This research work conveys the computationally investigation of Hafnium (IV) oxide and its doped crystals by Si, Ge and Sn atom replacing on the oxygen atom in HfO2. As Hafnium (IV) oxide has been used in power-electronics devices of MOSFETs and electronics as RRAM due to wide band gap which makes a vast problems creating high resistance. Regarding this case, the Hafnium (IV) oxide has selected and inputs how the band gap has reduced after doping the large surface area of atoms, such as Si, Ge and Sn. The lattice parameters and bandgaps were calculated with the Perdew-Burke-Ernzerhof (PBE), Revised Perdew-Burke-Ernzerhof (RPBE), Perdew Wang (PW91), Wu-Cohen (WC), and Perdew-BurkeErnzerhof for solids (PBEsol) non-local functionals of the generalized gradient approximations (GAA). The Perdew-Burke-Ernzerhof (PBE) functional provided better result which is similar to the reference value of mother crystal, HfO2. This first principle method in view of density functional theory (DFT) focuses the structural geometry, electronic structure and optical properties employing conventional calculations pertaining to HfO2 executing the computational tools of the CASTAP code from material studio 8.0. The band gap was recorded by 4.340 eV, 2.033 eV, 1.686 eV and 3.210 eV for HfO2, Hf0.88Si0.12O2 Hf0.88Ge0.12O2 and Hf0.88Sn0.12O2 crystals through the Generalized Gradient Approximation (GGA) with Perdew Burke Ernzerhof (PBE). Secondly, it had also justified doing further investigations by GGA with RPBE, GGA with PW91, GGA with WC and GGA with PBESOL, the band gap for HfO2, Hf0.88Si0.12O2, Hf0.88Ge0.12O2 and Hf0.88Sn0.12O2 were at 4.427 eV, 2.093 eV, 1.744 eV, and 3.262 eV, respectively using GGA with WC, 4.333 eV, 2.032 eV, 1.675 eV and 3.172 eV, respectively using GGA with PW91, 4.252 eV, 2.002 eV, 1.632eV and 3.086 eV, respectively using GGA with WC 4.245 eV, 2.001 eV, 1.629 eV, and 3.076 eV, respectively using GGA with PBESOL. Moreover the DFT and PDOS were simulated for evaluating the nature of 6s2, 5p6, 4f14, 5d2 orbital for a Hf atom, 3s2, 2p6 orbital for Si atom, and 4s2, 3p6, 3d10 orbital for Ge atom, 4d10, 5s2, 5p2 for Sn atom and 2s and 2p orbital for O atom of Hf0.88Ge0.12O2 and Hf0.88Sn0.12O2 crystals. The optical properties, for instance, absorption, reflection, refractive index, conductivity, dielectric function, loss function, electrostatic potential map and aquatic toxicity were calculated.