{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T22:22:38Z","timestamp":1768342958898,"version":"3.49.0"},"reference-count":17,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,2,11]],"date-time":"2022-02-11T00:00:00Z","timestamp":1644537600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Electronic structure calculations in the framework of density functional theory are based on complex numerical codes which are used in a multitude of applications. Frequently, existing experimental information is used as a gauge for the reliability of such codes. However, their results depend both on the chosen exchange-correlation energy functional and on the specific numerical implementation of the Kohn-Sham equations. The only way to disentangle these two items is a direct comparison of two or more electronic structure codes. Here, we address the achievable numerical accuracy and numerical precision in the total energy computation of the two all-electron density-functional codes Wien2k and FPLO. Both codes are based on almost independent numerical implementations and largely differ in the representation of the Bloch wave function. Thus, it is a highly encouraging result that the total energy data obtained with both codes agree within less than 10\u22126. We here relate the term numerical accuracy to the value of the total energy E, while the term numerical precision is related to the numerical noise of E as observed in total energy derivatives. We find that Wien2k achieves a slightly higher accuracy than FPLO at the price of a larger numerical effort. Further, we demonstrate that the FPLO code shows somewhat higher precision, i.e., less numerical noise in E than Wien2k, which is useful for the evaluation of physical properties based on derivatives of E.<\/jats:p>","DOI":"10.3390\/computation10020028","type":"journal-article","created":{"date-parts":[[2022,2,13]],"date-time":"2022-02-13T20:32:30Z","timestamp":1644784350000},"page":"28","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Accuracy and Precision in Electronic Structure Computation: Wien2k and FPLO"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9999-8290","authenticated-orcid":false,"given":"Manuel","family":"Richter","sequence":"first","affiliation":[{"name":"Institute for Theoretical Solid State Physics, Leibniz IFW Dresden, Helmholtzstr. 20, D-01069 Dresden, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0477-3900","authenticated-orcid":false,"given":"Seo-Jin","family":"Kim","sequence":"additional","affiliation":[{"name":"MPI-CPfS Dresden, N\u00f6thnitzer Str. 40, D-01187 Dresden, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4483-0423","authenticated-orcid":false,"given":"Klaus","family":"Koepernik","sequence":"additional","affiliation":[{"name":"Institute for Theoretical Solid State Physics, Leibniz IFW Dresden, Helmholtzstr. 20, D-01069 Dresden, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0716-1731","authenticated-orcid":false,"given":"Helge","family":"Rosner","sequence":"additional","affiliation":[{"name":"MPI-CPfS Dresden, N\u00f6thnitzer Str. 40, D-01187 Dresden, Germany"}]},{"given":"Arnulf","family":"M\u00f6bius","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Physik, Technische Universit\u00e4t Chemnitz, D-09107 Chemnitz, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2022,2,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"aad3000","DOI":"10.1126\/science.aad3000","article-title":"Reproducibility in density functional theory calculations of solids","volume":"351","author":"Lejaeghere","year":"2016","journal-title":"Science"},{"key":"ref_2","unstructured":"(2022, January 05). Accuracy and Precision. Available online: https:\/\/en.wikipedia.org\/wiki\/Accuracy_and_precision."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Eschrig, H. (1988). Optimized LCAO Method and the Electronic Structure of Extended Systems, Akademie-Verlag.","DOI":"10.1515\/9783112483466"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/S0927-0256(03)00112-5","article-title":"Solid state calculations using WIEN2k","volume":"28","author":"Schwarz","year":"2003","journal-title":"Comput. Mater. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1743","DOI":"10.1103\/PhysRevB.59.1743","article-title":"Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme","volume":"59","author":"Koepernik","year":"1999","journal-title":"Phys. Rev. B"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"095502","DOI":"10.1103\/PhysRevLett.93.095502","article-title":"Experimental Evidence for a High-Pressure Isostructural Phase Transition in Osmium","volume":"93","author":"Occelli","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"214103","DOI":"10.1103\/PhysRevB.74.214103","article-title":"Lifshitz transitions and elastic properties of Osmium under pressure","volume":"74","author":"Koudela","year":"2006","journal-title":"Phys. Rev. B"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1103\/PhysRev.116.555","article-title":"Fermi Surface in Aluminum","volume":"116","author":"Harrison","year":"1959","journal-title":"Phys. Rev."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1088\/0305-4608\/10\/1\/012","article-title":"Fermi surface of aluminium under homogeneous strain","volume":"10","author":"Joss","year":"1980","journal-title":"J. Phys. F Met. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"015501","DOI":"10.1088\/0953-8984\/26\/1\/015501","article-title":"Nuclear magnetic resonance at up to 10.1 GPa pressure detects an electronic topological transition in aluminum metal","volume":"26","author":"Meissner","year":"2014","journal-title":"J. Phys. Condens. Matter"},{"key":"ref_11","unstructured":"(2022, January 05). Available online: https:\/\/www.fplo.de\/."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3107","DOI":"10.1088\/0022-3719\/10\/16\/019","article-title":"A technique for relativistic spin-polarised calculations","volume":"10","author":"Koelling","year":"1977","journal-title":"J. Phys. C Solid State Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3865","DOI":"10.1103\/PhysRevLett.77.3865","article-title":"Generalized Gradient Approximation Made Simple","volume":"77","author":"Perdew","year":"1996","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"16223","DOI":"10.1103\/PhysRevB.49.16223","article-title":"Improved tetrahedron method for Brillouin-zone integrations","volume":"49","author":"Jepsen","year":"1994","journal-title":"Phys. Rev. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/0370-1573(94)90103-1","article-title":"The theory of electronic topological transitions","volume":"245","author":"Blanter","year":"1994","journal-title":"Phys. Rep."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1038\/nphys341","article-title":"Magneto-elastic lattice collapse in YCo5","volume":"2","author":"Rosner","year":"2006","journal-title":"Nat. Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1080\/08957959.2021.1957863","article-title":"High pressure stability of \u03b2-Zr: No evidence for isostructural phase transitions","volume":"41","author":"Sneed","year":"2021","journal-title":"High Press. Res."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/10\/2\/28\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:18:05Z","timestamp":1760134685000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/10\/2\/28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,11]]},"references-count":17,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2]]}},"alternative-id":["computation10020028"],"URL":"https:\/\/doi.org\/10.3390\/computation10020028","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,11]]}}}