In this paper we calculate the low energy spin-orbit multiplet terms of trivalent lanthanide cations Ce3+ to Yb3+, except for Gd3+, with three different RECPs, including the spin-orbit effect explicitly, to assess their reliability. Although there is fairly good agreement with experiment for the ground LS multiplet splittings, implying the accuracy of the spin-orbit Hamiltonian, the agreement is less for the higher LS terms. The source of the error was found to be the significant semi-core correlations in the 4d, 5s, and 5p shells, which have very strong effects on the spin-free excitation energies. The degree of the intermediate coupling is also studied and related to the deviation from the Landé interval rule. The differences between the intermediate coupling method and the fully variational spin-orbit CI method are numerically analyzed.
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