Unveiling the Impact of Nanoscale Cation Arrangement on Bandgap Tunability and Structural Stability in Cs_0.5A_0.5PbI₃ (A = FA⁺, MA⁺) Perovskites

Nanoscale cation ordering in mixed-cation lead iodide perovskites (Cs_xA_1-xPbI₃; A = formamidinium: CH(NH₂)₂⁺, FA⁺; methylammonium: CH₃NH₃⁺, MA⁺) profoundly affects optoelectronic performance; however, the atomic-scale origins of this connection remain underexplored. Here, we combine first-principles density functional theory calculations and experimental observation to reveal that it is not the composition but the spatial arrangement of Cs⁺, FA⁺, and MA⁺ cations that governs lattice strain, bandgap dispersion, and stability. FA⁺ produces larger lattice expansion and Pb-I-Pb bond angle distortion minima (134°-171°) than MA⁺ (132°-173°), affecting octahedral tilting dynamics. Cation clustering (Type A) induces indirect bandgaps (1.37-2.11 eV), while uniform distributions (Type B) sustain direct gaps, justifying composition-independent photoluminescence redshifts (Δλ = 10-15 nm). Configuration-dependent formation energies reveal strain-mitigated configurations as thermodynamically preferred, yet localized lattice distortions (>2.8%) persist, buffered by iodine sublattice flexibility. Importantly, we reveal a nonmonotonic link between cation size disparity and octahedral distortion, contradicting the common assumption of entropy-driven homogeneous mixing in hybrid perovskites. By linking atomic-scale cation arrangement and macroscopic optoelectronic response, our results offer a predictive, design-oriented framework for producing stable, color-pure perovskite quantum dots. This discovery paves the way for a targeted cation ordering to unlock next-generation high-performance optoelectronic devices.