Roadmap for electronic structure, anharmonicity, and electron-phonon calculations in locally disordered inorganic and hybrid halide perovskites

Abstract

The role of data in modern materials science becomes more valuable and accurate when effects such as electron-phonon coupling and anharmonicity are included, providing a more realistic representation of finite-temperature material behavior. Furthermore, positional polymorphism, characterized by correlated local atomic disorder usually not reported by standard diffraction techniques, is a critical yet underexplored factor in understanding the electronic structure and transport properties of energy-efficient materials, like halide perovskites. In this manuscript, we present a first-principles methodology for locally disordered (polymorphous) cubic inorganic and hybrid halide perovskites, rooted in the special displacement method, that offers a systematic and alternative approach to molecular dynamics for exploring finite-temperature properties. By enabling a unified and efficient treatment of anharmonic lattice dynamics, electron-phonon coupling, and positional polymorphism, our approach generates essential data to predict temperature-dependent phonon properties, free energies, band gaps, and effective masses. Designed with a high-throughput spirit, this framework has been applied across a range of inorganic and hybrid halide perovskites: CsPbI3, CsPbBr3, CsSnI3, CsPbCl3, MAPbI3, MAPbBr3, MASnI3, MAPbCl3, FAPbI3, FAPbBr3, FASnI3, and FAPbCl3. We provide a comprehensive comparison between theoretical and experimental results and we systematically uncover trends and insights into their electronic and thermal behavior. For all compounds, we demonstrate strong and consistent correlations between local structural disorder, band gap openings, and effective mass enhancements.

Figures (16)

• Figure 1: Top view of the schematic representation of an anharmonic PES showing minima and maxima defined by the polymorphous (locally disordered) and monomorphous halide perovskite structures, respectively. $\Delta \tau$ indicates atomic displacements away from static-equilibrium positions of the monomorphous structure along the Cartesian directions $x$ and $y$. The example ABX$_3$ structure used at the top is for MASnI$_3$ and consists of the A-site cation (MA), the B-site metal (Sn), and the X-site halide anions (I). In this study we explore cases where A = methylammonium (MA), formamidinium (FA), or Cs, B = Pb or Sn, and X = I, Br, or Cl.
• Figure 2: (a) Schematic representation of the transitions of the PES from the monomorphous to the polymorphous, and from the polymorphous to the reference structure, indicated by ball and stick models of cubic FAPbI$_3$. (b) DFT total energy lowering per formula unit ($\Delta U$) of polymorphous cubic halide perovskites relative to their reference structures, evaluated using Eq. \ref{['eq11']}, assuming $T=300$ K, and 10 configurations in $2 \times 2 \times 2$ supercells for each system. One formula unit (f. u.) refers to the unit cell containing 5 atoms. Horizontal gray, red, and light-blue lines indicate the mean $\Delta U$ of FA-, MA-, and Cs-based compounds, respectively. (c-h) Scatter plots showing the dependence of the band gap and effective mass increase due to polymorphism on the average B-X bond length and B-X-B bond angle variations. The 120 data points correspond to 10 polymorphous configurations generated for 4 FA (black), 4 MA (red), and 4 Cs (blue) -based compounds. The straight thick lines represent the least squares regression fit to the data, with the slopes indicated on each plot. The shaded regions represent three standard deviations on either side of the lines. All calculations refer to the DFT-PBEsol approximation. Our calculations for the band gaps and effective masses include spin-orbit coupling (SOC) effects.
• Figure 3: (a) Example reference structure of FAPbI$_3$ with relaxed random molecular orientations in a $2 \times 2 \times 2$ sypercell. (b) Example fictitious reference structure of FAPbI$_3$ obtained by applying unit cell translations to the molecules in the reference structure, placing all back to a single unit cell. This fictitious structure serves as the reference point for calculating the interatomic force constants within the SCP theory.
• Figure 4: Structures considered throughout this study using the example of MAPbBr$_3$. Reference structures can contain symmetrized-constrained or relaxed random molecular orientations. These structures lead to distinct polymorphous structures after geometry optimization. The ZG structures, labelled as green, incorporate electron-phonon coupling effects at finite temperatures ($T$). For the ZG structures, we considered a 4$\times$4$\times$4 supercell (768 atoms) to accommodate a broader sampling of vibrational modes.
• Figure 5: Dependence of the average B-X-B bond angle decrease on the average B-X bond length variation. The 120 data points correspond to 10 polymorphous configurations generated for 4 FA (black), 4 MA (red), and 4 Cs (blue) -based compounds. The straight thick line represents the least squares regression fit to the data, with the slope indicated on the plot. The shaded region represents three standard deviations on either side of the lines.