Theoretical Determination of Energy Transfer Processes and Influence of Symmetry in Lanthanide(III) Complexes: Methodological Considerations

This work presents a theoretical protocol to analyze the symmetry effect on the allowed character of the transitions and to estimate the probability of energy transfer in lanthanide(III) complexes. For this purpose, a complete study was performed based on the multireference CASSCF/PT2 technique along with TDDFT, to build the energy level diagrams and determine the spectral overlap integrals, respectively. This approach was applied on a series of LnIII complexes, viz. [LnCl₃(DMF)₂(Dpq)]/[Ln(NO₃)₃(DMF)₂(Dpq)], where Ln = Sm^III, Tb^III, Er^III/Eu^III, Nd^III and dpq = dipyridoquinoxaline, synthesized and characterized by Patra et al. (Dalton Trans. 2015, 44 (46), 19844-19855; CrystEngComm 2016, 18 (23), 4313-4322; Inorg. Chim. Acta 2016, 451, 73-81). A fragmentation scheme was applied where both the ligand and the lanthanide fragments were treated separately but at the same level of theory. The symmetry analysis only partially reproduced the expected results, and a more detailed analysis of the crystal field became necessary. On the other hand, the most probable energy transfer pathways that take place in the complexes were elucidated from the energy gaps between the ligand-localized triplet state and the emitting levels of the lanthanide fragments. These gaps, which are related to the energy transfer rate, properly reproduced the trend reported experimentally for the best and worst yields. Finally, the spectral overlap integral was calculated from the emission spectra of the dpq ligand and the absorption spectra of the lanthanide fragment. The obtained values are in good agreement with the quantum yields calculated for the systems. The most remarkable aspect of this protocol was its ability to explain the emission and nonemission of the studied compounds.