The k-point set used in a calculation defines the accuracy of the Brillouin zone sampling. The Monkhorst-Pack k-points used in CASTEP are characterized by divisions along three reciprocal space axes and by an optional origin shift. However, the origin shift should not be used. Thus, the k-points setup procedure simply involves selecting three integer divisions.
The quality of the k-point set can be quantified in a number of ways; CASTEP uses the distance between the points in reciprocal space as a numerical measure. The simplest way to define the set is the following:
Simple way of setting the k-points
This method creates either a Monkhorst-Pack set of the selected quality (Coarse, Medium, or Fine) or instructs CASTEP to use only one Γ-point (the origin in reciprocal space).
Explicit selection of Γ-point sampling is not recommended. CASTEP will automatically
use this option if the cell is very large in real space, so that the Brillouin zone is small and no sampling is required.
In all other cases, the Γ-point is the least representative of all Brillouin zone points and using it as the only sampling point can distort the results severely.
Puska (2000) showed, for example, that there is a 1-2 eV error in the vacancy formation energy in silicon when the Γ-point is used for cells containing up to 128 atoms.
Finer control over k-point sets can be exercised by using the k-points tab on the CASTEP Electronic Options dialog. This tab allows you to enter the actual Monkhorst-Pack mesh parameters by selecting the Custom grid parameters option.
CASTEP automatically optimizes the mesh parameters according to the point group symmetry of the 3D model. For example, in a cubic crystal the even mesh parameters, N, will generate the set with as many k-points as the one with the odd mesh parameters, N-1. Since the former set provides better sampling, it will be selected automatically when either Quality or k-point separation is used to define the k-point set. Custom grid parameters is the only option which allows you to specify a suboptimal mesh with odd divisions.
The quality of the k-point sampling is particularly important for metallic systems, where rapid changes in electronic structure may occur along the energy band that crosses the Fermi level. Insulators or semiconductors, even when they are treated using variable occupation numbers for electronic states, are less sensitive to the quality of k-point sampling. The default settings used by CASTEP are designed to give accurate sampling for metallic systems. This means that you can get good results for insulators and semiconductors with a slightly less fine k-point mesh than the default.
The total energy is not guaranteed to decrease as more k-points are added. Therefore, when carrying out convergence testing, you should strive to find a set of k-points such that further improvements do not alter the total energy beyond the tolerance level you require. However, the energy is not likely to converge smoothly and oscillations are to be expected.
Setting up electronic options
Electronic tab - CASTEP Calculation dialog
k-points tab - CASTEP Electronic Options dialog