Reproducibility in density functional theory calculations of solids

Lejaeghere, Kurt; Bihlmayer, Gustav; Bjoerkman, Torbjoern; Blaha, Peter; Bluegel, Stefan; Blum, Volker; Caliste, Damien; Castelli, Ivano E.; Clark, Stewart J.; Dal Corso, Andrea; de Gironcoli, Stefano; Deutsch, Thierry; Dewhurst, John Kay; Di Marco, Igor; Draxl, Claudia; Dulak, Marcin; Eriksson, Olle; Flores-Livas, Jose A.; Garrity, Kevin F.; Genovese, Luigi; Giannozzi, Paolo; Giantomassi, Matteo; Goedecker, Stefan; Gonze, Xavier; Granaes, Oscar; Gross, E.K.U.; Gulans, Andris; Gygi, Francois; Hamann, D.R.; Hasnip, Phil J.; Holzwarth, N.A.W.; Iusan, Diana; Jochym, Dominik B.; Jollet, Francois; Jones, Daniel; Kresse, Georg; Koepernik, Klaus; Kuecuekbenli, Emine; Kvashnin, Yaroslav O.; Locht, Inka L.M.; Lubeck, Sven; Marsman, Martijn; Marzari, Nicola; Nitzsche, Ulrike; Nordstrom, Lars; Ozaki, Taisuke; Paulatto, Lorenzo; Pickard, Chris J.; Poelmans, Ward; Probert, Matt I.J.; Refson, Keith; Richter, Manuel; Rignanese, Gian-Marco; Saha, Santanu; Scheffler, Matthias; Schlipf, Martin; Schwarz,...

Abstract

NTRODUCTION The reproducibility of results is one of the underlying principles of science. An observation can only be accepted by the scientific community when it can be confirmed by independent studies. However, reproducibility does not come easily. Recent works have painfully exposed cases where previous conclusions were not upheld. The scrutiny of the scientific community has also turned to research involving computer programs, finding that reproducibility depends more strongly on implementation than commonly thought. These problems are especially relevant for property predictions of crystals and molecules, which hinge on precise computer implementations of the governing equation of quantum physics. RATIONALE This work focuses on density functional theory (DFT), a particularly popular quantum method for both academic and industrial applications. More than 15,000 DFT papers are published each year, and DFT is now increasingly used in an automated fashion to build large databases or apply multiscale techniques with limited human supervision. Therefore, the reproducibility of DFT results underlies the scientific credibility of a substantial fraction of current work in the natural and engineering sciences. A plethora of DFT computer codes are available, many of them differing considerably in their details of implementation, and each yielding a certain “precision” relative to other codes. How is one to decide for more than a few simple cases which code predicts the correct result, and which does not? We devised a procedure to assess the precision of DFT methods and used this to demonstrate reproducibility among many of the most widely used DFT codes. The essential part of this assessment is a pairwise comparison of a wide range of methods with respect to their predictions of the equations of state of the elemental crystals. This effort required the combined expertise of a large group of code developers and expert users. RESULTS We calculated equation-of-state data for four classes of DFT implementations, totaling 40 methods. Most codes agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Even in the case of pseudization approaches, which largely depend on the atomic potentials used, a similar precision can be obtained as when using the full potential. The remaining deviations are due to subtle effects, such as specific numerical implementations or the treatment of relativistic terms. CONCLUSION Our work demonstrates that the precision of DFT implementations can be determined, even in the absence of one absolute reference code. Although this was not the case 5 to 10 years ago, most of the commonly used codes and methods are now found to predict essentially identical results. The established precision of DFT codes not only ensures the reproducibility of DFT predictions but also puts several past and future developments on a firmer footing. Any newly developed methodology can now be tested against the benchmark to verify whether it reaches the same level of precision. New DFT applications can be shown to have used a sufficiently precise method. Moreover, high-precision DFT calculations are essential for developing improvements to DFT methodology, such as new density functionals, which may further increase the predictive power of the simulations.

Citation

Lejaeghere, K., Bihlmayer, G., Bjoerkman, T., Blaha, P., Bluegel, S., Blum, V., …Cottenier, S. (2016). Reproducibility in density functional theory calculations of solids. Science, 351(6280), Article aad3000. https://doi.org/10.1126/science.aad3000

• Journal Article Type: Article
• Acceptance Date: Feb 19, 2016
• Online Publication Date: Mar 25, 2016
• Publication Date: Mar 25, 2016
• Deposit Date: Nov 15, 2016
• Publicly Available Date: Feb 24, 2017
• Journal: Science
• Print ISSN: 0036-8075
• Electronic ISSN: 1095-9203
• Publisher: American Association for the Advancement of Science
• Peer Reviewed: Peer Reviewed
• Volume: 351
• Issue: 6280
• Article Number: aad3000
• DOI: https://doi.org/10.1126/science.aad3000
• Public URL: https://durham-repository.worktribe.com/output/1371650