Interaction of Radical Pairs Through-Bond and Through-Space: Scope and Limitations of the Point-Dipole Approximation in Electron Paramagnetic Resonance Spectroscopy

摘要

The validity of the popular point dipole approximation for interpretation of the zero-field splitting (ZFS) parameter (D-value) in EPR spectroscopy is studied. This approximation is of central importance for the determination of distances by analysis of EPR data. In this work, a detailed experimental (EPR spectroscopy and X-ray crystallography) and theoretical study for a model system (2,2’,5,5’-tetra(t-butyl)-4,4’-bis(ethoxy-carbonyl)-3,3’-bipyrrolyl-1,1’-dioxyl) was performed to understand the scope and limitations of the point dipole model in EPR spectroscopy. For this diradical, the radical-radical distance derived with the point-dipole approximation deviates significantly (by ~40%) from the results derived from the X-ray analysis. Explicit quantum chemical calculation of the D-value on the basis of B3LYP density functional calculations leads to excellent quantitative agreement with the measured D-value. The quantitative accuracy of the employed methodology was confirmed for two additional systems that have previously been experimentally characterized. We therefore analyzed the contributions to the D-value of the target system in detail. This analysis leads to insight into the reasons for the failure of the point-dipole approximation. The analysis was then extended to an in silico study of five classes of model systems. Linkers of varying length and bond saturation were introduced between the radical-carrying groups. This allows for the analysis of the distance dependence of the D-parameter as well as the through-bond and through-space spin-spin interaction. From these results we established the limitations of the point-dipole approximation. The results of this analysis demonstrate that even very modest amounts of spin delocalization can cause significant deviations from pure point-dipole behavior and consequently cause the EPR derived distances to deviate from the N-O midpoint distance by up to several Ångström. If unsaturated linkers are used, the distance dependence of D does not follow the inverse cubic behavior predicted by the point dipole model. However, for commonly-used non-aromatic nitroxide rings connected by a saturated linker, the point dipole approximation works well. Among the various point dipole variants tested in this work for delocalized spins, the most successful one is based on distributed point dipoles with spin populations derived from quantum chemical calculations. The distance dependence of the isotropic Heisenberg exchange parameter J has also been studied theoretically. The decay was found to be monoexponential with a decay constant of ~1 Å⁻¹. Thus at linker lengths between 6–8 carbon atoms between a nitroxide radical pair a switch from the strong to the weak exchange limit is predicted.