# An Approximate Method for Exploring Nonradiative Decay Pathways From Highly Excited States of Lanthanide Complexes: Application to Luminescent Cerium Complexes

## TL;DR

A new method is introduced to study nonradiative decay in lanthanide complexes, helping to understand their luminescent properties.

## Contribution

The ion energy shift method allows efficient exploration of excited-state pathways in lanthanide complexes.

## Key findings

- The IES method is validated against multiconfigurational wavefunction results.
- The method elucidates differences in excited-state lifetimes of Ce3+ complexes with and without carboxylate ligands.

## Abstract

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 (Ln3+) 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−1X excited states) of Ln3+ complexes, we propose a new approximation, the ion energy shift (IES) method. In this approach, the 4f
N−1X excited state is represented using density functional theory (DFT) with the large‐core relativistic effective core potential (RECP) for Ln4+, which has a higher formal charge than the actual ion (Ln3+), 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 Ce3+ complexes with and without coordination of a carboxylate ligand.

We present the ion energy shift method, a new approach that enables the optimization of critical structures on and between the ground state and the 4f
N−1X excited state, involving either 4f–5d or charge‐transfer excited states in lanthanide complexes.