Experimental measurement and theoretical assessment of fast lanthanide electronic relaxation in solution with four series of isostructural complexes.

The rates of longitudinal relaxation for ligand nuclei in four isostructural series of lanthanide(III) complexes have been measured by solution state NMR at 295 K at five magnetic fields in the range 4.7-16.5 T. The electronic relaxation time T(le) is a function of both the lanthanide ion and the local ligand field. It needs to be considered when relaxation probes for magnetic resonance applications are devised because it affects the nuclear relaxation, especially over the field range 0.5 to 4.7 T. Analysis of the data, based on Bloch-Redfield-Wangsness theory describing the paramagnetic enhancement of the nuclear relaxation rate has allowed reliable estimates of electronic relaxation times, T(1e), to be obtained using global minimization methods. Values were found in the range 0.10-0.63 ps, consistent with fluctuations in the transient ligand field induced by solvent collision. A refined theoretical model for lanthanide electronic relaxation beyond the Redfield approximation is introduced, which accounts for the magnitude of the ligand field coefficients of order 2, 4, and 6 and their relative contributions to the rate 1/T(le). Despite the considerable variation of these contributions with the nature of the lanthanide ion and its fluctuating ligand field, the theory explains the modest change of measured T(le) values and their remarkable statistical ordering across the lanthanide series. Both experiment and theory indicate that complexes of terbium and dysprosium should most efficiently promote paramagnetic enhancement of the rate of nuclear relaxation.