Theoretical analysis of energy transfer between transition metals and lanthanides in heterometallic complexes
energy transfer, lanthanides, transition metals, d-f heterometallic complexes
There is a growing interest in alternatives to lanthanide ions (Ln3+) luminescence sensitizing chromophores for in vivo usage, mainly in the optical biological windows. Transition metals (M) are good candidates as chromophores as they have high absorption rates and emission bands covering a wide range of visible to near-infrared spectrum. However, despite the importance of theoretical models for the development of more efficient M-Ln3+ complexes, few works have been devoted efforts to elucidating the energy transfer process (ET) between the M and Ln3+ ions. In this context, this work aims to adapt and apply the intramolecular energy transfer theories developed by Malta and collaborators to treat ET between M–Ln3+ in heterometallic complexes. As an example, the new model can estimate the ET rates between Cr3+ and Ln3+ ions. The work also aims to verify whether the ET model for isotropic exchange interaction can be used between the M and Ln3+ ions, by investigating the orbital overlap between the valence subshells of the transition metal and the 4f subshell of the Ln3+ ions. DFT-based calculations of overlap integrals associated with the diatomic-like pairs M-Ln3+ are presented. Parameters such as dipole strength (SD) and spectral overlap factor (F) were calculated from the spectroscopic data available in the literature for the studied data and the theoretical intensity parameters (Ωλ) were calculated with the JOYSpectra program. The estimated values for the ET rates with the proposed model were compared with the experimental results available for several complexes M-Ln3+, such as containing Cr3+ and Ln3+ ions. The results showed that the exchange interaction is negligible for the typical intermetallic distances (> 5 Å) in M-Ln3+ complexes. On the other hand, the results for theoretical estimates of ET, considering the dipole-dipole and dipole-multipole mechanisms, in general, are in agreement with the experimental data available for the studied cases, mainly in situations where the donor and acceptor states are resonant. Under low resonance conditions, such as the Cr-Yb case, the models were extended to consider phonon assistance in ET. The fit of the model to the experimental data was obtained for Huang-Rhys factor values within the typical ranges expected for lanthanides and for the Cr3+ ion. At the present stage, the proposed model can be useful to predict and explain photophysical properties guided by the energy transfer between the transition metal and the Ln3+ ion.