Structural parameters, electronic band structure, optical spectra, and thermoelectric properties of trigonal Ba 3 B(Nb, Ta) 2 O 9 (B═Sr, Mg, Ca, Hg, Zn, Fe, Ni, Mn, Co, and Ca) compound materials are investigated. The computations are performed using density-functional calculations within the generalized gradient approximation. The calculated a and c parameters agree with those of the experiment to within 2%. The Ba 3 B(Nb, Ta) 2 O 9 (B=Sr,Mg,Ca, Hg, Zn, Fe, Ni, Mn, Co, and Ca) materials are found to be semiconductors with a band-gap energy varying from 0.82 to 3.17 eV. A metallic character is observed in Ba 3 B(Nb, Ta) 2 O 9 (B═Ni, Mn, and Co) compounds indicating the presence of conductivity features. A small carrier effective mass indicates the increase of the electron mobility leading to a high n-type conductivity. The p states dominate the lower valence band region. The optical spectra show an anisotropic character between x and z directions. The excitonic effects tend to increase the strength of the oscillator at M 0 and M points. The effect is reduced when increasing the photon energy, indicating that the Ba 3 BB 2 'O 9 compound can be used for devices such as Bragg's reflectors, and optical and optoelectronic devices. The calculations were performed using the BoltzTrap code, which depends on the semi-classical Boltzmann transport equation. The Seebeck coefficient, electrical conductivity, thermal conductivity, power factor, and the figure of merit for Ba 3 (Fe, Sr, Hg, Zn)B 0 2 O 9 are calculated. At higher temperatures, the mobility increases by reducing the electrical conductivity. Ba 3 (Fe, Sr, Hg, Zn) B 2 ' O 9 shows a considerable thermoelectric performance accompanied by a sign point figure of merit larger than many full perovskites reported till date. K E Y W O R D S ab initio calculations, Ba 3 BB 0 2 O 9 , electronic structure, optical properties, thermoelectric properties 1 | INTRODUCTION Complex perovskites Ba 3 BB 0 2 O 9 are composed of at least two different B cations that can take a variety of valences. 1,2The difference in the nature of the B cations leads to an ordering in the B site. Some of these complex oxides exhibit NaCl-type B-site ordering with cubic symmetry (SG Number 225), often referred to as 1:1 type, whereas