We report the results of the full-potential linearized augmented plane wave (FP-LAPW) calculations on the structural, elastic, optoelectronic and magnetic properties of CdHo$_2$S$_4$ spinel. Both the generalized gradient approximation (GGA) and Trans-Blaha modified Becke-Johnson potential (TB-mBJ) are used to model the exchange-correlation effects. The computed lattice parameter, internal coordinate and bulk modulus are in good agreement with the existing experimentaldata. According to the calculated elastic moduli, CdHo$_2$S$_4$ is mechanically stable with a ductile nature and a noticeableelastic anisotropy. The ferromagnetic phase of CdHo2S4 is energetically favourable compared to non-magnetic one, with ahigh magnetic moment of about 8.15 $\mu$B. The calculated band structure demonstrates that the title compound is a direct bandgap semiconductor. The TB-mBJ yields a band gap of $\sim$1.86 and $\sim$2.17 eV for the minority and majority spins, respectively.The calculated optical spectra reveal a strong response in the energy range between the visible light and the extreme UVregions.

A number of ternary-semiconductor oxides have shown promise for potential applications in catalysis, thermoelectricity, optoelectronics and electrochemistry. In this work, the thermoelectric and optoelectronic properties of La$_2$Pd$_2$O$_5$ compound are studied by the full-potential linearized augmented plane wave method based on density functional theory. The electronic band structure shows an indirect band gap of 1.342 eV for La$_2$Pd$_2$O$_5$. Partial and total density of states indicate strong hybridization among different electronic orbitals. The upper part of the valence band is dominated by the Pd-d and O-p states, while the lower conduction band originates mainly from the Pd-d state. Dielectric functions including the imaginary and real parts, along with other optical constants, such as absorption coefficient, energy loss function, reflectivity and refractive index, have been reported for the first time. Thermoelectric properties, including electrical and thermal conductivity, Seebeck coefficient and power factor with variation in temperature are also presented and discussed using semi-classical Boltzmann transport theory for the first time for La$_2$Pd$_2$O$_5$. It has been found that La$_2$Pd$_2$O$_5$ has attractive optoelectronic and thermal properties that can make it a suitable candidate for efficient thermoelectric and optoelectronic device applications.