Computation of charge distribution and electrostatic potential in silicates with the use of chemical potential equalization models

New parameters for the electronegativity equalization model (EEM) and the split-charge equilibration (SQE) model are calibrated for silicate materials, based on an extensive training set of representative isolated systems. In total, four calibrations are carried out, two for each model, either using iterative Hirshfeld (HI) charges or ESP grid data computed with density functional theory (DFT) as a reference. Both the static (ground state) reference quantities and their responses to uniform electric fields are included in the fitting procedure. The EEM model fails to describe the response data, whereas the SQE model quantitatively reproduces all of the training data. For the ESP-based parameters, we found that the reference ESP data are only useful at those grid points where the electron density is lower than 0.001 a.u. The density value correlates with a distance criterion used for selecting grid points in common ESP fitting schemes. All parameters are validated with DFT computations on an independent set of isolated systems (similar to the training set), and on a set of periodic systems including dense and microporous crystalline silica structures, zirconia, and zirconium silicate. Although the transferability of the parameters to new isolated systems poses no difficulties, the atomic hardness parameters in the HI-based models must be corrected to obtain accurate results for periodic systems. The SQE/ESP model permits the calculation of the ESP with similar accuracy in both isolated and periodic systems

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

Predictions of observable properties by density-functional theory calculations (DFT) are used increasingly often in experimental condensed-matter physics and materials engineering as data. These predictions are used to analyze recent measurements, or to plan future experiments. Increasingly more experimental scientists in these fields therefore face the natural question: what is the expected error for such an ab initio prediction? Information and experience about this question is scattered over two decades of literature. The present review aims to summarize and quantify this implicit knowledge. This 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 Delta 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 with respect to WIEN2k yields Delta values of 1.9 and 3.3 meV/atom, respectively. 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.Comment: 27 pages, 20 figures, supplementary material available (v5 contains updated supplementary material