The effect of the A-site cation on the phase transition temperature of metal halide perovskites
A key challenge for the practical application of metal halide perovskites (MHPs) is the instability of the desired perovskite phase relative to the optically non-active $\delta$ phase. To determine the phase stability, we previously developed a procedure to compute the harmonic free energy as a function of temperature, which was suited for CsPbI$_3$ but fails when Cs is replaced by organic cations due to their rotational freedom. Herein we propose a multistep thermodynamic integration (TI) approach that corrects the harmonic free energy to obtain the Gibbs free energy. Given the abundance of local minima in these materials, we employ replica exchange to prevent simulations from getting trapped, while introducing an intermediate potential energy surface to improve convergence and reduce computational cost. Benchmarking energy and forces from different exchange-correlation functionals and dispersion methods against high-level RPA+HF calculations identifies PBE+D3(BJ) as the best trade-off between accuracy, computational efficiency, and precision. To perform molecular dynamics simulations within the TI framework, it was necessary to train a machine learning potential using the MACE architecture on ab initio data calculated with density functional theory. Our results show that, for all three materials, the free energy difference between the $\gamma$ and $\delta$ phases exhibits a very similar temperature dependence. This suggests that phase stability is primarily governed by differences in ground-state energy, rather than by material-specific thermal effects. Beyond these three materials, our methodology provides a robust framework for investigating the phase behavior of other MHPs, paving the way for the discovery of more stable perovskites.