# Rapid Generation of Optimal Generalized Monkhorst-Pack Grids

## TL;DR

This paper introduces new algorithms and open-source tools for rapidly generating optimized generalized Monkhorst-Pack grids, significantly speeding up Brillouin zone integrations in crystalline materials simulations.

## Contribution

The authors present novel algorithms and software for on-the-fly generation of optimized generalized Monkhorst-Pack grids, enhancing computational efficiency in materials modeling.

## Key findings

- Algorithms generate grids in under 0.2 seconds for typical structures.
- Optimized grids improve calculation speed by roughly doubling efficiency.
- Tools are available for offline use and integration into existing software.

## Abstract

Computational modeling of the properties of crystalline materials has become an increasingly important aspect of materials research, consuming hundreds of millions of CPU-hours at scientific computing centres around the world each year, if not more. A routine operation in such calculations is the evaluation of integrals over the Brillouin zone. We have previously demonstrated that performing such integrals using generalized Monkhorst-Pack k-point grids can roughly double the speed of these calculations relative to the widely-used traditional Monkhorst-Pack grids, and such grids can be rapidly generated by querying a free, internet-accessible database of pre-generated grids. To facilitate the widespread use of generalized k-point grids, we present new algorithms that allow rapid generation of optimized generalized Monkhorst-Pack grids on the fly, an open-source library to facilitate their integration into external software packages, and an open-source implementation of the database tool that can be used offline. We also present benchmarks of the speed of our algorithms on structures randomly selected from the Inorganic Crystal Structure Database. For grids that correspond to a real-space supercell with at least 50 angstroms between lattice points, which is sufficient to converge density functional theory calculations within 1 meV/atom for nearly all materials, our algorithm finds optimized grids in an average of 0.19 seconds on a single processing core. For 100 angstroms between real-space lattice points, our algorithm finds optimal grids in less than 5 seconds on average.

---
Source: https://tomesphere.com/paper/1907.13610