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Article

Accuracy and Precision in Electronic Structure Computation: Wien2k and FPLO

1
Institute for Theoretical Solid State Physics, Leibniz IFW Dresden, Helmholtzstr. 20, D-01069 Dresden, Germany
2
MPI-CPfS Dresden, Nöthnitzer Str. 40, D-01187 Dresden, Germany
3
Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
*
Author to whom correspondence should be addressed.
Academic Editor: Henry Chermette
Computation 2022, 10(2), 28; https://doi.org/10.3390/computation10020028
Received: 6 January 2022 / Revised: 4 February 2022 / Accepted: 7 February 2022 / Published: 11 February 2022
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 106. 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. View Full-Text
Keywords: density functional theory; DFT codes; electronic structure calculation; numerical accuracy and precision density functional theory; DFT codes; electronic structure calculation; numerical accuracy and precision
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MDPI and ACS Style

Richter, M.; Kim, S.-J.; Koepernik, K.; Rosner, H.; Möbius, A. Accuracy and Precision in Electronic Structure Computation: Wien2k and FPLO. Computation 2022, 10, 28. https://doi.org/10.3390/computation10020028

AMA Style

Richter M, Kim S-J, Koepernik K, Rosner H, Möbius A. Accuracy and Precision in Electronic Structure Computation: Wien2k and FPLO. Computation. 2022; 10(2):28. https://doi.org/10.3390/computation10020028

Chicago/Turabian Style

Richter, Manuel, Seo-Jin Kim, Klaus Koepernik, Helge Rosner, and Arnulf Möbius. 2022. "Accuracy and Precision in Electronic Structure Computation: Wien2k and FPLO" Computation 10, no. 2: 28. https://doi.org/10.3390/computation10020028

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