All previously published nonrelativistic and scalar relativistic electronic structure calculations of platinum hexafluoride predict a paramagnetic distorted octahedral molecule with a triplet ground state. The four-component spin-free method also predicts a distorted octahedral molecule with longest axial Pt-F bond due to the Jahn-Teller effect. However, four-component Dirac molecular Hartree-Fock and density-functional theory (DFT) and the two-component zeroth-order regular approach (ZORA) including spin-orbit interaction calculations predict a diamagnetic octahedral molecule with a closed-shell ground state, which is in accordance with the observation of the $^{\text{19}}\text{F}$ and $^{\text{195}}\text{P}\text{t}$ high-resolution nuclear magnetic resonance spectra and its undisturbed ir and Raman spectra of ${\text{PtF}}_{6}$. The excitation energies involving the $d\text{\ensuremath{-}}d$ transitions are well calculated by performing time-dependent DFT calculations using the two-component ZORA method. Thus, its octahedral molecular structure with a closed-shell ground state is stabilized by the effect of a spin-orbit interaction.