Exploring Librational Pathways with on-the-Fly Machine-Learning Force Fields: Methylammonium Molecules in MAPbX₃ (X = I, Br, Cl) Perovskites

(X = I, Br, Cl) perovskites, but with different relative methylammonium (MA) ordering, have appeared as representatives of this orthorhombic phase. Distinguishing them by X-ray diffraction experiments is difficult, and conventional first-principles-based molecular dynamics approaches are often too computationally intensive to be feasible. Therefore, to determine the thermodynamically stable structure, we use a recently introduced on-the-fly machine-learning force field method, which reduces the computation time from years to days. The molecules exhibit a large degree of anharmonic motion depending on temperature: that is, rattling, twisting, and tumbling. We observe the crystal's "librational pathways" while slowly heating it in isothermal-isobaric simulations. Marked differences in the thermal evolution of structural parameters allow us to determine the real structure of the system via a comparison with experimentally determined crystal structures.