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.

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Site-directed spin labeling (SDSL) and electron paramagnetic resonance (EPR) spectroscopy offer accurate, sensitive tools for the characterization of structure and function of macromolecules and their assemblies. A new rigid spin label, spirocyclohexyl nitroxide α-amino acid and its N-(9-fluorenylmethoxycarbonyl) (Fmoc) derivative, has been synthesized that exhibit slow enough spin echo dephasing to permit accurate distance measurements by pulse EPR at temperatures up to 125 K in 1:1 water:glycerol and at higher temperatures in matrices with higher glass transition temperatures. Distance measurements in the liquid nitrogen temperature range are less expensive than those that require liquid helium, which will greatly facilitate applications of pulsed EPR to the study of structure and conformation for peptides and proteins.

To determine the impact of electron-electron spin-spin interactions on electron spin relaxation rates, 1/T1 and 1/Tm were measured for nitroxide monoradical, diradical, and tetraradical derivatives of 1,3-alternate calix[4]arenes, for two pegylated high-spin nitroxide diradicals, and for an azine-linked nitroxide diradical. The synthesis and characterization by SQUID (superconducting quantum interference device) magnetometry of one of the high-spin diradicals, in which nitroxides are conformationally constrained to be coplanar with the m-phenylene unit, is reported. The interspin distances ranged from about 5-9 A, and the magnitude of the exchange interaction ranged from >150 to >0.1 K. 1/T1 and 1/Tm were measured by long-pulse saturation recovery, three-pulse inversion recovery, and two-pulse echo decay at X-band (9.5 GHz) and Q-band (35 GHz). For a diradical with interspin distance about 9 A, relaxation rates were only slightly faster than for a monoradical with analogous structure. For interspin distances of about 5-6 A, relaxation rates in glassy solvents up to 300 K increased in the order monoradical < diradical < tetraradical. Modulation of electron-electron interaction enhanced relaxation via the direct, Raman, and local mode processes. The largest differences in 1/T1 were observed below 10 K, where the direct process dominates. For the three diradicals with comparable magnitude of dipolar interaction, 1/Tm and 1/T1 were faster for the molecules with more flexible structures. Relaxation rates were faster in the less rigid low-polarity sucrose octaacetate glass than in the more rigid 4:1 toluene/chloroform or in hydrogen-bonded glycerol glasses, which highlights the impact of motion on relaxation.