Simple question about KPOINT grids

[discoduck]

Could somebody explain to me the concepts of KPOINT grids please. I know what k-space/reciprocal space is

What is the difference between an nxnxn grid and a nxnx1 grid for example, and why is it important to use even or odd grids for specific calculations

 

[kanato]

The calculation of many quantities in solid state physics require some sort of integral over the Brillouin zone. When doing numerical calculations, these integrals cannot be carried out analytically, so you approximate the integral by using a grid in k-space. This is exactly the same as using, say, the trapezoid rule to integrate a function in one dimension, only we generalize it to a function of two or three dimensions.

An nxnx1 grid only is a single plane of k-points. You would only use this in a case where you have a system which is strongly 2-dimensional (examples might be cuprates and systems like ZrNCl). An even grid is usually best to take advantage of symmetries to speed the computation.

 

[discoduck]

What type of grid would I need to use for a surface calculation i.e. bulk structure next to a vacuum?

 

[kanato]

For a surface calculation, you would only use one k=point in the direction of the surface normal. So if your surface is in the x-y plane, then your grid would be NxNx1