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.

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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Density functional theory (DFT) codes are commonly treated as a ‘black box’ in high-throughput screening of materials, with users opting for the default values of the input parameters. Often, non-experts may not sufficiently consider the effect of these parameters on prediction quality. In this work, we attempt to identify a robust set of parameters related to smearing and tetrahedron methods that return numerically accurate and efficient results for a wide variety of metallic systems. The effects of smearing and tetrahedron methods on the total energy, number of self-consistent field cycles, and forces on atoms are studied in two popular DFT codes: the Vienna ab initio Simulation Package and Quantum Espresso. From nearly 40 000 computations, it is apparent that the optimal smearing depends on the system, smearing method, smearing parameter, and k-point density. The benefit of smearing is a minor reduction in the number of self-consistent field cycles, which is independent of the smearing method or parameter. A large smearing parameter—what is considered large is system dependent—leads to inaccurate total energies and forces. Blöchl’s tetrahedron method leads to small improvements in total energies. When treating diverse systems with the same input parameters, we suggest using as little smearing as possible due to the system dependence of smearing and the risk of selecting a parameter that gives inaccurate energies and forces.