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This study utilizes density functional theory (DFT) with the Tran–Blaha modified Becke–Johnson (TB-mBJ) exchange potential in the WIEN2k framework to comprehensively investigate the structural, electronic, elastic, and optical properties of Rb2TlIrF6 and Rb2TlRhF6 double perovskite compounds. Structural stability assessments affirm that both materials maintain their integrity under standard conditions, demonstrating robust frameworks. The calculated elastic constants reveal mechanical stability, elasticity, and directional anisotropy, emphasizing their resilience and adaptability in varied environments. Electronic band structure calculations categorize Rb2TlIrF6 and Rb2TlRhF6 as direct bandgap semiconductors, with respective bandgaps of 2.61 eV and 1.94 eV at the L–L symmetry points, underscoring their potential in optoelectronic applications. The optical properties were analyzed through key parameters: refractive index n(ω), optical conductivity σ(ω), reflectivity R(ω), absorption coefficient α(ω), and extinction coefficient k(ω). Additionally, the real and imaginary parts of the dielectric function ∊1(ω) and ∊2(ω) were evaluated, indicating effective light interaction and absorption properties in the visible to UV range. These findings suggest that Rb2TlIrF6 and Rb2TlRhF6 exhibit advantageous optoelectronic characteristics suitable for semiconductor and next-generation electronic devices.