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

## TL;DR

This study compares point-dipole models and machine-learning force fields in predicting molecular ordering in methylammonium lead iodide, revealing the effectiveness of short-range pd models with cutoff radii in capturing low-temperature order.

## Contribution

It demonstrates that short-range point-dipole models with cutoff radii can accurately describe the long-range order in MAPbI$_3$, aligning with machine-learning force field results and DFT calculations.

## Key findings

- Point-dipole models with cutoff radii capture low-temperature order.
- Short-range interactions suffice to describe molecular ordering.
- Machine-learning force fields agree with DFT-based effective interactions.

## Abstract

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 anti-ferroelectric 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 6 A 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.