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The results of first-principles calculations of the structural, electronic, elastic, vibrational, dielectric and optical properties, as well as the Raman and infrared (IR) spectra, of potassium hexafluorosilicate (K2SiF6; KSF) crystal are discussed. KSF doped with manganese atoms (KSF:Mn4+) is known for its ability to function as a phosphor in white LED applications due to the efficient red emission from Mn⁴⁺ activator ions. The simulations were performed using the CRYSTAL23 computer code within the linear combination of atomic orbitals (LCAO) approximation of the density functional theory (DFT). For the study of KSF, we have applied and compared several DFT functionals (with emphasis on hybrid functionals) in combination with Gaussian-type basis sets. In order to determine the optimal combination for computation, two types of basis sets and four different functionals (three advanced hybrid—B3LYP, B1WC, and PBE0—and one LDA functional) were used, and the obtained results were compared with available experimental data. For the selected basis set and functional, the above-mentioned properties of KSF were calculated. In particular, the B1WC functional provides us with a band gap of 9.73 eV. The dependencies of structural, electronic and elastic parameters, as well as the Debye temperature, on external pressure (0–20 GPa) were also evaluated and compared with previous calculations. A comprehensive analysis of vibrational properties was performed for the first time, and the influence of isotopic substitution on the vibrational frequencies was analyzed. IR and Raman spectra were simulated, and the calculated Raman spectrum is in excellent agreement with the experimental one. [ABSTRACT FROM AUTHOR]