Peak Shapes in NMR Spectroscopy

by Stanislav Sykora (Extra Byte, Castano Primo, Italy)
and Carlos Cobas (Mestrelab Research, Santiago de Compostela, Spain)

at the meeting MMCE - Magnetic Moments in Central Europe,
Otocec (Slovenia), February 11-15, 2009.

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Presentation Abstract

When analyzing liquid-state NMR spectra, we use terms such as lines, peaks, and multiplets, while those who simulate spectra of coupled systems are more likely to speak about transitions. All these semantic differences are somewhat vague and intuitive, but they have real roots which any automatic spectral evaluation software should at some point acknowledge and cope with. Since these terms are based on decades of experience, a modern object-oriented software should better respect them and match them with corresponding software constructs.

This, however, turns out to be anything but trivial.

Ideally, under the conditions of fast rotational narrowing, NMR transition probabilities should exhibit the venerated Lorentzian line shapes which can be normalized and scaled to L(ν) = 1/(1-iν). In practice, however, the Lorentzian shape is a rarity.
The principal reasons are:

  • Magnetic field inhomogeneity (imperfect shimming)
  • Magnetic field noise (see this article)
  • Sample spinning
  • Sample temperature gradients
  • FID weighting before Fourier Transform (FT)
  • Discrete Fourier Transform (DFT) artifacts
  • Overlap of transitions into unresolved peaks in coupled spin systems
  • Spectral overcrowding in chemically complex systems
  • Molecular dynamics effects (chemical exchange, limited mobility)

We will briefly discuss these peak-shape distortion sources, their characteristics, their impact on different types of NMR spectra, and the problems they cause when trying to automatically extract meaningful digital information from a spectrum, or fit a spectrum to a particular molecular model. It will be shown, in particular, that even in molecules considered 'small' by today's standards, the overlap (enveloping) of enormous numbers of theoretical transitions (millions) into relatively few spectral peaks (hundreds) does by itself almost completely invalidate the Lorentzian hypothesis and often dominates the shape of the resolvable peaks.

Considering, in addition, the fact that even ideal Lorentzian lines are inherently unsuitable for unambiguous spectral deconvolution, computer tasks such as 'reduction' of a spectrum into a meaningful list of peaks and multiplets are algorithmically extremely arduous. Yet it is clear that such a reduction is the first step towards even more complex tasks such as automatic NMR verification of suggested molecular structures or elucidation of unknown structures. In addition, algorithms of this type will undoubtedly enable new methods of assessing spectral similarity which are a pre-requisite to efficient handling of large spectral databases.

We wish to illustrate some heuristic avenues that might substantially alleviate the peak-shape problems listed above. In particular, we have tried with considerable success several peak-shape 'template' functions based on the Lorentzian profile, but made remarkably more flexible by adding a limited number of extra parameters. Combined with modern feature-enhancement tools such as the Resolution Booster, such peak-shape templates embody the promise of extracting all the information available in a spectrum, without introducing any new artifacts.


Notes added on February 21, 2009:

This work has been stimulated by the development of the long announced algorithm we call GSD (Global Spectral Deconvolution). Since the first version of GSD became fully operative about a week before the MMCE meeting, the presentation concentrates more on GSD than on peak shapes as such (except for what the aspects which directly regard GSD).

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