Most DFT practitioners use regular grids (Monkhorst-Pack, MP) for integrations in the Brillioun zone. Although regular grids are the natural choice and easy to generate, more general grids whose generating vectors are not merely integer divisions of the reciprocal lattice vectors, are usually more efficient. 1 We demonstrate the efficiency of generalized regular (GR) grids compared to Monkhorst-Pack (MP) and simultaneously commensurate (SC) grids. In the case of metals, for total energy accuracies of one meV/atom, GR grids are 60% faster on average than MP grids and 20% faster than SC grids. GR grids also have greater freedom in choosing the k-point density, enabling the practitioner to achieve a target accuracy with the minimum computational cost. arXiv:1804.04741v2 [cond-mat.mtrl-sci]

We develop an algorithm for i) computing generalized regular k-point grids, ii) reducing the grids to their symmetrically distinct points, and iii) mapping the reduced grid points into the Brillouin zone. The algorithm exploits the connection between integer matrices and finite groups to achieve a computational complexity that is linear with the number of k-points. The favorable scaling means that, at a given k-point density, all possible commensurate grids can be generated (as suggested by Moreno and Soler) and quickly reduced to identify the grid with the fewest symmetrically unique k-points. These optimal grids provide significant speed-up compared to Monkhorst-Pack k-point grids; they have better symmetry reduction resulting in fewer irreducible k-points at a given grid density. The integer nature of this new reduction algorithm also simplifies issues with finite precision in current implementations. The algorithm is available as open source software.

Modeling potential alloys requires the exploration of all possible configurations of atoms. Additionally, modeling the thermal properties of materials requires knowledge of the possible ways of displacing the atoms. One solution to finding all symmetrically unique configurations and displacements is to generate the complete list of possible configurations and remove those that are symmetrically equivalent. This approach, however, suffers from the combinatorial explosion that happens when the supercell size is large, when there are more than two atom types, or when there are multiple displaced atoms. This problem persists even when there are only a relatively small number of unique arrangements that survive the elimination process. Here, we extend an existing algorithm 1-3 to include the extra configurational degree of freedom from the inclusion of displacement directions. The algorithm uses group theory to eliminate large classes of configurations, avoiding the combinatoric explosion. With this approach we can now enumerate previously inaccessible systems, including atomic displacements. arXiv:1701.02382v1 [cond-mat.mtrl-sci]

In the DFT community, it is common practice to use regular k-point grids (Monkhorst-Pack, MP) for Brillioun zone integration. Recently Wisesa et. al. 1 and Morgan et. al. 2 demonstrated that generalized regular (GR) grids offer advantages over traditional MP grids. GR grids have not been widely adopted because one must search through a large number of candidate grids. This work describes an algorithm that can quickly search over GR grids for those that have the most uniform distribution of points and the best symmetry reduction. The grids are ∼60% more efficient, on average, than MP grids and can now be generated on the fly in seconds.

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