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

Abstract

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.

Transient versus Static Electron Spin Relaxation in Mn2+ Complexes Relevant as MRI Contrast Agents

“…Thus, the lower electric charge and weaker metal–donor electrostatic interactions of Mn 2+ complexes compared to those for Gd 3+ analogues is likely responsible for the shorter τ c values of the former. Recent measurements of the longitudinal relaxation rates of ligand nuclei around complexed Ln 3+ ions and previous theoretical discussion about these systems indicated that the vibrational correlation time gives a lower bound to the longitudinal electronic relaxation time values, which should not be significantly less than the inverse of the solvent collision frequency (∼0.1 ps). , …”

“…Recent measurements of the longitudinal relaxation rates of ligand nuclei around complexed Ln 3+ ions and previous theoretical discussion about these systems indicated that the vibrational correlation time gives a lower bound to the longitudinal electronic relaxation time values, which should not be significantly less than the inverse of the solvent collision frequency (∼0.1 ps). 75,76 The transient ZFS (Δ T ) was estimated from the spread of the Δ values along the trajectories obtained with ADMP simulations (Figure 6). The ZFS energy calculated for [Mn(MeNO2A)(H 2 O)]•2H 2 O shows important fluctuations along the trajectory of our MD simulations, whereas it fluctuates to a lesser extent for [Mn(EDTA)(H 2 O)] 2− •2H 2 O.…”

Water Exchange on [Ln(DO3A)(H2O)2] and [Ln(DTTA–Me)(H2O)2]− Studied by Variable Temperature, Pressure, and Magnetic Field NMR

“…The correlation time for dipolar relaxation is governed by the electron spin relaxation time T e which is, for lanthanides (except Gd 3+ ), much shorter than τ m and τ R , the rotational correlation time for the reorientation of the electron spin–proton vector …”

“…The correlation time for dipolar relaxation is governed by the electron spin relaxation time T e which is, for lanthanides (except Gd 3+ ), much shorter than τ m and τ R , the rotational correlation time for the reorientation of the electron spin− proton vector. 25 The outer sphere relaxivity refers to relaxation enhancement due to solvent molecules in the second coordination sphere and bulk solvent and is given as the sum of the dipolar and Curie relaxations. The dipole−dipole relaxation is described by eq 7, developed by Freed 26,27 and Ayant.…”

MRICEST at 1T with large µeffLn3+ complexes T m3+‐HPDO3A: An efficient MRI pH reporter

“…, although temperature‐dependent changes in viscosity of biological matrixes, and thus rotational correlation times, are nontrivial. Values of T 1e for the considered lanthanides are in the order of 10 −13 s, just above the solvent‐complex collision boundary . Because τ r >> T 1e for the studied ions, the first term of Eq.…”