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 Ln(3+) 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 Ln(3+) 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 mainly by the magnitude of the transient ligand-field, and not by its particular expression. The range of expected values of this ligand-field together with the lower limit of relaxation time enforced by the values of the vibration-distortion correlation time in liquids give rise to effective electronic relaxation times which are in satisfactory overall agreement with the experimental data. In particular, these considerations explain why the electronic relaxation times vary little with the coordinating ligand and are practically independent of the external field magnitude.