Relating static shifts in the ESR spectra of a nitroxide radical in solution to second order perturbation theory

Using perturbation theory, expressions were derived for the six energy levels resulting from the interaction between the spin (1/2 or -1/2) of the unpaired electron and the nuclear spin (1, 0, or - 1) of the nitrogen nucleus in a nitroxide radical in solution. Allowed transitions between these energy levels led to expressions for the dependence of the positions of the three EPR lines and in turn the ratio, r, of the high-field splitting to the low-field splitting on the applied magnetic field H. An r slightly greater than 1 that decreases, initially drastically then gradually, to approach unity as H increases is predicted. Experimental r values for the nitroxide spin probe, perdeuterated 4-oxo-2,2,6,6-tetramethylpiperidene-1-oxy (PD-Tempone) in toluene at 295 K were obtained at four microwave frequencies; 1.12 (L-band), 3.98 (S-band), 9.54 (X-band), and 34.2 (Q-band) GHz. The experimental r values were found to be higher than the theoretical r values (all greater than 1) but followed the same trend. The higher experimental r values are possibly a consequence of the dynamic frequency shift.