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Rapid yet accurate first principle based predictions of alkali halide crystal phases using alchemical perturbation

We assess the predictive power of alchemical perturbations for estimating fundamental properties in ionic crystals. Using density functional theory we have calculated formation energies, lattice constants, and bulk moduli for all sixteen iso-valence-electronic combinations of pure pristine alkali halides involving elements $A \in \{$Na, K, Rb, Cs$\}$ and $X \in \{$F, Cl, Br, I$\}$. For rock salt, zincblende and cesium chloride symmetry, alchemical Hellmann-Feynman derivatives, evaluated along lattice scans of sixteen reference crystals, have been obtained for all respective 16$\times$15 combinations of reference and predicted target crystals. Mean absolute errors (MAE) are on par with density functional theory level of accuracy for energies and bulk modulus. Predicted lattice constants are less accurate. NaCl is the best reference salt for alchemical estimates of relative energies (MAE $<$ 40 meV/atom) while alkali fluorides are the worst. By contrast, lattice constants are predicted best using NaF as a reference salt (MAE $<$ 0.5Å), yielding only semi-quantitative accuracy. The best reference salt for the prediction of bulk moduli is CsCl (MAE $<$ 0.4$\times$10$^{11}$ dynes/cm$^2$). Alchemical derivatives can also be used to predict competing rock salt and cesium chloride phases in binary and ternary solid mixtures with CsCl. Alchemical predictions based on dispersion corrected density functional theory with pure RbI as a reference salt reproduce reasonably well the reversal of the rock salt/cesium chloride stability trend for binary $(AX)_{1-x}$CsCl$_x$ as well as for ternary $(AX)_{0.5-0.5x}(BY)_{0.5-0.5x}$CsCl$_x$ mixtures.