Long-range order imposed by short-range interactions in methylammonium lead iodide: Comparing point-dipole models to machine-learning force fields

The crystal structure of the MAPbI(3) hybrid perovskite forms an intricate electrostatic puzzle with different ordering patterns of the MA molecules at elevated temperatures. For this perovskite three published model Hamiltonians based on the point-dipole (pd) approximation combined with short-range effective interactions are compared to a recently developed machine-learning force field. A molecular order parameter is used to consistently compare the transformation of the antiferroelectric ordering in the orthorhombic phase upon raising the temperature. We show that the ground states and the order-disorder transition of the three models are completely different. Our analysis indicates that the long-range order in the low-temperature orthorhombic phase can be captured by pd-based models with a short cutoff radius, including the nearest and next-nearest neighbor molecules. By constructing effective atomic interactions the ordering can already be described within a 6 angstrom radius. By extracting the coupling energetics of the molecules from density functional theory calculations on MA(x)Cs(1-x)PbI(3) test systems, we show that the pd approximation holds at least for static structures. To improve the accuracy of the pd interaction an Ewald summation is applied combined with a distance dependent electronic screening function.