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

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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 \rightarrow 4T2 and 4A2 \rightarrow 4T\text{1a transition energies, while such corrections are not necessary for the prediction of the 4A2 \rightarrow 2E transition energy. The cluster size dependence of the multiplet energies is small. However, the 4A2 \rightarrow 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.
2012-02-25