Title: First-principles calculations to investigate structural, elastic, electronic, thermodynamic, and thermoelectric properties of CaPd$_3$B$_4$O$_{12}$ (B = Ti, V) perovskite

Abstract: This study has explored numerous physical properties of CaPd$_3$Ti$_4$O$_{1}$2 (CPTO) and CaPd$_3$V$_4$O$_{12}$ (CPVO) quadruple perovskites employing the density functional theory (DFT) method. The mechanical permanence of these two compounds was observed by the Born stability criteria as well. The band structure of CPTO reveals a 0.88 and 0.46 eV direct narrow band gap while using GGA-mBJ and GGA-PBE potentials, respectively, which is an indication of its fascinating semiconducting nature. The calculated partial density of states indicates the strong hybridization between Pd-4d and O-2p orbital electrons for CPTO, whereas Pd-4d and V-3d-O-2p for CPVO. The study of the chemical bonding nature and electronic charge distribution graph reveals the coexistence of covalent O-V/Pd bonds, ionic O-Ti/Ca bonds, as well as metallic Ti/V-Ti/V bonding for both compounds. The Fermi surface of CPVO ensures a kind of hole as well as electron faces simultaneously, indicating the multifarious band characteristic. The prediction of the static real dielectric function (optical property) of CPTO at zero energy implies its promising dielectric nature. The photoconductivity and absorption coefficient of CPBO display good qualitative compliance with the consequences of band structure computations. The calculated thermodynamic properties manifest the thermodynamical stability for CPBO, whereas phonon dispersions of CPVO exhibit stable phonon dispersion in contrast to slightly unstable phonon dispersion of CPTO. The predicted Debye temperature ($\theta_D$) has been utilized to correlate its topical features including thermoelectric behaviors. The studied thermoelectric transport properties of CPTO yielded the Seebeck coefficient (186 V/K), power factor (11.9 Wcm$^{-1}$K$^{-2}$), and figure of merit (ZT) value of about 0.8 at 800 K, indicating that this material could be a promising candidate for thermoelectric applications.