Algorithms for the Generation of Generalized Monkhorst-Pack Grids

Computational simulations of crystalline materials properties have become an increasingly important research paradigm over the last decade. A routine operation in such calculations is the evaluation of integrals over the Brillouin zone. Traditional Monkhorst-Pack grids are widely used across popular simulation packages. Researchers have previously demonstrated that generalised Monkhorst-Pack k-point grids are much more efficient than traditional Monkhorst-Pack grids and can roughly double the speed of well-converged calculations on crystalline materials. In this paper, we present algorithms that can rapidly generate the optimized generalized Monkhorst Pack grid both dynamically and using a pre-generated database. The algorithms identify highly efficient grids by performing an exhaustive search over all symmetry-preserving grids, and they also incorporate designs to maximally accelerate such searches. Implementations of these algorithms in three different formats are also provided, to meet the diverse demands of users.