Theoretical Study on the f−f Transition Intensities of Lanthanide Trihalide Systems

Abstract

The photoabsorption intensities of intra-4f(N) transitions (f-f transitions) in lanthanide systems have been extensively studied with the semiempirical Judd-Ofelt theory. The oscillator strengths of most f-f transitions are insensitive to a change of surrounding environment because 4f electrons are shielded by closed-shell 5s and 5p electrons from outside. However, there are some exceptional transitions, so-called hypersensitive transitions, whose intensities are very sensitive to a change of surrounding environment, and the reason for this hypersensitivity has not been clarified. In this study, we calculated the oscillator strengths of lanthanide trihalides (LnX(3); Ln = Pr, Tm; X = Br, I) with the multireference spin-orbit configuration interaction method and obtained reasonably accurate values. To clarify the cause of hypersensitivity, we examined various possible effects on the oscillator strengths, such as molecular vibration, f-d mixing, ligand to metal charge transfer (LMCT), and intraligand excitation, and concluded that the effect of molecular vibration is very small and that the oscillator strengths of most f-f transitions including hypersensitive transitions arise from both the LMCT and dynamic-coupled intraligand excitations through their configuration mixings with the dominant configurations of 4f(N).

An ab initio study on the f-f hypersensitive transition intensities of lanthanide tribromide molecules

“…[29,30]. It should be noted that the oscillator strengths of PrBr 3 and TmBr 3 in Table 1 are larger than our previous values [16], which were underestimated by the previous smaller basis set for Br, with which a small polarizability a(Br À ) = 12 a.u. was produced.…”

“…With these less diffuse basis sets, the excitation energies were increased by 10-100 cm À1 , whose magnitudes were smaller than typical crystal field splittings, and the oscillator strengths were reduced by 10-20%, which still keeps sufficient accuracy for the analysis of the mechanism of f-f intensities. The bond lengths between Ln and Br in the D 3h structure, the effective nuclear charges Z eff , and molecular orbitals (MOs) were determined as in our previous work [16]. For the SOCI calculations, the configuration state functions (CSFs) with all the possible spin multiplicities derived from the 4f N reference CSFs were generated in the first-order CI scheme, in which all the one-electron excitations from/to the reference CSFs were generated.…”

“…For the SOCI calculations, the configuration state functions (CSFs) with all the possible spin multiplicities derived from the 4f N reference CSFs were generated in the first-order CI scheme, in which all the one-electron excitations from/to the reference CSFs were generated. The doubly occupied orbital spaces consisting of 5s 2 5p 6 of Ln 3+ and 4s 2 4p 6 of Br À , and the external space consisting of all the SCF virtual orbitals were fully considered as before [16]. We carried out the 'standard SOCI' [17] calculations where the total Hamiltonian including the SO term was diagonalized in the basis of all the CSFs for PrBr 3 , EuBr 3 , TbBr 3 and TmBr 3 .…”

“…(2). The polarizability of Br À was calculated with the corresponding first-order SOCI method and the values of h4fjr 2 j4fi 2 were calculated with the same state-averaged SCF method as before [16] with the more diffuse MCP basis set [20-23] mentioned above. Table 1 shows the excitation energies and oscillator strengths of hypersensitive transitions of LnBr 3 .…”

“…Though there were several ab initio studies concerning the structures of LnX 3 [12][13][14][15], such calculations for the oscillator strengths of f-f transitions had never been carried out. In a recent theoretical work on PrX 3 and TmX 3 , we have suggested that intra-ligand excitation configurations make a dominant contribution to their intensities, but ligand-to-metal charge transfer (LMCT) configurations are also mixed into the 4f N states and cannot be disregarded [16]. If the oscillator strengths can be explained only by the DC model, the JO intensity parameters s k (ab), which can be extracted from ab initio data in terms of Eq.…”