An Analytical Derivation of a Popular Approximation of the Voigt Function for Quantification of NMR Spectra

Abstract

The approximation of the Voigt line shape by the linear summation of Lorentzian and Gaussian line shapes of equal width is well documented and has proved to be a useful function for modeling in vivo1H NMR spectra. We show that the error in determining peak areas is less than 0.72% over a range of simulated Voigt line shapes. Previous work has concentrated on empirical analysis of the Voigt function, yielding accurate expressions for recovering the intrinsic Lorentzian component of simulated line shapes. In this work, an analytical approach to the approximation is presented which is valid for the range of Voigt line shapes in which either the Lorentzian or Gaussian component is dominant. With an empirical analysis of the approximation, the direct recovery of T2 values from simulated line shapes is also discussed.