Ab initiobased thermal property predictions at a low cost: An error analysis

Abstract

Ab initio calculations often do not straightforwardly yield the thermal properties of a material yet. It requires considerable computational efforts, for example, to predict the volumetric thermal expansion coefficient α V or the melting temperature T m from first principles. An alternative is to use semiempirical approaches. They relate the experimental values to first-principles predictors via fits or approximative models. Before applying such methods, however, it is of paramount importance to be aware of the expected errors. We therefore quantify these errors at the density-functional theory level using the Perdew-Burke-Ernzerhof functional for several semiempirical approximations of α V and T m , and compare them to the errors from fully ab initio methods, which are computationally more intensive. We base our conclusions on a benchmark set of 71 ground-state elemental crystals. For the thermal expansion coefficient, it appears that simple quasiharmonic theory, in combination with different approximations to the Grüneisen parameter, provides a similar overall accuracy as exhaustive firstprinciples phonon calculations. For the melting temperature, expensive ab initio molecular-dynamics simulations still outperform semiempirical methods.

Error estimates for density-functional theory predictions of surface energy and work function

“…This predictable part of the DFT error can subsequently be distinguished from a material specific error and utilized to transform the calculated result to the expected true value, serving as an a posteriori calibration. This decomposition of the computational error has been applied to DFT results [19,20,63] and was recently reviewed by Pernot et al [64]. Note that, whereas the present work discusses computational errors in terms of predictable and material-specific contributions, literature sometimes refers to systematic and random errors.…”

“…The present work uses a test set of elemental materials, spanning most of the periodic table, for a statistical analysis of the agreement between DFTcalculated and experimentally measured surface properties. It makes use of the framework established by Lejaeghere et al, who estimated the accuracy of DFT predictions for structural, elastic, and thermal properties of crystalline solids [19,20]. In the same spirit, the objective is to characterize the DFT value as a predictor for the experimental result.…”

Probabilistic performance estimators for computational chemistry methods: Systematic improvement probability and ranking probability matrix. II. Applications

“…If the ranking study is to reflect the methods performances, the curation and possible pruning of the dataset from such global outliers is a necessary preliminary step. Otherwise, more complex statistical models have to be used to alleviate the impact of those points (see Paper I 1 -Appendix A and references [26][27][28] ).…”

Is the error on first-principles volume predictions absolute or relative?

“…6 In addition to these relatively simple approaches, some authors also assessed DFT errors more rigorously. Some of the present authors 6,18 , for example, applied a linear regression between experimental and DFT results to distinguish between systematic and residual deviations. In the current article, a systematic error denotes the predictable over-or underestimation of DFT compared to experiment, which can be corrected for by means of a regression analysis.…”