KPoints

Name KPoints
Section Mesh::KPoints
Type block

This block defines an explicit set of k-points and their weights for a periodic-system calculation. The first column is the weight of each k-point and the following are the components of the k-point vector. You only need to specify the components for the periodic directions. Note that the k-points should be given in Cartesian coordinates (not in reduced coordinates), in the units of inverse length. The weights will be renormalized so they sum to 1 (and must be rational numbers).

For example, if you want to include only the Gamma point, you can use:

%KPoints
  1.0 | 0 | 0 | 0
%

Name KPointsGrid
Section Mesh::KPoints
Type block
Default $\backslash Gamma$-point only

When this block is given (and the KPoints block is not present), k-points are distributed in a uniform grid, according to a modified version of the Monkhorst-Pack scheme. For the original MP scheme, see James D. Pack and Hendrik J. Monkhorst, Phys. Rev. B 13, 5188 (1976) and Phys. Rev. B 16, 1748 (1977).

The number of columns should be equal to Dimensions, but the grid and shift numbers should be 1 and zero in finite directions.

The first row of the block is a set of integers defining the number of k-points to be used along each direction in reciprocal space. The numbers refer to the whole Brillouin zone, and the actual number of k-points is usually reduced exploiting the symmetries of the system. By default the grid will always include the $\Gamma$-point.

Optional rows can be added to specify multiple shifts in the k-points (between 0.0 and 1.0), in units of the Brillouin zone divided by the number in the first row. Please note that without specifying any shift, an implicit shift of -0.5 is added for odd number of k-points, such that the Gamma point is always included.

For example, the following input samples the BZ with 100 points in the xy-plane of reciprocal space:

%KPointsGrid
  10 | 10 | 1
%

is equivalent to

%KPointsGrid
10 | 10 | 1
0 | 0 | -0.5
%

Name KPointsPath
Section Mesh::KPoints
Type block

When this block is given, k-points are generated along a path defined by the points of the list. The points must be given in reduced coordinates.

The first row of the block is a set of integers defining the number of k-points for each segments of the path. The number of columns should be equal to Dimensions, and the k-points coordinate should be zero in finite directions.

For example, the following input samples the BZ with 15 points:

%KPointsPath
  10 | 5
   0 | 0 | 0
   0.5 | 0 | 0
   0.5 | 0.5 | 0.5
%

Name KPointsReduced
Section Mesh::KPoints
Type block

Same as the block KPoints but this time the input is given in reduced coordinates, i.e. what Octopus writes in a line in the ground-state standard output as

#k = 1, k = ( 0.154000, 0.154000, 0.154000).

Name KPointsUseSymmetries
Section Mesh::KPoints
Type logical
Default no

This variable defines whether symmetries are taken into account or not for the choice of k-points. If it is set to no, the k-point sampling will range over the full Brillouin zone.

When a perturbation is applied to the system, the full symmetries of the system cannot be used. In this case you must not use symmetries or use the SymmetryBreakDir to tell Octopus the direction of the perturbation (for the moment this has to be done by hand by the user, in the future it will be automatic).

Name KPointsUseTimeReversal
Section Mesh::KPoints
Type logical

If symmetries are used to reduce the number of k-points, this variable defines whether time-reversal symmetry is taken into account or not. If it is set to no, the k-point sampling will not be reduced according to time-reversal symmetry.

The default is yes, unless symmetries are broken in one direction by the SymmetryBreakDir block.

Warning: For time propagation runs with an external field, time-reversal symmetry should not be used.

Name QPointsGrid
Section Mesh::KPoints
Type block
Default KPointsGrid

This block allows to define a q-point grid used for the calculation of the Fock operator with k-points. The q-points are distributed in a uniform grid, as done for the KPointsGrid variable. See J. Chem Phys. 124, 154709 (2006) for details

For each dimension, the number of q point must be a divider of the number of k point

%QPointsGrid
  2 | 2 | 1
%

At the moment, this is not compatible with k-point symmetries.