Abstract: | A simple expression is derived to compute the total Gaussian linewidth of a Voigt line that is broadened by sinusoidal magnetic-field modulation as follows: ΔHGpp(Hm)2= ΔHGpp(0)2+ κ2H2m, where ΔHGpp(Hm) is the Gaussian linewidth observed with an modulation amplitudeHm/2 and ΔHGpp(0) is the Gaussian linewidth in the limit of zero modulation. The field modulation contributes an additional Gaussian broadening of κHm, where κ is a constant, which adds in quadrature to ΔHGpp(0) to give the total Gaussian linewidth. Denoting the overall linewidth of the Voigt line in the absence of modulation broadening by ΔH0pp(0), it is shown, both by analytical means and by spectral simulation, that the constant κ is equal to 1/2 in the limit ofHm ΔH0pp(0); however, using values ofHmas large as ΔH0pp(0) leads to only minor departures from κ = 1/2. The formulation is valid both for Lorentzian and Voigt lines and is tested for 2,2,5,5-tetramethylpyrrolidin-1-oxyl-3-carboxylic acid (3-carboxy proxyl) in CCl4and in aqueous buffer. This spin probe was studied because the proxyl group is the only major spin-probe moiety whose Gaussian linewidth had not been characterized in the literature. For 3-carboxy proxyl, it is found that ΔHGpp(0) = 1.04 ± 0.01 G independent of solvent polarity. Precision values of the14N hyperfine coupling constant for 3-carboxy proxyl at 9.5°C are as follows: 14.128 ± 0.001 G in CCl4and 16.230 ± 0.002 G in aqueous buffer. The temperature dependence of ΔHGpp(0) and the14N hyperfine coupling constant are reported as empirical equations. Results of the present work taken together with previously published data permits accurate correction for the effects of inhomogeneous broadening due to unresolved hyperfine structure and modulation broadening for the majority of spin probes in common use. |