lattice. We have a a database containing space group information about many common (and some not-so-common) space groups. If the lattice you want is in our database, you can find the space group file there. If the space group file is not there, you three choices:

• Generate your own space group file using our format. The International Crystallography Tables are invaluable here.
• Ask us to generate your space group. The lattice will appear on our web site within a week or two.
• If you are very desperate, use the totally unsymmetrized space group (#1 in the Crystallography tables). This is not a good choice if the lattice has any symmetry at all, as the program will generate many equivalent k-points.

We'll assume your spacegroup file is named, logically enough, "spcgrp". Then to generate a new set of k-points you need the following sequence:

NEWSYM=T
LATTIC=1
spcgrp
ILAT=F
    0
lspec=f,linfok=f
    8    8    8

This looks much like the input in our example, except that the "-1313" flag has been replaced by a zero, and the k-point file name has been replaced by two lines:

in the line "lspec=f,linfok=f"

• "lspec=f" indicates that the points are going to be "regular", as opposed to "special" (lspec=t). Regular k-points include the origin, while special k-points do not. Special k-points are generated according to the algorithm of Monkhorst and Pack. As this method is known to have problems for many non-cubic lattices, we do not recommend using special k-points generated by this code.
• The string ",linfok=f" should be left as is. This is a flag indicating that no "information only" k-points will be generated.

The "    8    8    8" (note the (3I5) formating) is used to specify the mesh size: 8 points will be generated along the direction of each reciprocal lattice vector, and the resulting grid will by symmetrized by the space group file. Larger numbers will result in a denser mesh. This also increase the CPU time, both to generate the k-points and to do the calculations, so you will probably have to compromise.

The program will now generate the k-points, and then use these points to determine the energy of the lattice.

Return to the examples.

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