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  • Expert Recommendation
  • Published:

How to verify the precision of density-functional-theory implementations via reproducible and universal workflows

Nature Reviews Physics volume 6, pages 45–58 (2024)Cite this article

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Abstract

Density-functional theory methods and codes adopting periodic boundary conditions are extensively used in condensed matter physics and materials science research. In 2016, their precision (how well properties computed with different codes agree among each other) was systematically assessed on elemental crystals: a first crucial step to evaluate the reliability of such computations. In this Expert Recommendation, we discuss recommendations for verification studies aiming at further testing precision and transferability of density-functional-theory computational approaches and codes. We illustrate such recommendations using a greatly expanded protocol covering the whole periodic table from Z = 1 to 96 and characterizing 10 prototypical cubic compounds for each element: four unaries and six oxides, spanning a wide range of coordination numbers and oxidation states. The primary outcome is a reference dataset of 960 equations of state cross-checked between two all-electron codes, then used to verify and improve nine pseudopotential-based approaches. Finally, we discuss the extent to which the current results for total energies can be reused for different goals.

Key points

  • Verification efforts are critical to assess the reliability of density-functional theory (DFT) simulations and provide results with properly quantified uncertainties.

  • Developing standard computation protocols to perform verification studies and publishing curated and FAIR reference datasets can greatly aid their use to improve codes and computational approaches.

  • The use of fully automated workflows with common interfaces between codes can guarantee uniformity, transferability and reproducibility of results.

  • A careful description of the numerical and methodological details needed to compare with the reference datasets is essential; we discuss and illustrate this point with a dataset of 960 all-electron equations of state.

  • Reference datasets should always include an explanation of the target property for which they were generated, and a discussion of their limits of applicability.

  • Further extensions of DFT verification efforts are needed to cover more functionals, more computational approaches and the treatment of magnetic and relativistic (spin–orbit) effects. They should also aim at concurrently delivering optimized protocols that not only target ultimate precision, but also optimize the computational cost for a target accuracy.

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Fig. 1: Differences in results for codes FLEUR and WIEN2k.
Fig. 2: Discrepancy between the all-electron results obtained with WIEN2k and FLEUR in our reference dataset.
Fig. 3: Effect of different choices of smearing on the equation of state of the artificial diamond structure of erbium computed with the Quantum ESPRESSO code.
Fig. 4: Comparing the results of different computational approaches.

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Code availability

The source code of the common workflows is released under the MIT open-source licence and is made available on GitHub (https://github.com/aiidateam/aiida-common-workflows). It is also distributed as an installable package through the Python Package Index (https://pypi.org/project/aiida-common-workflows). The source code of the scripts to generate the plots is released under the MIT open-source licence and is made available on GitHub (https://github.com/aiidateam/acwf-verification-scripts). All codes to generate the figures of this paper are available in the data entry of ref. 62.

Data availability

The data and the scripts used to create all the images in this work are available on the Materials Cloud Archive62. Moreover, the data are accessible via an interactive website, https://acwf-verification.materialscloud.org, that offers various analysis and visualization possibilities. Note that the data include the entire AiiDA provenance graph of each workflow execution presented in the main text (therefore including all input files and output files of all simulations, as well as their logical relationship, in AiiDA format), as well as the curated data extracted from that database to produce the images.

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Acknowledgements

This work was inspired and is supported in part by the European Union (EU)’s Horizon 2020 research and innovation programme under grant agreements no. 676598 and no. 824143 (European MaX Centre of Excellence ‘Materials Design at the Exascale’) and by NCCR MARVEL, a National Centre of Competence in Research, funded by the Swiss National Science Foundation (SNSF, grant no. 205602). For the purpose of Open Access, a CC BY public copyright licence is applied to any Author Accepted Manuscript (AAM) version arising from this submission. We thank F. J. dos Santos for discussions on the analysis of the smearing types and k-point convergence, and X. Gonze, M. Torrent and F. Jollet for discussions on PAW pseudopotentials. M.F. and N.M. acknowledge the contribution of S. Shankar in early discussions about the use of prototype oxides as general platform to explore the transferability of pseudopotentials. Work at ICMAB (E.B., A.G., V.D.) is supported by the Severo Ochoa Centers of Excellence Program (MCIN CEX2019-000917-S), by grant PGC2018-096955-B-C44 of MCIN/AEI/10.13039/501100011033, ‘ERDF A way of making Europe’, and by GenCat 2017SGR1506. We also thank the Barcelona Supercomputer Center (BSC) for computational resources. V.D. acknowledges support from DOC-FAM, EU Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement no. 754397. O.R. acknowledges travel support from WIEN2k (Technical University of Vienna). The Jülich team (S.B., J.B., H.J., G.M., D.W.) acknowledge support by the Joint Lab Virtual Materials Design of the Forschungszentrum Jülich, the Helmholtz Platform for Research Software Engineering — Preparatory Study, the Joint Virtual Laboratory AI, Data Analytics and Scalable Simulation of the Forschungszentrum Jülich and the French Alternative Energies and Atomic Energy Commission, and the computing time granted through JARA on the supercomputers JURECA80 at Forschungszentrum Jülich and CLAIX at RWTH Aachen University. H.M. and T.D.K. (Univ. Paderborn) acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for funding this project by providing computing time on the GCS supercomputer JUWELS at Jülich Supercomputing Centre. S.P. and G.-M.R. (Univ. catholique de Louvain) acknowledge support from the Fonds de la Recherche Scientifique de Belgique (F.R.S.-FNRS). Computational resources have been provided by the PRACE-21 resources MareNostrum at the BSC-CNS and by the Consortium des Équipements de Calcul Intensif, funded by the F.R.S.-FNRS under grant no. 2.5020.11 and by the Walloon Region as well as computational resources awarded on the Belgian share of the EuroHPC LUMI supercomputer. G.Ka. and S.V. received funding from the VILLUM Centre for the Science of Sustainable Fuels and Chemicals (9455) from VILLUM FONDEN. Computational resources were provided by the Niflheim supercomputing cluster at the Technical University of Denmark. They also thank J. J. Mortensen and A. H. Larsen for discussions on optimizing the workflow for the GPAW code. S.C. acknowledges financial support from OCAS NV by an OCAS-endowed chair at Ghent University. The computational resources and services used at Ghent University were provided by the Vienna Scientific Cluster (VSC; Flemish Supercomputer Center), funded by the Research Foundation Flanders and the Flemish Government department EWI. M.W. acknowledges computational resources provided by the VSC. This research was funded in part by the Austrian Science Fund (FWF) [P 32711]. E.F.L. acknowledges resources provided by Sigma2 — the National Infrastructure for High Performance Computing and Data Storage in Norway, and support from the Norwegian Research Infrastructure Services. B.Z. is grateful to the UK Materials and Molecular Modelling Hub for computational resources, which is partially funded by EPSRC (EP/P020194/1 and EP/T022213/1), and acknowledges the use of the UCL Myriad and Kathleen High Performance Computing Facility (Myriad@UCL, Kathleen@UCL), and associated support services, in the completion of this work. N.M., G.Pi. and A.G. acknowledge support from the EU Horizon 2020 research and innovation programme under grant agreement no. 957189 (BIG-MAP), also part of the BATTERY 2030+ initiative under grant agreement no. 957213. G.P., J.Y. and G.-M.R. acknowledge support by the SNSF and by the F.R.S.-FNRS through the ‘FISH4DIET’ Project (SNSF grant 200021E_206190 and F.R.S.-FNRS grant T.0179.22). G.P. acknowledges support by the Open Research Data Program of the ETH Board, under the Establish project ‘PREMISE’. J.Y. acknowledges support from the EU Horizon 2020 research and innovation programme under grant agreement no. 760173 (MARKETPLACE).

Author information

Authors and Affiliations

  1. Institut de Ciència de Materials de Barcelona, ICMAB-CSIC, Bellaterra, Spain

    Emanuele Bosoni, Vladimir Dikan & Alberto Garcia

  2. Université Grenoble-Alpes, CEA, IRIG-MEM-L_Sim, Grenoble, France

    Louis Beal, Augustin Degomme & Luigi Genovese

  3. Theory and Simulation of Materials (THEOS) and National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

    Marnik Bercx, Kristjan Eimre, Sebastiaan P. Huber, Nicola Marzari, Jusong Yu, Austin Zadoks & Giovanni Pizzi

  4. Institute for Materials Chemistry, Technical University of Vienna, Vienna, Austria

    Peter Blaha, Georg K. H. Madsen & Thomas Ruh

  5. Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, Jülich, Germany

    Stefan Blügel, Jens Bröder, Henning Janssen, Gregor Michalicek & Daniel Wortmann

  6. Institute for Advanced Simulation, Materials Data Science and Informatics (IAS-9), Forschungszentrum Jülich, Jülich, Germany

    Jens Bröder

  7. Department of Electromechanical, Systems and Metal Engineering, Ghent University, Ghent, Belgium

    Martin Callsen, Stefaan Cottenier, Michael Sluydts & Danny E. P. Vanpoucke

  8. Center for Molecular Modeling (CMM), Ghent University, Ghent, Belgium

    Martin Callsen, Stefaan Cottenier, Kurt Lejaeghere, Thomas Ruh & Michael Sluydts

  9. Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, Taiwan

    Martin Callsen

  10. Norwegian EuroHPC Competence Center, Sigma2 AS, Trondheim, Norway

    Espen Flage-Larsen

  11. SINTEF Industry, Materials Physics, Oslo, Norway

    Espen Flage-Larsen

  12. Department of Physics and Science of Advanced Materials Program, Central Michigan University, Mount Pleasant, MI, USA

    Marco Fornari

  13. Institut de la Matière Condensée et des Nanosciences (IMCN), Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Matteo Giantomassi, Guido Petretto, Samuel Poncé & Gian-Marco Rignanese

  14. National Centre of Competence in Research (NCCR) Catalysis, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

    Sebastiaan P. Huber

  15. Center for Catalysis Theory (Cattheory), Department of Physics, Technical University of Denmark (DTU), Kongens Lyngby, Denmark

    Georg Kastlunger & Sudarshan Vijay

  16. Laboratory for Materials Simulations (LMS), Paul Scherrer Institut (PSI), Villigen PSI, Switzerland

    Matthias Krack, Nicola Marzari, Jusong Yu & Giovanni Pizzi

  17. University of Vienna, Faculty of Physics and Center for Computational Materials Science, Vienna, Austria

    Georg Kresse, Martijn Marsman & Michael Wolloch

  18. VASP Software GmbH, Vienna, Austria

    Georg Kresse, Martijn Marsman & Michael Wolloch

  19. Center for Advanced Systems Understanding (CASUS) and Helmholtz-Zentrum Dresden-Rossendorf, Görlitz, Germany

    Thomas D. Kühne

  20. Paderborn Center for Parallel Computing (PC2) and Center for Sustainable Systems Design, University of Paderborn, Paderborn, Germany

    Thomas D. Kühne

  21. OCAS NV/ArcelorMittal Global R&D Gent, Zelzate, Belgium

    Kurt Lejaeghere

  22. Dynamics of Condensed Matter, Chair of Theoretical Chemistry, University of Paderborn, Paderborn, Germany

    Hossein Mirhosseini

  23. HPE HPC EMEA Research Lab, Basel, Switzerland

    Tiziano M. A. Müller

  24. Department of Materials Science and Metallurgy, University of Cambridge, Cambridge, United Kingdom

    Chris J. Pickard

  25. Advanced Institute for Materials Research, Tohoku University, Sendai, Japan

    Chris J. Pickard

  26. Department of Materials Science and Engineering, McMaster University, Hamilton, Ontario, Canada

    Oleg Rubel

  27. Chair of Physical Chemistry, Montanuniversitaet Leoben, Leoben, Austria

    Thomas Ruh

  28. ePotentia, Deurne, Antwerp, Belgium

    Michael Sluydts

  29. Institute for Materials Research (IMO-IMOMEC), UHasselt — Hasselt University, Hasselt, Belgium

    Danny E. P. Vanpoucke

  30. Swiss Federal Laboratories for Materials Science and Technology (Empa), nanotech@surfaces laboratory, Dübendorf, Switzerland

    Aliaksandr V. Yakutovich

  31. Department of Chemistry, University College London, London, UK

    Bonan Zhu

  32. The Faraday Institution, Didcot, UK

    Bonan Zhu

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  1. Emanuele Bosoni
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Contributions

M.F. and N.M. contributed the idea of using prototype oxides to test pseudopotentials across different coordinations and chemistries. S.C. and K.L. performed an initial assessment of this idea and analysed, together with M.C., the first exploratory datasets. M.S. was responsible for job, queue and data management in the first exploratory phase. E.B. and G.Pi. contributed the idea of using the AiiDA and aiida-common-workflows infrastructure to carry on the thousands of DFT simulations required by the project. E.B. and G.Pi. coordinated the whole project. P.B., G.M. and O.R. performed the iterative refinement of the input parameters for the AE calculations that ultimately resulted in the generation of the central volumes of our dataset. O.R. proposed the ε metric. N.M. proposed the ν metric. S.P. raised the issue of the smearing selection that ultimately led to the decision of a fixed k-point integration mesh and smearing broadening. K.E. contributed to the data analysis and the conversion of the data into a dynamic website. D.E.P.V. contributed the Hirshfeld-I calculated charges and their analysis. E.B., M.W. and G.Pi. performed the analysis of the error propagation in the fit and the estimation of the parameters of the ν metric. E.B., S.C., O.R. and G.Pi. analysed in detail the dependency and sensitivity of the metrics Δ, ε and ν. A.Z. and S.P. developed the ABINIT implementation of the common workflow which relies on the aiida-abinit plugin developed and maintained by A.Z., G.Pe. and S.P. M.G. created new pseudopotentials used for ABINIT and improved the parameter profile. A.Z. and S.P. performed the ABINIT calculations, including verification tests. The work on ABINIT was supervised by G.-M.R. and S.P. L.B., A.D. and L.G. contributed to the BigDFT-related parts of the work. A.D. developed the BigDFT implementation of the common workflows. L.B. and A.D. generated the BigDFT results under the supervision of L.G. B.Z. developed the CASTEP implementation of the common workflow, which relies on the aiida-castep plugin also maintained by B.Z., and performed all CASTEP simulations. C.J.P. created new on-the-fly generated pseudopotentials using the verification tests performed by B.Z. M.K., T.D.K., H.M., T.M.A.M. and A.V.Y. contributed to all CP2K-related parts of this work. A.V.Y. implemented the workflows and performed preliminary calculations. The workflows rely on the aiida-cp2k plugin developed by A.V.Y., T.M.A.M. and others. M.K. performed preliminary calculations, created new pseudopotentials and contributed to the design of the protocol, T.D.K. contributed to the CP2K setup, discussed the results and supervised the calculations, H.M. conducted all AiiDA calculations and analysed the results, T.M.A.M. provided implementations of CP2K input and output parsers. S.B., J.B., H.J., G.M. and D.W. contributed the FLEUR-related parts of this work. G.M. developed the parameter profile and performed the calculations, and is the contact person for the FLEUR contributions. J.B. and H.J. adapted and extended the AiiDA-FLEUR plugin and the related parts of the AiiDA common-workflows package. S.B. and D.W. contributed to the analysis and discussion of the FLEUR results. G.Ka. and S.V. contributed to the GPAW-related parts of the work. S.V. developed the GPAW implementation of the common workflows, which relies on the aiida-ase plugin, and ran the calculations. G.Ka. and S.V. analysed the GPAW calculations. M.B., S.P.H., N.M., J.Y. and G.Pi. contributed to all Quantum ESPRESSO-related parts of this work. M.B. and S.P.H. developed the Quantum ESPRESSO implementation of the common workflow, which relies on the aiida-quantumespresso plugin developed and maintained by M.B., S.P.H., G.Pi. and others. J.Y. generated and tested new pseudopotentials used for Quantum ESPRESSO. The work on Quantum ESPRESSO was supervised by G.Pi. and N.M. H.M. and T.D.K. contributed to all SIRIUS/CP2K-related parts of this work. The workflows rely on the aiida-cp2k plugin developed by A.V.Y., T.M.A.M., and others. H.M. conducted all AiiDA calculations and analysed the results. T.D.K. contributed to the SIRIUS/CP2K setup, discussed the results and supervised the calculations. E.B., V.D. and A.G. contributed to the SIESTA-related parts of the work. E.B. developed the SIESTA implementation of the common workflows, which relies on the aiida-siesta plugin developed by E.B., A.G., V.D. and others. E.B. generated the SIESTA results in collaboration with A.G. M.W., M.M. and E.F.-L. performed the execution and analysis of the VASP-related workflows used to generate the data for this work. G.Kr. generated updated potentials for the lanthanides. E.F.-L. maintains the VASP implementation of the common-workflows project and the aiida-vasp plugin (developed by a community of contributors; see full contributor list in the plugin documentation) which is used to execute the VASP calculations. P.B., G.K.H.M., O.R. and T.R. contributed the WIEN2k-related parts of this work. T.R. performed preliminary calculations, P.B. created the setup of the WIEN2k calculations and supervised and analysed the results, G.K.H.M. contributed the conversion of AiiDA structures to a WIEN2k struct file, and O.R. developed the aiida-wien2k plugin and performed all AiiDA-WIEN2k calculations. E.B., M.F. and G.Pi. wrote the first version of the manuscript, and all authors contributed to the editing and revision of the manuscript.

Corresponding author

Correspondence to Giovanni Pizzi.

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Competing interests

G.Pe. and G.-M.R. are shareholders and directors of Matgenix SRL. G.Kr. is a shareholder of the VASP Software GmbH, and M.W. and M.M. are part-time employees of the VASP Software GmbH. C.J.P. is an author of the CASTEP code and receives income from its commercial sales.

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Nature Reviews Physics thanks Vikram Gavini, Ann Mattson and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Bosoni, E., Beal, L., Bercx, M. et al. How to verify the precision of density-functional-theory implementations via reproducible and universal workflows. Nat Rev Phys 6, 45–58 (2024). https://doi.org/10.1038/s42254-023-00655-3

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