The structural, electronic, elastic, magnetic and optical properties of transition metal-based full Heusler compounds Cu₂TiSi, Cu₂ZrGe, Ru₂TiSi, Ru₂VSi, Rh₂TiSi and Rh₂VSi have been investigated by utilizing self-consistent full potential linearized augmented plane wave (FP-LAPW) method within density functional theory. The calculation has been performed in WEIN2k by Perdew-Burke-Ernzerhof generalized gradient approximations (PBE-GGA). We get the stable structure for ferromagnetic minimum energy calculations of these compounds. The symmetric behavior in the DOS at the Fermi level of both spin channels shows Cu₂TiSi and Cu₂ZrGe true metallic nature. Also, the direct band gap and zero value of the indirect band gap of Ru₂TiSi with minimum DOS in both spin channels at the Fermi level indicate the antiferromagnetic behavior. Ru₂TiSi alloys can be used as future material for opto-electronics. In the band structure of Ru₂VSi, there has been band overlapping across the fermi level in the majority spin channel denotes metallic nature and direct band gap at the gamma point in the down spin channel denotes the semicondutor behaviour but it is not true half metal. The Rh₂TiSi, Rh₂VSi system has paramagnetic and ferromagnetic properties respectively from their density of states which shows metallic nature. As low magnetic moments of all compounds that do not obey the Slater-Pauling rule. However, the bulk modulus (B), Young’s modulus (E), the shear modulus (G) and Poisson’s ratio (ν) have been obtained. The optical parameters that are complex dielectric tensor, refractive index, extinction coefficient, reflectivity, absorption coefficient, Electron energy loss and optical conductivity has been calculated.

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