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Manual Pseudopotentials and orbitals Examples


4.3 Boundary conditions and k-points


ABACUS uses periodic boundary conditions for both crystals and finite systems. For isolated systems, such as atoms, molecules, clusters, etc., one uses so called the supercell model. Lattice vectors of the supercell are set in the STRU file.
For the input k-point (KPT) file, the file should either contain the k-point coordinates and weights or the mesh size for creating the k-point gird. Both options are allowed in ABACUS.


1. To generate k-mesh automatically
To generate k-mesh automatically, it requires the input subdivisions of the Brillouin zone in each direction and the origin for the k-mesh. ABACUS uses the Monkhorst-Pack method to generate k-mesh, and the following is the input k-point (KPT) file used in ABACUS.


K_POINTS //keyword for start
0 //total number of k-point, ’0’ means generate automatically
Gamma //which kind of Monkhorst-Pack method, ’Gamma’ or ’MP’
2 2 2 0 0 0 //first three number: subdivisions along recpri. vectors last three number: shift of the mesh


The third line controls generating k-mesh with origin at the Γ point(’Gamma’) or using the original Monkhorst-Pack scheme(’MP’).


2. To set up the k-points explicitly
If the user wants to set up the k-points explicitly, the input k-point file should contain the k-point coordinates and weights. An example is given as follows:


K_POINTS //keyword for start
8 //total number of k-point
Direct //’Direct’ or ’Cartesian’ coordinate
0.0 0.0 0.0 0.125 //coordinates and weights
0.5 0.0 0.0 0.125
0.0 0.5 0.0 0.125
0.5 0.5 0.0 0.125
0.0 0.0 0.5 0.125
0.5 0.0 0.5 0.125
0.0 0.5 0.5 0.125
0.5 0.5 0.5 0.125


3. Band structure calculations
ABACUS uses specified high-symmetry directions of the Brillouin zone for band structure calculations. The third line of k-point file should start with ’Line’ or ’Line Cartesian’ for line mode Line’ means the positions below are in Direct coordinates, while ’Line Cartesian’ means in Cartesian coordinates


K_POINTS # keyword for start
6 # number of high symmetry lines
Line # line-mode
0.5 0.0 0.5 20 # X
0.0 0.0 0.0 20 # G
0.5 0.5 0.5 20 # L
0.5 0.25 0.75 20 # W
0.375 0.375 0.75 20 # K
0.0 0.0 0.0 1 # G

The fourth line and the following are special k-point coordinates and number of k-points between this special k-point and the next.


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