Ab-initio simulations using density functional theory (DFT) were employed to investigate the structural, mechanical, electronic, magnetic, optical, and thermoelectric properties of halide perovskites \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {BaCoX}_3$$\\end{document} (X = Cl, Br, I). Structural optimization and mechanical stability assessments confirm the reliability of these perovskites in a hexagonal P\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$6_3$$\\end{document}mc symmetry. The stability of the ferromagnetic phase was validated through total crystal energy minimization via Murnaghan’s equation of state. Electronic band structures and density of states, derived from the generalized gradient approximation (GGA), reveal a semiconducting ferromagnetic nature in the spin up channel, spotlighting their potential in semiconductor spintronic applications. Phonon dispersion analysis of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {BaCoCl}_3$$\\end{document} and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {BaCoBr}_3$$\\end{document} revealed positive phonon modes throughout the entire Brillouin zone, confirming their dynamical stability. In contrast, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {BaCoI}_3$$\\end{document} demonstrated dynamical instability. The elastic constants confirm the mechanical stability and ductile nature of the perovskites. Optical and dielectric properties of these perovskites show significant UV absorption and photoconductivity, making them highly suitable for optoelectronic and solar cell applications. Finally, transport properties, such as the Seebeck coefficient, electrical conductivity, thermal conductivity, power factor, and figure of merit (ZT) unveil their exceptional thermoelectric performance. Combining half-metallic ferromagnetic traits with superior thermoelectric and optoelectronic performance positions \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {BaCoX}_3$$\\end{document} compounds as exceptional candidates for applications in spintronics, optoelectronics, and thermoelectrics. This comprehensive investigation demonstrates their ability to excel across a diverse array of advanced technological applications.
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