First-principles investigations of geometrical and electronic structures of Mn⁴⁺ doped A₂SiF₆ (A= K, Rb, Cs) red phosphors

The first-principle calculations of the structural and electronic properties for a series of the Mn⁴⁺ doped A₂SiF₆ (A = K, Rb, Cs) phosphors within a density functional theory are performed to investigate influence of the first cation on the crystal field strength 10Dq and energy of the Mn^{4+ 2}E→⁴A₂ red emission transition. The structural changes due to an inclusion of the Mn⁴⁺ ions into A₂SiF₆ hosts are studied in detail here. The obtained results show that the shorter Mn–F bond length leads to higher emission energy of ²E→⁴A₂ transition and 10Dq value. The emission energy for ²E→⁴A₂ transition and 10Dq parameter of the Mn⁴⁺ doped A₂SiF₆ have been estimated using different functionals, such as conventional electron-electron correlation functional, generalized gradient approximation and local density approximation, the Hubbard type correction, i.e., DFT + U method, to the Mn 3d electrons, to identify most suitable calculating settings for the studied systems.