Machine learning the vibrational free energy of perovskites

Abstract

Scanning the potential energy surface of a given compositional space via E_hull analysis is not sufficient to comment on thermodynamic stability, since the contribution stemming from the vibrational free energy is typically ignored in high-throughput searches of compositional spaces for stable compounds. The calculation of the vibrational free energy through first principles can be computationally very expensive owing to the complexity of the structures, which is directly proportional to the number of symmetrically non-unique terms to be evaluated for the creation of the dynamical matrix. In this work, we use machine learning (ML) to predict the free energy of a given compositional space (ternary perovskite compounds belonging to different symmetric structures) using the elemental and structural descriptors as fingerprints. The temperature dependence of the free energy is modeled using a 3^rd-order polynomial fit, where the coefficients are learned and predicted using ML. Thereby, a highly accurate model is built for the zero-point energy (with a root mean square error (RMSE) of 18.9 meV per atom), which is further improved by employing a symbolic regression technique, SISSO, giving a very low RMSE of 8 meV per atom. This model, while providing a computationally inexpensive means for predicting the harmonic vibrational free energy of compounds, also provides an aid to obtain the free energy and hence assess the thermodynamic stability of a given composition at any temperature. This work also provides important insights on how the elemental and compound properties are related to the vibrational free energy and hence, may aid in its prediction.