# Band gap calculation,how to choose the Kpoints?

## Main Question or Discussion Point

hello, is there anyone who can help me in the band gap calculation.

my situation is that:
I can calculate the band gap of sigle crystalline graphene, because i know the high symmetrical pionts of the first Brillouin zone of an hexagonal crystalline(M-G-K-M).
But the problem is that:
if i want to add some defects in graphene, I need to construct the unit cell in rectangular lattice style. Therefore, I can't use the high symmetrical pionts as before. So I want to know how to choose the Kpoints in this condition.
Should I use the the high symmetrical pionts of the first Brillouin zone of the rectangular lattice? Or I can simply scan these Kpions in the kx or ky direction?
I find some paper that calculates band structure in one direction(G-X), but i don't know what's the meaning of getting the band structure in one direction. If the band gap calculated in this direction can represent the band gap of the materials?

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The band gap shouldn't be calculated just from high symmetry points. It should be calculated by taking a mesh of k-points within the zone, the denser the better.

Thanks for your reply. i know what you say. What I really want to know is how to choose the path for the mesh.

Find what parts of the BZ are related through symmetry. E.g. you only need 1/6 because you have 6-fold rotational symmetry. Taking mirror planes into account you can reduce this further.

Keep only the smallest "pie slice" possible. Sometimes you can cut bits and re-attach them elsewhere (in a symmetry-equivalent position) to get a more regular shape that is more easily covered by a regular grid.

If you have done this properly, then all high symmetry axes should be in or on the edge of your slice.

Run a test calculation on a few random points to figure out how long each point takes.
Determine the number of points you can calculate by dividing the available time by the time needed for 1 point.

Then spread the available points evenly throughout your slice, e.g. in a regular grid, or along high symmetry axes first, and then evenly spaced in between.

Find what parts of the BZ are related through symmetry. E.g. you only need 1/6 because you have 6-fold rotational symmetry. Taking mirror planes into account you can reduce this further.

Keep only the smallest "pie slice" possible. Sometimes you can cut bits and re-attach them elsewhere (in a symmetry-equivalent position) to get a more regular shape that is more easily covered by a regular grid.

If you have done this properly, then all high symmetry axes should be in or on the edge of your slice.

Run a test calculation on a few random points to figure out how long each point takes.
Determine the number of points you can calculate by dividing the available time by the time needed for 1 point.

Then spread the available points evenly throughout your slice, e.g. in a regular grid, or along high symmetry axes first, and then evenly spaced in between.
Thanks. As you said, I can cut the rectangular box into hexgonal box, but it will need more atoms in one unit box in order to make that structure. Maybe it will be costly. Can I use these high symmetry kpoints of rectangular box to get the band gap?