Modeling the chemical shift of lanthanide 4f electron binding energies

Lanthanides in compounds can adopt the tetravalent [Xe]4f(n-1) (like Ce4+, Pr4+, Tb4+), the trivalent [Xe]4f(n) (all lanthanides), or the divalent [Xe]4f(n+1) configuration (like Eu2+, Yb2+, Sm2+, Tm2+). The 4f-electron binding energy depends on the charge Q of the lanthanide ion and its chemical environment A. Experimental data on three environments (i.e., the bare lanthanide ions where A = vacuum, the pure lanthanide metals, and the lanthanides in aqueous solutions) are employed to determine the 4f-electron binding energies in all divalent and trivalent lanthanides. The action of the chemical environment on the 4f-electron binding energy will be represented by an effective ambient charge Q(A) = -Q at an effective distance from the lanthanide. This forms the basis of a model that relates the chemical shift of the 4f-electron binding energy in the divalent lanthanide with that in the trivalent one. Eu will be used as the lanthanide of reference, and special attention is devoted to the 4f-electron binding energy difference between Eu2+ and Eu3+. When that difference is known, the model provides the 4f-electron binding energies of all divalent and all trivalent lanthanide ions relative to the vacuum energy.