The high efficiency of lead organo-metal-halide perovskite solar cells has raised many questions about the role of the methylammonium (MA) molecules in the Pb-I framework. Experiments indicate that the MA molecules are able to ``freely'' spin around at room temperature even though they carry an intrinsic dipole moment. We have performed large supercell (2592 atoms) finite-temperature ab initio molecular dynamics calculations to study the correlation between the molecules in the framework. An underlying long-range antiferroelectric ordering of the molecular dipoles is observed. The dynamical correlation between neighboring molecules shows a maximum around room temperature in the mid-temperature phase. In this phase, the rotations are slow enough to (partially) couple to neighbors via the Pb-I cage. This results in a collective motion of neighboring molecules in which the cage acts as the mediator. At lower and higher temperatures, the motions are less correlated.
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