The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements

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 firstprinciples 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.

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More than a third of all exoplanets can be classified as super-Earths based on radius (1´2 R C ) and mass (< 10 M C ).Here we model mass-radius relations based on silicate mantle and iron core equations of state to infer to first order the structure and composition range of rocky super-Earths assuming insignificant gas envelopes. As their core pressures exceed those in the Earth by an order of magnitude, significant extrapolations of equations of state for iron are required. We develop a new equation of state of hexagonal close packed (hcp) iron for super-Earth conditions (SEOS) based on density functional theory results for pressures up to 137 TPa. A comparison of SEOS and extrapolated equations of state for iron from the literature reveals differences in density of up to 4% at 1 TPa and up to 20% at 10 TPa. Such density differences significantly affect mass-radius relations. On mass, the effect is as large as 10% for Earth-like super-Earths (core radius fraction of 0.5) and 20% for Mercury-like super-Earths (core radius fraction of 0.8). We also quantify the effects of other modeling assumptions such as temperature and composition by considering extreme cases. We find that the effect of temperature on mass (< 5%) is smaller than that resulting from the extrapolation of the equations of state of iron and lower mantle temperatures are too low to allow for rock and iron miscibility for R < 1.75 R C . Our end-member cases of core and mantle compositions create a spread in mass-radius curves reaching more than 50% in terms of mass for a given planetary radius, implying that modeling uncertainties dominate over observational uncertainties for many observed super-Earths. We illustrate these uncertainties explicitly for Kepler-36b with well-constrained mass and radius. Assuming a core composition of 0.8ρ Fe (equivalent to 50 mol% S) instead of pure Fe leads to an increase of the core radius fraction from 0.53 to 0.64. Using a mantle composition of Mg 0.5 Fe 0.5 SiO 3 instead of MgSiO 3 leads to a decrease of the core radius fraction to 0.33. Effects of thermal structure and the choice of equation of state for the core material on the core radius of Kepler-36b are small but non-negligible, reaching 2% and 5%, respectively.

Density-functional theory (DFT) predictions of materials properties are becoming ever more widespread. With increased use comes the demand for estimates of the accuracy of DFT results. In view of the importance of reliable surface properties, this work calculates surface energies and work functions for a large and diverse test set of crystalline solids. They are compared to experimental values by performing a linear regression, which results in a measure of the predictable and material-specific error of the theoretical result. Two of the most prevalent functionals, the local density approximation (LDA) and the Perdew-Burke-Ernzerhof parametrization of the generalized gradient approximation (PBE-GGA), are evaluated and compared. Both LDA and GGA-PBE are found to yield accurate work functions with error bars below 0.3 eV, rivaling the experimental precision. LDA also provides satisfactory estimates for the surface energy with error bars smaller than 10%, but GGA-PBE significantly underestimates the surface energy for materials with a large correlation energy.