Mechanisms of non-radiative energy transfer involving lanthanide ions revisited

In this work, the theoretical background of the Coulomb direct and exchange interactions in non-radiative energy transfer involving lanthanide ions is critically reviewed. Emphasis is given to the shielding effect produced by the filled 5s and 5p sub-shells of the lanthanide ion and the appropriate use of the so-called forced electric dipole intensity parameters of 4f–4f transitions, two aspects that have been often overlooked in the literature. An effective exchange hamiltonian, based on Mülliken-type approximations, and an expression for the resonant or quasi-resonant energy mismatch spectral overlap factor are proposed. Both cases of ion-to-ion and intramolecular energy transfer processes are discussed. Numerical estimates are compared with previous calculations, showing that order of magnitude differences appear. The analysis indicates that the donor–acceptor distance dependence of transfer rates by the exchange mechanism goes beyond the single exponential behavior adopted from Dexter’s approach.