An approximate method for exploring nonradiative decay pathways from highly excited states of lanthanide complexes: application to luminescent cerium complexes

The exploration of minimum energy crossing points (MEXs) between potential energy surfaces (PESs) is essential for understanding nonradiative decay mechanisms and plays a key role in the design of photofunctional materials. In lanthanide (Ln(III)) complexes, however, the presence of open-shell 4f(N) electrons leads to quasi-degenerate electronic states, making MEX searches particularly challenging. To describe the PESs of 4f-5d or charge-transfer excited states (i.e., 4f(N-1)X excited states) of Ln(III) complexes, we propose a new approximation, the ion energy shift (IES) method. In this approach, the 4f(N-1)X excited state is represented using density functional theory (DFT) with the large-core relativistic effective core potential (RECP) for Ln(IV), which has a higher formal charge than the actual ion (Ln(III)), and the PES is shifted to reproduce the target excitation energy. In this study, we validate the IES method against the multiconfigurational wavefunction results and apply it to elucidate the origin of the different excited-state lifetimes of hydrated Ce(III) complexes with and without coordination of a carboxylate ligand.