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Thermal effects on CH$_3$NH$_3$PbI$_3$ perovskite from ab-initio molecular dynamics simulations

We present a molecular dynamics simulation study of CH$_3$NH$_3$PbI$_3$ based on forces calculated from density functional theory. The simulation were performed on model systems having 8 and 27 unit cells, and for a total simulation time of 40 ps in each case. Analysis of the finite size effects, in particular the mobility of the organic component, suggests that the smaller system is over correlated through the long range electrostatic interaction. In the larger system this finite size artifact is relaxed producing a more reliable description of the anisotropic rotational behavior of the methyl ammonium molecules. The thermal effects on the optical properties of the system were also analyzed. The HOMO-LUMO energy gap fluctuates around its central value with a standard deviation of approximately 0.1 eV. The projected density of states consistently place the Fermi level on the $p$ orbitals of the I atoms, and the lowest virtual state on $p$ orbitals of the Pb atoms throughout the whole simulation trajectory.