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?
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.