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<b><font size="6.4">Error estimates from high-accuracy electronic-structure reference calculations</font></b>
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<b> Notebook designed and created by:</b> Björn Bieniek, Mikkel Strange, Christian Carbogno, Mohammad-Yasin Arif, Luigi Sbailò, and Matthias Scheffler. <i>Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany</i><br> <br>
<b> Curated ab initio data: </b>
Elisabeth Wruss, and Oliver T. Hofmann. <i>Institute of Solid State Physics, Graz University of Technology, NAWI Graz, Petergasse 16, 8010 Graz, Austria</i><br>
Mikkel Strange, and Kristian Sommer Thygesen. <i>CAMD, Department of Physics, Technical University of Denmark. Fysikvej 1 2800 Kgs. Lyngby, Denmark</i><br>
Sven Lubeck, and Andris Gulans. <i>Humboldt-Universität zu Berlin, Department of Physics, Zum Grossen Windkanal 6, D-12489 Berlin</i><br>
Björn Bieniek, and Christian Carbogno. <i>Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany</i></p>
<span class="nomad--last-updated" data-version="v1.1.0">[Last updated: Jan 21, 2021]</span>
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# Introduction
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<div style="max-width: 900px;">Electronic-structure theory has become an invaluable tool in materials science. Still, the precision of different approaches has only recently been scrutinized thoroughly (for the PBE functional) using extremely accurate numerical settings [1]. A synergistic effort showed that "most recent codes and methods converge toward a single value", if extremely accurate and computationally expensive numerical settings
are employed. Little is known, however, about code- and method-specific deviances and errors that arise under numerical settings commonly used in actual calculations. <br><br>
In this notebook, we use the NOMAD infrastructure to shed light on this issue by systematically investigating and analyzing the deviances in total and relative energies as function of typical settings for basis sets, k-grids, etc. For this purpose, the NOMAD team has systematically computed the properties of 71 elemental [1] and 81 binary solids in three different electronic-structure codes using various different computational settings, including extremely accurate ones that constitute a fully converged reference.<br><br>
On one hand, this allows to analyze and compare the convergence behavior of different codes with respect to different settings. On the other hand, this allows to develop models
to estimate the errors in calculations for which no highly converged reference is available. As an example, we here discuss the following function
that is used to estimate and predict the (total energy and relative energy) errors in binary systems from the high-accuracy calculations performed for the elemental solids. Here, $N_A$ and $N_B$ denote the number of atoms of species A and B
in the binary system and $\Delta E_{A} $ and $ \Delta E_{B}$ occurring in the respective elemental solids.</div>
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<b>[1]</b> K. Lejaeghere et al., Science 351 (2016).<br>
<b>[2]</b> Reference for calculations: http://dx.doi.org/10.17172/NOMAD/2017.01.24-1 (https://nomad-repository.eu.)
