Magnitude processing

Most modern NMR experiments are run in a phase sensitive mode, which means that after fourier transformation the peaks require phase correction to become all positive. The HMBC experiment, however, generates signals that cannot all be phased simultaneously. The commonly used solution is magnitude processing.

The figure below shows a region of a HMBC spectrum. The blue contours are positive and the teal ones negative. The peaks are a mix of positive and negative intensity and there is no possible phase correction that could make all the peaks positive. To understand how to make all the peaks positive we need to discuss phase correction a little.

Phase correcting NMR spectra amounts to shuffling data between the orthogonal "real" and "imaginary" spectra so that the real spectrum contains absorptive peaks and the imaginary spectrum contains dispersive peaks. The figure below shows absorptive (blue) and dispersive (red) lorentzian lineshapes.

The two lineshapes are obtained from the two channels used to detect magnetisation precessing in the x-y plane. The channels are 90^o out of phase from each other and simply measure the intensity of the signal as it rotates past a fixed point. One can visualize this as resolving the magnetisation vector precessing in the x-y plane into two orthogonal components, one along the x-axis and one along the y-axis. As an alternative to resolving the vector into two components, the magnitude of the vector can be calculated using the Pythagorean theorem and a value that is always positive will be obtained. In the equation below, I_x represents the intensity of the signal along the x-axis, the real signal, and I_y the signal along the y-axis, the imaginary signal.

magnitude = √(I_x² + I_y²)

Processing NMR spectra in this way is known as "magnitude calculation". For 2D spectra the magnitude calculation can be done in either the horizontal or the vertical dimension. The figure below shows the results of applying a magnitude calculation in the two dimensions of the HMBC spectrum shown at the start of the post. The result of applying a magnitude calculation in F1, or the ¹³C dimension, is on the left and the result of applying it in F2, or the ¹H dimension, on the right.

In both spectra all the peaks are now positive and appear correctly phased. The MC in F1 spectrum, however, has vertical noise streaks and the peaks are very broad in the ¹³C dimension. The MC in F2 spectrum looks much better. The problem with applying a magnitude calculation is that the linewidth is greatly increased. Note in the earlier lineshape figure how the dispersive lineshape does not lie on the horizontal axis. Incorporating the dispersive signal from the imaginary spectrum leads to much broader peaks due to the "wings" of the lorentzian lineshape. Applying a magnitude calculation in the F2 dimension does not harm the appearance of the spectrum as much because the resolution in this directly detected dimension is much higher than in the indirect dimension. Even so, the linewidths in the ¹H dimension of the MC in F2 spectrum are much larger than those of the original spectrum.

For HMBC spectra the recommended processing scheme is linear prediction, apodization, zero filling and fourier transformation followed by a magnitude calculation in the F2 dimension. In TopSpin, the command "xf2m" will apply a magnitude calculation in F2. HMBC experiments are not the only ones that benefit from applying a magnitude calculation in F2. The standard COSY sequence implemented at the Facility, UCSD_COSY, is not phase sensitive and also needs application of a magnitude calculation in F2 to give reasonable looking spectra.