Creation of 4fn-4fn-15d1 Transition Energy Diagram of Trivalent Lanthanide Ions in Fluorides Based on First-Principles Calculations

Abstract

The theoretical prediction of the 4fn-4fn-15d1 transition energies of lanthanides in crystals is an important issue in the development of novel luminescent materials such as solid-state lasers or phosphors. In our previous work, the first-principles calculations of the entire multiplet structures of lanthanide (Ln) ions in LiYF4 (YLF) corresponding to 4fn and 4fn-15d1 configurations were performed using the relativistic discrete variational multi-electron (DVME) method [1]. However, the lowest 4fn-4fn-15d1transition energy was overestimated for light lanthanides while it was underestimated for heavy lanthanides. In this work, in order to improve the accuracy of the theoretical transition energy, a correction based on the molecular orbital (MO) calculation in the Slater’s transition state was introduced. The LnF8 clusters were constructed based on the crystal structures of YLF and CaF2. The fully-relativistic MO calculations were performed using the relativistic DV-Xα code. The multiplet calculations were performed using the relativistic DVME code. The Slater determinants corresponding to 4fn and 4fn-15d1 configurations were constructed from the four-component relativistic MOs and used as the basis functions to diagonalize the relativistic many-electron Hamiltonian. In order to correct the errors in the transition energy, MO calculations in the Slater’s transition state where a half electron was excited from the Ln 4f level to the Ln 5d level were also performed. A constant correction term was added to the diagonal matrix element of the many-electron Hamiltonian for 4fn-15d1 configuration so that the 4fn -4fn-15d1transition energy is consistent with the 4f-5d transition energy obtained by the MO calculation in the Slater’s transition state. The diagrams representing the lowest 4fn-4fn-15d1transition energies of trivalent lanthanide ions in YLF calculated with and without the above correction are shown in Fig. 1. The overestimation in the light lanthanides and the underestimation in the heavy lanthanides are significantly reduced by the correction and the theoretical transition energies approached to the experimental values in the literature [2-5].