A Simple Numerical Method for Calculating Gaussian NMR Spectral Line Shapes Partially Narrowed Due to a Motion with the Exponential Spectral Autocorrelation Function

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Title:A Simple Numerical Method for Calculating Gaussian NMR Spectral Line Shapes Partially Narrowed Due to a Motion with the Exponential Spectral Autocorrelation Function
Creators:
Jakeš, Jaromír
Journal or Publication Title:
Collection of Czechoslovak Chemical Communications, 67, 4, pp. 405-428
Uncontrolled Keywords:NMR line shape calculation, Partial motional narrowing of Gaussian line, Exponential spectral autocorrelation function, Anisotropic motion, Second moment, NMR spectroscopy

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<sub>c</sub>) 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<sub>p</sub><sup>2</sup> but also than the Lorentzian line with the half-width of 2ω<sub>p</sub><sup>2</sup>τ<sub>c</sub> 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 - ω<sub>0</sub> and for large values of ω<sub>p</sub>τ<sub>c</sub> 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<sub>p</sub><sup>2</sup>. Analysis of this modified Lorentzian line showed that attempts to estimate ω<sub>p</sub><sup>2</sup> from truncated second moments of Lorentzian lines without knowledge of τ<sub>c</sub> 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. <p>

Title:A Simple Numerical Method for Calculating Gaussian NMR Spectral Line Shapes Partially Narrowed Due to a Motion with the Exponential Spectral Autocorrelation Function
Creators:
Jakeš, Jaromír
Uncontrolled Keywords:NMR line shape calculation, Partial motional narrowing of Gaussian line, Exponential spectral autocorrelation function, Anisotropic motion, Second moment, NMR spectroscopy
Divisions:Life and Chemical Sciences > Institute of Organic Chemistry and Biochemistry > Collection of Czechoslovak Chemical Communications
Journal or Publication Title:Collection of Czechoslovak Chemical Communications
Volume:67
Number:4
Page Range:pp. 405-428
ISSN:0010-0765
E-ISSN:1212-6950
Publisher:Institute of Organic Chemistry and Biochemistry
Related URLs:
URLURL Type
http://dx.doi.org/10.1135/cccc20020405UNSPECIFIED
ID Code:1931
Item Type:Article
Deposited On:06 Feb 2009 17:14
Last Modified:06 Feb 2009 16:14

Citation

Jakeš, Jaromír (2002) A Simple Numerical Method for Calculating Gaussian NMR Spectral Line Shapes Partially Narrowed Due to a Motion with the Exponential Spectral Autocorrelation Function. Collection of Czechoslovak Chemical Communications, 67 (4). pp. 405-428. ISSN 0010-0765

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