We obtain the multiplet energies for several rare earth (RE) ions by
ab initio molecular orbital calculations including the spin-orbit interaction working on 4
f electrons of RE. Because of a limitation of the ability of computations, the lower lying multiplet energies for Ce
3+, Nd
3+, Eu
3+, Gd
3+ and Er
3+ ions were calculated in this report. For the excitations of 4
f electrons, the spin multiplicity in the multiplet terms for 4
f n electrons does not hold (not always ΔS=0) both in initial and final states by mixing different
S states upon spin-orbit interaction. We estimated the possibility of the transitions for the multiplet terms for RE ions with use of the obtained electronic spin states of the 4
f electrons.
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