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Error estimates for solid-state density-functional theory predictions: an overview by means of the ground-state elemental crystals

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Abstract
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 scientistexperimental or theoreticalto 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 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 -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.
Keywords
density-functional theory, benchmarking, error estimate, code comparison, GENERALIZED-GRADIENT-APPROXIMATION, BRILLOUIN-ZONE INTEGRATIONS, AUGMENTED-WAVE METHOD, EQUATION-OF-STATE, THERMAL-EXPANSION, ELASTIC-CONSTANTS, LATTICE-DYNAMICS, ISOTHERMAL COMPRESSIBILITY, TEMPERATURE-DEPENDENCE, STRUCTURAL-PROPERTIES

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MLA
Lejaeghere, Kurt, et al. “Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals.” CRITICAL REVIEWS IN SOLID STATE AND MATERIALS SCIENCES, vol. 39, no. 1, 2014, pp. 1–24.
APA
Lejaeghere, K., Van Speybroeck, V., Van Oost, G., & Cottenier, S. (2014). Error estimates for solid-state density-functional theory predictions: an overview by means of the ground-state elemental crystals. CRITICAL REVIEWS IN SOLID STATE AND MATERIALS SCIENCES, 39(1), 1–24.
Chicago author-date
Lejaeghere, Kurt, Veronique Van Speybroeck, Guido Van Oost, and Stefaan Cottenier. 2014. “Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals.” CRITICAL REVIEWS IN SOLID STATE AND MATERIALS SCIENCES 39 (1): 1–24.
Chicago author-date (all authors)
Lejaeghere, Kurt, Veronique Van Speybroeck, Guido Van Oost, and Stefaan Cottenier. 2014. “Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals.” CRITICAL REVIEWS IN SOLID STATE AND MATERIALS SCIENCES 39 (1): 1–24.
Vancouver
1.
Lejaeghere K, Van Speybroeck V, Van Oost G, Cottenier S. Error estimates for solid-state density-functional theory predictions: an overview by means of the ground-state elemental crystals. CRITICAL REVIEWS IN SOLID STATE AND MATERIALS SCIENCES. 2014;39(1):1–24.
IEEE
[1]
K. Lejaeghere, V. Van Speybroeck, G. Van Oost, and S. Cottenier, “Error estimates for solid-state density-functional theory predictions: an overview by means of the ground-state elemental crystals,” CRITICAL REVIEWS IN SOLID STATE AND MATERIALS SCIENCES, vol. 39, no. 1, pp. 1–24, 2014.
@article{4188194,
  abstract     = {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 scientistexperimental or theoreticalto 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 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 -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.},
  author       = {Lejaeghere, Kurt and Van Speybroeck, Veronique and Van Oost, Guido and Cottenier, Stefaan},
  issn         = {1040-8436},
  journal      = {CRITICAL REVIEWS IN SOLID STATE AND MATERIALS SCIENCES},
  keywords     = {density-functional theory,benchmarking,error estimate,code comparison,GENERALIZED-GRADIENT-APPROXIMATION,BRILLOUIN-ZONE INTEGRATIONS,AUGMENTED-WAVE METHOD,EQUATION-OF-STATE,THERMAL-EXPANSION,ELASTIC-CONSTANTS,LATTICE-DYNAMICS,ISOTHERMAL COMPRESSIBILITY,TEMPERATURE-DEPENDENCE,STRUCTURAL-PROPERTIES},
  language     = {eng},
  number       = {1},
  pages        = {1--24},
  title        = {Error estimates for solid-state density-functional theory predictions: an overview by means of the ground-state elemental crystals},
  url          = {http://dx.doi.org/10.1080/10408436.2013.772503},
  volume       = {39},
  year         = {2014},
}

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