Multi-scale model for disordered hybrid perovskites: the concept of organic cation pair modes

Abstract

We have studied the properties of the prototype hybrid organic-inorganic perovskite ${\text{CH}}_3^{}{\text{NH}}_3^{}{\text{PbI}}_3^{}$ using relativistic density functional theory (DFT). For our analysis we introduce the concept of ${\text{CH}}_3^{}{\text{NH}}_3^{+}$ "pair modes", that is, characteristic relative orientations of two neighboring ${\text{CH}}_3^{}{\text{NH}}_3^{+}$ cations. In our previous work [Phys. Rev. B \textbf{94}, 045201 (2016)] we identified two preferential orientations that a single ${\text{CH}}_3^{}{\text{NH}}_3^{+}$ cation adopts in a unit cell. The total number of relevant pairs can be reduced from the resulting 196 combinations to only 25 by applying symmetry operations. DFT results of several $2\times 2\times 2$ supercell models reveal the dependence of the total energy, band gap and band structure on the distribution of ${\text{CH}}_3^{}{\text{NH}}_3^{+}$ cations and the pair modes. We have then analyzed the pair-mode distribution of a series of $4\times 4\times 4$ supercell models with disordered ${\text{CH}}_3^{}{\text{NH}}_3^{+}$ cations. Our results show that diagonally-oriented ${\text{CH}}_3^{}{\text{NH}}_3^{+}$ cations are rare in optimized ${\text{CH}}_3^{}{\text{NH}}_3^{}{\text{PbI}}_3^{}$ supercell structures. In the prevailing pair modes, the $\text{C–N}$ bonds of the two neighboring ${\text{CH}}_3^{}{\text{NH}}_3^{+}$ cations are aligned approximately vertically. Furthermore, we fit the coefficients of a pair-mode expansion to our supercell DFT reference structures. The pair-mode model can then be used to quickly estimate the energies of disordered perovskite structures. Our pair-mode concept provides combined atomistic-statistical insight into disordered structures in bulk hybrid perovskite materials.

23 pages (including a manuscript of 13 pages and a supplemental material of 10 pages); 11 figures and 5 tables in the manuscript; 4 figures in the supplemental material

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• Long-range order imposed by short-range interactions in methylammonium lead iodide: Comparing point-dipole models to machine-learning force fields
• Surface reconstruction of tetragonal methylammonium lead triiodide
• Domain boundaries in Luttinger-Tisza ordered dipole lattices
• Multi-scale model for the structure of hybrid perovskites: Analysis of charge migration in disordered MAPbI${}_3$ structures
• Role of host/guest coupling in stabilizing the phases of the over-tolerant hybrid perovskite MHyPbX3
• Review: Solid-state physics of halide perovskites