autoGR: Generate Generalized Regular k-point Grids

Implementation of an algorithm to generate generalized regular k-point grids. The algorithm searches over many GR grids that meet a specified k-point density and returns the one with the highest high symmetry reduction and a good packing fraction. On average, this will yield about a 60% speed-up over the standard Monkhorst-Pack k-point grids. More information can be found in the following:

• Generalized Regular Grids On-The-Fly describes the algorithm and method of the code in this repository. It describes how the combinatorial explosion of searching over all possible grids is tamed by generating only symmetry-preserving grids.
• Performance of Generalized Regular Grids vs Monkhorst-Pack Grids using over 7,000 calculations of different unit cells and different metallic elements that GR grids are 60% more efficient than MP grids on average. Supplements the work of Wisesa, McGill and Mueller (2016) listed below.
• Efficient Algorithm For K-Point Folding discusses in detail an O(N) algorithm for k-point symmetry reduction. This algorithm is essential to enable the on-the-fly method in the paper above.
• Optimal Meshes by Moreno and Soler (1992). The original proposal to use Generalized Regular grids to accelerate DFT calculations. Common Grids Froyen (1989) had essentially the same idea earlier but applied it to a specific use case.
• K-point Server by Wisesa, McGill and Mueller (2016). The first practical implementation of Moreno and Soler's idea. Now available offline as well.

The algorithm works for all crystal classes, but it can fail occasionally when the user-provided structural information is "sloppy", resulting in large finite precision errors. An update that will fix this known issue is being developed.

Compiling the code

To compile the executable, first clone this repository:

git clone --recursive git@github.com:msg-byu/autoGR.git

(If you have trouble with the recursive cloning, it is probably because you don't have ssh keys set up on github for your local machine.

Cloning into 'autoGR'...
Warning: Permanently added the RSA host key for IP address '140.82.113.3' to the list of known hosts.
Permission denied (publickey).
fatal: Could not read from remote repository.

Please make sure you have the correct access rights
and the repository exists.

Try this: Adding a new SSH key to your GitHub account.)

The --recursive is required so that the dependent repos are also cloned.

To compile the executable, navigate to the src directory:

cd autoGR/src

Compile the executable using:

make F90=gfortran DEBUG=false kpoints.x

The makefile is set up so that the dependencies are also compiled.

Using the code

The code reads two files, 1) a file the contains the lattice vectors and atomic basis vectors for the crystal (currently only the VASP POSCAR is supported) and 2) a KPGEN file that contains the desired grid density. The code outputs a KPOINTS file containing the irreducible k-points and their weights. The KPGEN file requires one of the following keyword inputs to be present to determine the number of points that will be needed in the grid:

• NKPTS: the total number of desired k-points.
• KPDENSITY: the desired target k-point density.
• KSPACING: the linear space desired between k-points (same as CASTEP inputs).
• KPPRA: the desired number of k-points per reciprocal atom.
• RMIN: the minimal distance between points in real space desired.

(We recommend KPDENSITY or KSPACING.) Only one of these keywords needs to be specified for the code to run.

If a specific offset for the k-point grid is desired then the following optional keyword can be used. If this is not specified, the code will select the best shift. If an unshifted grid is desired, specify a zero shift, SHIFT= 0.0 0.0 0.0.

• SHIFT: the shift away from the origin for the k-point grid (expressed in fractions of the reciprocal lattice vectors).

The code's default behavior is to find multiple candidate grids then select the grid that has the best ratio of irreducible points to reducible points. Alternatively the following flag can be used to have the code return the grid that has the fewest number of k-points:

MIN_IRR_KPTS = TRUE

• MIN_IRR_KPTS: when set to TRUE the grid with the fewest irreducible k-points will be returned.

It is also possible to restrict the symmetry operations used to fold the k-points using the `USE_SYMMETRY' key word.

• USE_SYMMETRY: can take the key words ALL, STRUCTURAL, TIME_REVERSAL, NONE where each key word indicates the level of symmetry to restrict the symmetry operations used to fold the k-point grid. All, the default, indicates that all the symmetry operations of the reciprocal cell should be used, STRUCTURAL indicates that time reversal symmetry should be excluded, TIME_REVERSAL indicates that the spacial symmetry operations should be omitted and only time reversal symmetry should be used, NONE indicates that the grid should not be folded at all.

Finite precision parameters can be adjusted from the default values using the REPS and AEPS keywords, for the relative and absolute tolerances, respectively.

Example input files

To generate a grid with a k-point density of 5000 k-points/Å^{^-3} and have the code determine the best offset, the KPGEN input file would be:

KPDENSITY=5000

To generate a grid with an offset of [0.5, 0.5, 0.5], expressed as fractions of the reciprocal lattice vectors, and 500 k-points the KPGEN input file would be:

NKPTS=500
SHIFT= 0.5 0.5 0.5

Generating the k-point grid

Once POSCAR and KPGEN file have been provided by the user, the KPOINTS file can be generated using the kpoints.x. The executable does not have any optional arguments since all relevant options have been included in the KPGEN file.

Plots

All the data and scripts used to generate the plots and analysis for the Generalized Regular Grids On-The-Fly paper can be found in the paper folder.