Collection of Czechoslovak Chemical Communications - digital archive 

Abstract

A simple numerical method for calculating NMR spectral line shapes resulting from a Gaussian line by a partial narrowing due to a motion with the exponential spectral autocorrelation function of the form exp (-|τ|/τ_c) was developed. It was found that the partially narrowed line is narrower not only than the parent Gaussian line with the second moment of ω_p² but also than the Lorentzian line with the half-width of 2ω_p²τ_c obtained from the extreme narrowing approximation. The central intensity increase compared with the closer of these two lines is less than 50.2%. Asymptotic developments for large values of ω - ω₀ and for large values of ω_pτ_c were derived. Two-term approximation applied to the extreme narrowing case led to a very simple modification of the Lorentzian line having the correct second moment ω_p². Analysis of this modified Lorentzian line showed that attempts to estimate ω_p² from truncated second moments of Lorentzian lines without knowledge of τ_c are hopeless. The case of the polyexponential spectral autocorrelation function with all but one correlation times fast enough to allow for the extreme narrowing, modelling the case of an anisotropic motion, is also considered.

Keywords: NMR spectroscopy; NMR line shape calculation; Partial motional narrowing of Gaussian line; Exponential spectral autocorrelation function; Second moment; Anisotropic motion.

References: 11 live references.