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In silico property prediction based on density functional theory (DFT) is increasingly performed for crystalline materials. Whether quantitative agreement with experiment can be achieved with current methods is often an unresolved question, and may require detailed examination of physical effects such as electron correlation, reciprocal space sampling, phonon anharmonicity, and nuclear quantum effects (NQE), among others. In this work, we attempt first-principles equation of state prediction for the crystalline materials ScF3 and CaZrF6, which are known to exhibit negative thermal expansion (NTE) over a broad temperature range. We develop neural network (NN) potentials for both ScF3 and CaZrF6 trained to extensive DFT data, and conduct direct molecular dynamics prediction of the equation(s) of state over a broad temperature/pressure range. The NN potentials serve as surrogates of the DFT Hamiltonian with enhanced computational efficiency allowing for simulations with larger supercells and inclusion of NQE utilizing path integral approaches. The conclusion of the study is mixed: while some equation of state behavior is predicted in semiquantitative agreement with experiment, the pressure-induced softening phenomenon observed for ScF3 is not captured in our simulations. We show that NQE have a moderate effect on NTE at low temperature but does not significantly contribute to equation of state predictions at increasing temperature. Overall, while the NN potentials are valuable for property prediction of these NTE (and related) materials, we infer that a higher level of electron correlation, beyond the generalized gradient approximation density functional employed here, is necessary for achieving quantitative agreement with experiment.

A new tetragonal polymorph of CaZrF6 can be prepared by high energy ball milling of a CaF2/ZrF4 mixture, followed by heat treatment at 325 °C. This polymorph is thermodynamically stable with respect to the well-known cubic form at low temperatures. However, it readily transforms to the cubic form on heating above ∼400 °C. The tetragonal (β) CaZrF6 is not isostructural with any previously known alkaline earth AZrF6 phase. Unlike the cubic form, which shows strong negative thermal expansion over a wide temperature range, the tetragonal form displays positive thermal expansion in all directions (100–400 K: αl ∼ +17 × 10−6 K−1 and +13 × 10−6 K−1 along the a- and c-axes, respectively).