Sorry if this question is too simple for this community but I still couldn't find an answer to it.
- Do gamma-centred and gamma only grid mean the same thing?
- If not, what's the difference?
- How do they differ from Monkhorst-Pack grid?
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1$\begingroup$ Sure. Sorry for that. $\endgroup$– BereauSep 10, 2020 at 15:07
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2$\begingroup$ Thanks. You have now added a part about Monkhorst-Pack grids, which means you might be asking too many questions here. The first two are certainly okay in my opinion, but asking a third question in one thread is stretching it I think. If you want to know all the different types of grids, then ask "What are the types of grid?" and one answer could be about the Monkhorst-Pack grid, one about gamma-centred, etc. Also when I searched on Google I immediately found this: researchgate.net/post/… $\endgroup$– Nike DattaniSep 10, 2020 at 16:12
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$\begingroup$ I also saw that and some other ones but answers were not satisfactory. $\endgroup$– BereauSep 10, 2020 at 16:30
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3$\begingroup$ This question should probably be split or reformulated as "what are the types of k-point grids available?" which can lead to other grids also being contained within this answer. adaptive grids and chadi-cohen grids come to mind as others that have not been addressed here. $\endgroup$– Tristan MaxsonSep 10, 2020 at 17:47
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$\begingroup$ @TristanMaxson I didn't see your comment in time, otherwise I would have changed the question. $\endgroup$– Nike DattaniSep 11, 2020 at 16:48
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1 Answer
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Gamma Only: A k-point mesh (grid) only includes (samples) the gamma point of the Brillouin zone.
Gamma Centred: A k-point mesh (grid) that is centred around the gamma point of the Brillouin zone, and includes other points (often equally spaced, though not always). A gamma centred k-point grid often reduces computation cost, and contains important information with regard to band-gaps. However, a gamma centred k-point grid can fail to describe metallic ground-states. In general, a gamma k-point grid is often more advantages (although check your system).
For instance, in relation to surface calculations (from Efficient creation and convergence of surface slabs): One must also be mindful that the k-point sampling accurately reflects the reciprocal Bravais lattice of the surface Brillouin zone — for example, the (111) surfaces of FCC and BCC crystals are hexagonal and require a gamma-centered odd k-point grid.
Monkhorst-Pack: A special type of k-point mesh (grid). The sampling k-points are distributed homogeneously in the Brillouin zone, with rows or columns of k-points running parallel to the reciprocal lattice vectors that span the Brillouin zone.
From the original paper Special points for Brillouin-zone integrations: A method is given for generating sets of special points in the Brillouin zone which provides an efficient means of integrating periodic functions of the wave vector. The integration can be over the entire Brillouin zone or over specified portions thereof.
Note: The question relates to k-point grids, often encountered in planewave density functional theory.
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1$\begingroup$ A note about the (111) surfaces being gamma-centered odd k-point grids. I think that you will also see even grids shifted to the gamma point. I am unsure about this enough to suggest an edit though. $\endgroup$ Sep 11, 2020 at 15:45
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$\begingroup$ @TristanMaxson. It is an interesting observation and you can use even grids shifted to the gamma point. Indeed, this is supported by VASP. However, in the utmost strictest sense, using an even numbered grid on the (111) FCC/BCC surface for a gamma-centred mesh would be bad practice. $\endgroup$– WychhSep 11, 2020 at 17:25
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$\begingroup$ For what reason would you call it bad practice out of curiosity? $\endgroup$ Sep 11, 2020 at 18:39