Quantitative interpretation of the very fast electronic relaxation of most Ln3+ ions in dissolved complexes

In a reference frame rigidly bound to the complex, we consider two Hamiltonians possibly at the origin of the very fast electronic relaxation of the paramagnetic lanthanide Ln3+ ions (Ln = Ce to Nd, Tb to Yb), namely the mean (static) ligand-field Hamiltonian and the transient ligand-field Hamiltonian. In the laboratory frame, the bombardment of the complex by solvent molecules causes its Brownian rotation and its vibration-distorsion dynamics governing the fluctuations of the static and transient terms, respectively. These fluctuations are at the origin of electronic relaxation. The electronic relaxation of a Ln3+ ion is defined by the decays of the time correlation functions (TCFs) of the longitudinal and transverse components of the total angular momentum J of its ground multiplet. The Brownian rotation of the complex and its vibration-distorsion dynamics are simulated by random walks, which enable us to compute the TCFs from first principles. It is shown that the electronic relaxation is governed main...