Tuesday, December 8, 2015

Processing: phase correction

The previous post mentioned that the fourier transform produces complex data - a set of "real" data points and a set of "imaginary" data points. Both datasets are equally legitimate - real and imaginary are simply labels to distinguish the two orthogonal datasets. Two datasets 90o out of phase with each other are collected to enable quadrature detection, the discrimination of positive and negative frequencies.

The fourier transform of an exponentially decaying sine wave produces an absorptive lorentzian peak (top panels in the figure below), while transforming a decaying cosine produces a dispersive function (the lower panels). Fourier transforming a decaying sinusoid whose phase is somewhere between a perfect sine and a perfect cosine produces a lorentzian peak with a mix of absorptive and dispersive character.

The signals detected by the NMR coil are rarely a perfect decaying sine wave so that after fourier transformation the peaks in an NMR spectrum have a mixture of absorptive and dispersive lineshapes. To obtain all positive peaks one must determine a phase correction angle that rotates the real dataset until it is absorptive and the imaginary dataset is dispersive. Typically, this phase correction (θ) is a linear function of the chemical shift (δ)

θ = m x δ + c

so phase correction requires determining the slope (m) and offset (c) of this relationship. Most NMR processing software can determine these parameters automatically, but for complex spectra the algorithms do not always give perfect results. In such cases manual phase correction is possible.

To manually phase correct an NMR spectrum the offset and slope are determined independently. First, a "pivot point" is selected. In the top panel of the figure below the red arrow indicates the peak selected as the pivot point. Choosing a peak on one edge of the spectrum simplifies determining the slope in the second step, but the position of the selected peak is not critical. Being able to see the baseline on either side of the peak is useful, as it makes adjusting the phase of this peak easier. After selecting the pivot, one finds a zero order phase correction (one that is independent of chemical shift as suggested by the horizontal dotted red line) by adjusting the phase of the selected peak until it is completely absorptive. This gives the middle spectrum in the figure below. Finally, one determines a first order phase correction (one that varies with chemical shift as indicated by the diagonal dotted red line) that corrects the phase of the peaks away from the pivot point while leaving the phase at the pivot point untouched. This produces the phase corrected lower spectrum.

Occasionally, automatic phase correction does not produce ideal results. Manual adjustment of the phase correction parameters will normally solve the problem but carbon spectra, and DEPT and APT experiments in particular, are often difficult to phase. A good strategy for phase correcting these spectra is to first apply the zero order phase correction as usual, then use the first order phase correction to correct peaks close to the pivot point, gradually moving further away from the pivot point adjusting the first order phase correction as necessary until all the peaks are corrected.

For a more detailed discussion of phase correction the books by Keeler and Jacobsen listed below are both excellent resources.

1. Keeler, James "Understanding NMR spectroscopy", John Wiley and Sons 2011, Chapter 4
2. Jacobsen, Neil J. "NMR spectroscopy explained", John Wiley and Sons 2007 pp126-130 

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