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Structural, elastic, electronic, magnetic and thermoelectric properties of the Heusler compounds: Zr2PdAl, Zr2PdGa, and Zr2PdIn are performed using generalized gradient approximation with exchange-correlation function of the Perdew-Burke-Ernzerhof. The elastic constants are calculated at P = 0 GPa. From the obtained elastic parameters, it is inferred that these compounds, with the Hg2TiCu-type structure, are elastically stable and ductile in nature. The calculated density of states, magnetic moments and band structure are also given. The band structures of these compounds reveal that all of them have almost half metallic character with the narrow indirect band gap in the minority spin channel that amounts to 0.36, 0.46, and 0.40 eV for Zr2PdAl, Zr2PdGa, and Zr2PdIn, respectively. The total spin magnetic moments (Mtot) of the considered compounds are very close to integer value 3, which satisfies a Slater-Pauling type rule for localized magnetic moment systems Mtot = ZT − 18, where ZT = 21 is the number of valence electrons in the primitive cell. The thermoelectric properties of these materials are discussed on the basis of the Seebeck coefficients, electrical and thermal conductivity relative to relaxation time as a function of temperature, at the Fermi level, using the Boltzmann transport theory. After several browse in the literature, the obtained results are the first predictions of the physical properties for the inverse full-Heusler compounds Zr2PdZ (Z = Al, Ga and In).

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