Structural, electronic, and optical properties of PbTiO3, SnTiO3, and GeTiO3 tetragonals (P4mm, 99 space group) were investigated using density functional theory as implemented in pseudo-potential plane wave in CASTEP computer code. The calculated equilibrium lattice parameter, electronic band structure, and optical properties for PbTiO3 (reference compound) are in good agreement with the available experiment data. The result also shows that GeTiO3 has a higher tetragonality (c/a=1.18) compared with SnTiO3 (c/a=1.15) and PbTiO3 (c/a=1.05). Calculations of the elastic constants of PbTiO3, SnTiO3, and GeTiO3 tetragonals show that they are mechanically stable. The electronic band structure shows that PbTiO3 has higher indirect band gap at X-G compared with SnTiO3 and GeTiO3, as explained in detail by the optical properties of ATiO3 (A=Pb, Sn, Ge) through the refractive index and absorption coefficient.

The geometry optimization of the tetragonal supercell 1x1x2 (P4mm, 99 space group) of PZT and PSnZT were calculated using different exchange correlation functional such as Local Density Approximate (LDA-CAPZ) and Generalized Gradient Approximation (GGA-PBE & GGA-PBEsol).The calculation using functional GGA-PBEsol exhibits the most accurate values of lattice parameter and volume of structure relative to the experiment results with typical error of approximately 1% underestimate (only for PZT-as reference materials). The electronic band structure and density of state (DOS) were also studied in order to understand the electron density and hybrization between cation and anion in the compound. The density of state studies indicated existing of hybridizations among anion O 2p, cation Pb 6s/Sn 5s (special lone pair) and the Ti 3d/Zr 4d states of PZT and PSnZT compound. An indirect band gap was respectively obtained for both cubic PZT and PSnZT at the F-G and Q-G point with 3.154 eV and 2.571 eV.