Comparative Study of Multiplet Structures of Mn⁴⁺ in K₂SiF₆, K₂GeF₆, and K₂TiF₆ Based on First-Principles Configuration–Interaction Calculations

Abstract

We performed first-principles configuration–interaction calculations of multiplet energies for Mn4+ in K2SiF6, K2GeF6, and K2TiF6 crystals. The results indicate that corrections based on a single-electron calculation are effective for the prediction of 4A2 → 4T2 and 4A2 → 4T1a transition energies, while such corrections are not necessary for the prediction of the 4A2 → 2E transition energy. The cluster size dependence of the multiplet energies is small. However, the 4A2 → 2E transition energy is slightly improved by using larger clusters including K ions. The theoretical multiplet energies are improved further by considering the lattice relaxation effect. As a result, the characteristic multiplet energy shifts depending on the host crystal are well reproduced without using any empirical parameters. Although K2GeF6 and K2TiF6 have lower symmetry than K2SiF6, the results indicate that the variation of the multiplet energy is mainly determined by the Mn–F bond length.

Luminescent Behavior of the K2SiF6:Mn4+Red Phosphor at High Fluxes and at the Microscopic Level

“…9,18 The multiplet structure originating from the 3d 3 configuration has been investigated in the framework of crystal field theory 16 and by coupling single-particle orbitals, obtained from Hartree-Fock-Slater calculations. 19 Both investigations started from the octahedral symmetry of the Si 4+ site of the K 2 SiF 6 host. The vibronic fine structure of the Mn 4+ emission and excitation spectra has been described in detail.…”

Multiplet Energy Level Diagrams for Cr3+and Mn4+in Oxides with OhSite Symmetry Based on First-Principles Calculations

“…9 Therefore, in order to develop oxide phosphors activated with Mn 4+ for white LED, guidelines to design phosphors with shorter emission wave length of Mn 4+ are necessary. Recently we performed first-principles calculation of entire multiplet levels of Mn 4+ in various fluorides 10,11 and oxides, [12][13][14] and investigated the effect of bond length, symmetry, covalency, electron correlation, lattice relaxation on the multiplet energy levels quantitatively. However, in order to clarify the relationship between the local structure and the optical properties, construction of multiplet energy diagrams based on systematic calculation for clusters with gradually changed structures would be useful.…”

Review—The K2SiF6:Mn4+ (PFS/KSF) Phosphor

“…Based on First-principles calculations, Novita and Ogasawara show that the Mn-F bond distance (not M 4+ -F bond distance) increases in the order K 2 SiF 6 -K 2 GeF 6 -K 2 TiF 6, irrespective of the presence or absence of lattice relaxation effect. 29 Therefore, the crystal field stabilization energy acquired by the Mn 4+ ion on the M 4+ site in K 2 MF 6 should increase in the order, K 2 TiF 6 -K 2 GeF 6 -K 2 SiF 6 . According to the Paulusz data, this is also the order of increasing T 50 .…”