Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals

• Published in: Critical reviews in solid state and materials sciences Vol. 39; no. 1; pp. 1 - 24
• Main Authors: Lejaeghere, K., Van Speybroeck, V., Van Oost, G., Cottenier, S.
• Format: Journal Article
• Language: English
• Published: Colchester Taylor & Francis Group 01.01.2014; Taylor & Francis; Taylor & Francis Ltd
• Subjects: Assessments; benchmarking; code comparison; Communities; Condensed matter: structure, mechanical and thermal properties; Crystalline state (including molecular motions in solids); Crystallographic aspects of phase transformations; pressure effects; Crystals; density-functional theory; Deviation; Elasticity, elastic constants; Error analysis; error estimate; Estimates; Exact sciences and technology; Mathematical analysis; Mechanical and acoustical properties of condensed matter; Mechanical properties of solids; Permissible error; Physics; Predictions; Quantum physics; Scientists; Spreads; Structure of solids and liquids; crystallography; error estimate; Errors; Elastic constants; Vienna ab initio simulation package; Statistical analysis; benchmarking; Linear regression; code comparison; PAW calculation; Density functional method; density-functional theory; Cohesive energy
• ISSN: 1040-8436; 1547-6561; 2331-4583
• DOI: 10.1080/10408436.2013.772503

Predictions of observable properties by density-functional theory calculations (DFT) are used increasingly often by experimental condensed-matter physicists and materials engineers as data. These predictions are used to analyze recent measurements, or to plan future experiments in a rational way. Increasingly more experimental scientists in these fields therefore face the natural question: what is the expected error for such a first-principles prediction? Information and experience about this question is implicitly available in the computational community, scattered over two decades of literature. The present review aims to summarize and quantify this implicit knowledge. This eventually leads to a practical protocol that allows any scientist-experimental or theoretical-to determine justifiable error estimates for many basic property predictions, without having to perform additional DFT calculations. A central role is played by a large and diverse test set of crystalline solids, containing all ground-state elemental crystals (except most lanthanides). For several properties of each crystal, the difference between DFT results and experimental values is assessed. We discuss trends in these deviations and review explanations suggested in the literature. A prerequisite for such an error analysis is that different implementations of the same first-principles formalism provide the same predictions. Therefore, the reproducibility of predictions across several mainstream methods and codes is discussed too. A quality factor Δ expresses the spread in predictions from two distinct DFT implementations by a single number. To compare the PAW method to the highly accurate APW+lo approach, a code assessment of VASP and GPAW (PAW) with respect to WIEN2k (APW+lo) yields Δ-values of 1.9 and 3.3 meV/atom, respectively. In both cases the PAW potentials recommended by the respective codes have been used. These differences are an order of magnitude smaller than the typical difference with experiment, and therefore predictions by APW+lo and PAW are for practical purposes identical.