Source-linked AI summary
Convergence and machine learning predictions of Monkhorst-Pack k-points and plane-wave cut-off in high-throughput DFT calculations
Kamal Choudhary, Francesca Tavazza
TL;DR
Choosing converged k-point and cut-off parameters remains unresolved. The paper develops an automated convergence procedure and machine-learning models, finding correlations with material parameters and prediction errors of 85 eV for cut-off and 9.09 Å for k-points.
Problem
The choice of parameters for converged calculations remains unresolved.
Method
An automated framework converges cut-off at fixed k-points and uses descriptors with machine-learning models to predict converged values.
Results
85 eV and 9.09 Å were the mean absolute errors for cut-off and k-points, respectively, on the 10% held set.
Takeaways & Limitations
The highest reported correlation was 0.637, supporting k-point and cut-off prediction as a useful approach.
Takeaways & Limitations
No single examined quantity was sufficient to determine converged cut-off or k-point values.
Abstract
from arXiv · showhide
In this work, we developed an automatic convergence procedure for k-points and plane wave cut-off in density functional (DFT) calculations and applied it to more than 30000 materials. The computational framework for automatic convergence can take a user-defined input as a convergence criterion. For k-points, we converged energy per cell (EPC) to 0.001 eV/cell tolerance and compared the results with those obtained using an energy per atom (EPA) convergence criteria of 0.001 eV/atom. From the analysis of our results, we could relate k-point density and plane wave cut-off to material parameters such as density, the slope of bands, number of band-crossings, the maximum plane-wave cut-off used in pseudopotential generation, crystal systems, and the number of unique species in materials. We also identified some material species that would require more careful convergence than others. Moreover, we statistically investigated the dependence of k-points and cutoff on exchange-correlation functionals. We utilized all this data to train machine learning models to predict the k-point line density and plane-wave cut-off for generalized materials. This would provide users with a good starting point towards converged DFT calculations. The code used, and the converged data are available on the following websites: https://jarvis.nist.gov/, and https://github.com/usnistgov/jarvis .
Introduction
The paper addresses the difficulty of selecting converged k-point and plane-wave cut-off parameters for high-throughput DFT, where direct property convergence is computationally expensive. It develops an automated, broadly applicable setup procedure and uses converged calculations to support parameter prediction for large materials collections.
- Motivation: Directly converging each property on k-points and cut-off is computationally expensive for high-throughput calculations.The paper therefore focuses on finding a practical balance between computational cost and precision.
- Motivation: Fixed parameters used by large DFT databases may not generalize because some materials require much higher cut-offs or k-point densities.Prior studies reported cut-offs up to 1400 eV and high k-point densities for accurately predicting selected properties.
- Contribution: The study develops an automatic procedure to identify converged k-point and energy-cutoff parameters for at least 30000 materials.The resulting calculations populated the JARVIS-DFT database.
- Contribution: The framework relates convergence parameters to material characteristics and can be adapted to other properties and DFT parameters.The authors focused on total-energy convergence but state that the framework can investigate other properties and parameters such as smearing.
- Contribution: The converged data are used to train machine-learning models that predict k-point density and plane-wave cut-off before DFT calculations.The models are intended to provide starting parameters for generalized materials.
Method:
The method uses VASP and PAW calculations with automated, sequential convergence of k-point meshes and plane-wave cut-offs against an energy tolerance. It generates gamma-inclusive Monkhorst-Pack meshes, applies fixed iteration rules, and uses the converged database to analyze material and computational trends.
- Computational setup: The workflow performs VASP calculations with projector-augmented wave potentials and uses plane-wave expansions truncated by a cut-off energy.The cut-off controls the included plane waves, while the number of plane waves depends on k and reciprocal wave vectors.
- Convergence criteria: Both convergence procedures use 0.001 eV per cell as the default criterion, while the tolerance can be changed for more demanding calculations.The workflow uses single-step electronic relaxation without ionic relaxation; complete relaxation may be needed for sophisticated calculations such as Raman intensities.
- K-point convergence: K-points are generated with the Monkhorst-Pack scheme and shifted to include the gamma point for properties requiring gamma-point contributions.The procedure defines a k-point line density from reciprocal-lattice vectors and increases it iteratively.
- K-point convergence: K-point line density increases by 5 Å while successive energy differences exceed the tolerance, followed by five extra points to verify convergence.The algorithm starts from the gamma point and stores generated points to avoid repeating calculations.
- Cut-off convergence: Plane-wave cut-off convergence increases the cut-off by 50 eV from 500 eV until six successive energy differences fall below the tolerance.The k-point and cut-off procedures are decoupled for computational speed, which may overestimate the parameters.
- Dataset and analysis: The study analyzes a large JARVIS-DFT collection spanning bulk and two-dimensional materials, multiple crystal systems, compositions, and calculated properties.The converged k-points and cut-offs are used for mechanical, optical, and electronic property calculations.
Results and discussion:
The study systematically relates converged k-point and plane-wave cut-off requirements to material characteristics, convergence criteria, crystal structure, elemental composition, and exchange-correlation functionals. It also evaluates machine-learning predictions and identifies trends that can guide convergence choices.
- Convergence procedure: The automated procedure converges cut-off and k-points sequentially, checking five extra points after the tolerance is reached.The workflow first converges cut-off at fixed k-points, then converges k-points at fixed cut-off.
- K-point convergence: Length-based k-point distributions span 10 Å to 200 Å, whereas atom-based values reach 20000*atom.The authors find similar behavior for EPC and EPA but prefer the smoother length-based formalism.
- Material classes: Metals generally require more k-points, while non-metals generally require higher cut-offs than metals.Band crossings at the Fermi level explain the higher k-point requirement for metals, whereas higher charge-density localization is given as an explanation for larger non-metal cut-offs.
- Material correlations: The maximum pseudopotential plane-wave cut-off correlates most strongly with converged cut-off energy, reaching PC 0.637.Volume per atom and density are also identified as important quantities for cut-off and k-point convergence, respectively.
- Material correlations: Band crossings correlate strongly with converged k-point length, with PC=0.62 for EPC and 0.66 for EPA.The strongest reported k-point correlations involve band crossings and band slopes, while individual examined properties are insufficient alone for prediction.
- Structural and compositional trends: Crystal systems and composition show opposing trends: hexagonal systems require higher k-points but lower cut-offs, while triclinic systems require fewer k-points but higher cut-offs.As the number of unique species increases, k-points decrease and cut-off increases; additional work is needed to interpret other trends.
- Elemental trends: Elements associated with higher k-point requirements include Be, Y, Lu, Hf, Ru, Os, Rh, Ir, Pd, Pt, Ni, Cu, B, Al, Ga and In, while higher cut-offs are associated with Cs, La, H, Li, Na, Ba, Tc, B, C, N, O, Zn, Bi and F.The authors note that further investigation is needed to explain these elemental trends, potentially involving sharper features for some elements.
- Exchange-correlation functionals: PBE and OptB88vdW have very similar convergence requirements, while LDA needs slightly fewer k-points and a slightly higher cut-off.Overall differences among the three functionals are very small, so convergence from one functional should be transferable to the others.
Conclusions:
The study developed an automatic, flexible convergence procedure for k-points and plane-wave cutoffs, applied it to more than 30,000 materials, and used the resulting data to guide parameter selection and train prediction models.
- More than 30,000 materials were analyzed with an automatic convergence procedure for k-points and plane-wave cutoffs.
- The framework supports user-defined convergence criteria and can converge properties beyond energy.
- Length-based k-point representations were preferred over per-atom formalism, with a mean of 44 Å k-point length and 856 eV cutoff.
- Individual materials should still be converged separately because the dataset contains large outliers.
- Cutoff and k-point parameters were related to density, electron count, pseudopotential cutoff, crystal systems, and other material parameters.
- The study identified species requiring more careful convergence and found that cutoff and k-points were mainly dependent on material type rather than exchange-correlation functional.
- Machine-learning models were developed to predict k-point line density and cutoff for materials on the fly.
Supplementary information: Convergence and machine learning predictions of
The supplementary material identifies the paper, its authors and institutional affiliation, and includes a table describing the PAW potentials used in the DFT database.
- The supplementary material concerns Monkhorst-Pack k-points and plane-wave cutoff in high-throughput DFT.
- Kamal Choudhary and Francesca Tavazza are listed as authors.
- The authors are affiliated with the Materials Science and Engineering Division at NIST in Gaithersburg, Maryland.
- Table S1 lists the PAW potentials used during generation of the DFT database.
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The supplementary figures concern band crossings and density-based average k-points across crystal systems, with references to atoms in the cell.
- Figure S1 presents an example of band crossings for Pr, identified as JVASP-14689.
- The band-crossing discussion refers to bands crossing the Fermi level.
- Figure S2 examines correlations of density-based average k-points across seven crystal systems.
- The supplementary material references atoms in the cell in connection with the k-point analysis.