Fig. 1. Optimized geometries of (a) pristine \begin{document}$ \alpha $\end{document}-FAPbI₃ and (b) R-FA systems, and (c, d) the corresponding projected density of states (PDOS). The bandgap changes little after FA cations rotating. The LUMO and HOMO of two systems are primarily composed by Pb and I orbitals. The Fermi energy is set to zero.

Fig. 2. The charge densities of HOMO and LUMO in (a) pristine and (b) R-FA systems. Rotation of FA cations leads to charge separation by localizing electron and hole, inhibiting electron-hole recombination.

Fig. 3. Spectral density obtained from Fourier transforms of bandgaps in pristine and R-FA systems.

Fig. 4. Pure-dephasing functions for HOMO-LUMO gaps in the two systems. The inset shows the unnormalized autocorrelation functions (un-ACF). The greater initial value of the un-ACF favors faster pure-dephasing process.

Fig. 5. The non-radiative electron-hole recombination of pristine and R-FA systems.