Assessing density functionals using many body theory for hybrid perovskites

Which density functional is the "best" for structure simulations of a particular material? A concise, first principles, approach to answer this question is presented. The random phase approximation (RPA)--- an accurate many body theory--- is used to evaluate various density functionals. To demonstrate and verify the method, we apply it to the hybrid perovskite MAPbI$_3$, a promising new solar cell material. The evaluation is done by first creating finite temperature ensembles for small supercells using RPA molecular dynamics, and then evaluating the variance between the RPA and various approximate density functionals for these ensembles. We find that, contrary to recent suggestions, van der Waals functionals do not improve the description of the material, whereas hybrid functionals and the SCAN (strongly constrained appropriately normed) density functional yield very good agreement with the RPA. Finally, our study shows that in the room temperature tetragonal phase of MAPbI$_3$, the molecules are preferentially parallel to the shorter lattice vectors but reorientation on ps timescales is still possible.