A moment method for determining isotropic g values from powder EPR spectra

Abstract

It is shown that the first moment of a powder EPR absorption spectrum calculated about g iso (=(1/3) Tr g) is zero, subject to certain approximations. This permits characterization of an unknown paramagnetic species by means of the rotationally invariant quantity g iso. The crossover of the first derivative, which has often been used to characterize a sample, is unreliable since it is not a spectroscopic invariant. If two of the three g values of a g matrix are known from the positions of high and low field extrema, this moment theorem permits determination of the third. Errors arising from the approximations in the proof are analyzed and found to be small. For a nitroxide spin label, the moment analysis yields a value of g iso that differs from its true value by less than 0.0001, whereas for Cu 2+ and Co 2+, which have larger anisotropies, the differences are somewhat larger, viz., ∼0.002 and 0.001, respectively.