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, while the SQE model quantitatively reproduces all 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 10 −3 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.

The mean bond length d between a central atom and its nearest neighbors can be estimated from the position of the first peak in the radial distribution function g(r). However, as we demonstrate here, this estimate does not allow one to deduce temperature-induced changes in d. Instead, skewness has to be included into the analysis, which can be achieved, for example, via the skew normal distribution (SND). Fits to the first peak using the SND give bond length in good agreement with direct measurements of nearest-neighbor distribution functions in crystals as well as with a Voronoi-tessellation based detection of nearest-neighbors in liquids. While the location of the first peak in g(r) may shift to smaller values with increasing temperature for three studied liquids-argon, copper, and the bulk-metallic-glass (BMG) forming alloy ZrCuAl-we find our improved estimates of d to systematically increase with temperature in all cases. Recent conclusions on temperature-induced bond contractions in simple metallic or BMG-forming liquids may therefore have arisen from the neglect of skewness effects.

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Using density-functional theory based simulations, we study how initially disconnected zinc phosphate molecules respond to different externally imposed deformations. Hybridization changes are observed in all cases, in which the coordination of zinc atoms changes irreversibly from tetrahedral to seesaw and square pyramidal, whereby the system stiffens substantially. The point at which stiff networks are formed does not only depend on the hydrostatic pressure. Stress anisotropy generally reduces the required hydrostatic network formation pressure. Moreover, networks obtained under isotropic deformations turn out stiffer, elastically more isotropic, and lower in energy after decompression than those produced under anisotropic stresses. We also find that the observed stress-memory effects are encoded to a significant degree in the arrangement of atoms in the second neighbor shell of the zinc atoms. These findings refine previously formulated conjectures of pressure-assisted cross-linking in zinc phosphate-based anti-wear films. Graphical Abstract