Reproducibility in density functional theory calculations of solids

Kurt Lejaeghere*, Gustav Bihlmayer, Torbjörn Björkman, Peter Blaha, Stefan Blügel, Volker Blum, Damien Caliste, Ivano E. Castelli, Stewart J. Clark, Andrea Dal Corso, Stefano De Gironcoli, Thierry Deutsch, John Kay Dewhurst, Igor Di Marco, Claudia Draxl, Marcin Dułak, Olle Eriksson, José A. Flores-Livas, Kevin F. Garrity, Luigi GenovesePaolo Giannozzi, Matteo Giantomassi, Stefan Goedecker, Xavier Gonze, Oscar Grånäs, E. K.U. Gross, Andris Gulans, François Gygi, D. R. Hamann, Phil J. Hasnip, N. A.W. Holzwarth, Diana Iuşan, Dominik B. Jochym, François Jollet, Daniel Jones, Georg Kresse, Klaus Koepernik, Emine Küçükbenli, Yaroslav O. Kvashnin, Inka L.M. Locht, Sven Lubeck, Martijn Marsman, Nicola Marzari, Ulrike Nitzsche, Lars Nordström, Taisuke Ozaki, Lorenzo Paulatto, Chris J. Pickard, Ward Poelmans, Matt I.J. Probert, Keith Refson, Manuel Richter, Gian Marco Rignanese, Santanu Saha, Matthias Scheffler, Martin Schlipf, Karlheinz Schwarz, Sangeeta Sharma, Francesca Tavazza, Patrik Thunström, Alexandre Tkatchenko, Marc Torrent, David Vanderbilt, Michiel J. Van Setten, Veronique Van Speybroeck, John M. Wills, Jonathan R. Yates, Guo Xu Zhang, Stefaan Cottenier

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1016 Scopus citations


The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions.We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements.

Original languageAmerican English
Article numberaad3000
Issue number6280
StatePublished - 25 Mar 2016
Externally publishedYes

Bibliographical note

Funding Information:
ACKNOWLEDGMENTS: This research benefited from financial support from the Research Board of Ghent University; the Fond de la Recherche Scientifique de Belgique (FRS-FNRS), through Projet de Recherches (PDR) grants T.0238.13-AIXPHO and T.1031.14-HiT4FiT; the Communauté Française de Belgique, through the BATTAB project (grant ARC 14/19-057); the U.S. NSF (grant DMR-14-08838); the Swedish Research Council; the Knut and Alice Wallenberg Foundation (grants 2013.0020 and 2012.0031); the Fund for Scientific Research-Flanders (FWO) (project no. G0E0116N); and the U.S. Department of Energy (grant DOE-BES DE-SC0008938). N.A.W.H. was supported by U.S. NSF grant DMR-1105485. J.A.F.-L. acknowledges financial support from the European Union's 7th Framework Marie-Curie Scholarship Program within the ExMaMa Project (project no. 329386). I.D.M., O.E., O.G., D.I., Y.O.K., I.L.M.L., and L.N. acknowledge support from eSSENCE. T.B. was supported by the Academy of Finland (grant 263416) and the COMP Centre of Excellence. C.D., A.G., and S.L. acknowledge support from the Deutsche Forschungsgemeinschaft (DFG) and the Einstein Foundation, Berlin. M.Sche. and C.D. received funding from the European Union's Horizon 2020 research and innovation program under grant agreement no. 676580 with The Novel Materials Discovery (NOMAD) Laboratory, a European Center of Excellence. A.D.C., S.d.G., and E.K. acknowledge support from the Italian Ministry of Education, Universities, and Research (MIUR) through PRIN (Projects of National Interest) 2010-2011 (registration no. 20105ZZTSE-005). P.J.H., D.B.J., and M.I.J.P. are grateful for financial support by the Engineering and Physical Sciences Research Council (EPSRC) under UK Car-Parrinello (UKCP) grant EP/K013564/1. C.J.P. and J.R.Y. acknowledge support from the Collaborative Computational Project for NMR Crystallography under EPSRC grant EP/J010510/1. W.P. acknowledges funding by FWO. D.J. is grateful for financial support by EPSRC under grant EP/J017639/1. S.Sa. acknowledges support from the Swiss National Science Foundation (SNSF). G.-M.R. is thankful for personal financial support from FRS-FNRS. The work by I.E.C. and N.M. was supported by the SNSF's National Centre of Competence in Research MARVEL. G.K. and P.B. acknowledge support by the Austrian Science Fund, project SFB-F41 (ViCoM). S.C. acknowledges financial support from OCAS NV by an OCASendowed chair at Ghent University. Computational resources were as follows: The Ghent University contributors used the Stevin Supercomputer Infrastructure at Ghent University, which is funded by Ghent University, FWO, and the Flemish Government (Economy, Science, and Innovation Department). The Université Catholique de Louvain contributors used the Tier-1 supercomputer of the Fédération Wallonie-Bruxelles (funded by the Walloon Region under grant agreement no. 1117545), the Centre de Calcul Intensif et de Stockage de Masse-Université Catholique de Louvain supercomputing facilities, and the Consortium des Équipements de Calcul Intensif en Fédération Wallonie-Bruxelles (CÉCI) (funded by the FRS-FNRS under convention 2.5020.11). The Science and Technology Facilities Council, Scientific Computing Department's SCARF (Scientific Computing Application Resource for Facilities) cluster was used for the CASTEP calculations. The Basel University and École Polytechnique Fédérale de Lausanne contributors used the Swiss National Supercomputing Center in Lugano. Finland's IT Centre for Science was used for the RSPt calculations. K.L. and F.T. thank C. Becker for instructive discussions on the comparison of atomic-scale simulations. K.L. and S.C. thank W. Dewitte for drafting the summary figure. S.J.C., P.J.H., C.J.P., M.I.J.P., K.R., and J.R.Y. declare the receipt of income from commercial sales of CASTEP by Biovia. N.M. and M.Sche. are members of the Board of Trustees of the Psi-k Electronic Structure Network. P.G. is director of the Quantum ESPRESSO Foundation, and N.M. is a representative member. X.G., D.R.H., M.T., D.C., F.J., and G.-M.R. are members of the Advisory Board of ABINIT, an organization that develops and publishes open-source software related to this article. Commercial software is identified to specify procedures. Such identification does not imply recommendation by the National Institute of Standards and Technology. Atomic Simulation Environment scripts (46) for several of the codes are available online (48). All data are listed in tables S3 to S42.


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