PROCESSING YOUR DATA
 
Peak Integration

Chemical shifts are not the only useful features of an NMR spectrum. The relative sizes, or areas, of peaks, are an indicator of the numbers of nuclei contributing to each. For example, in a properly acquired 1H spectrum of methanol (CH3OH), the area of the methyl proton resonance will be three times that of the hydroxyl. Or, if the sample is a 2:1 mixture of methanol to ethanol (CH3CH2OH), then the per-proton area of any methanol peaks will be twice that of the area/proton for ethanol. This direct relationship makes NMR a potentially very powerful tool for quantitative analysis.
The areas of NMR resonances are evaluated numerically by the system's computer. The area under the curve is broken up into small blocks, and the number of blocks is added up across the peak. The illustration below shows a crude version of this process for an expanded peak. Move your mouse into and out of the figure below to watch:

The boxes approximate the shape of the peak. The green integral or integration curve is shown as a cumulative sum of the number of small boxes.

In actual practice, the computer system divides the area much more finely than shown here, allowing for better simulation of the peak shape, and a smoother integral curve. Move your mouse over the figure below to view a more typical integral curve:
When measuring a peak integral, the starting and stopping points must be chosen with care. NMR peaks approach the baseline only very gradually, so if possible, the integration limits should be placed a short distance from the peak, in order to insure that as much as possible of the peak is included. Of course, if there are other peaks present in the spectrum, the the choices of starting and ending points may be restricted. The figures below show good and poor selections for integration limits:
Severely overlapping peaks provide a special challenge for integration. In an example like that shown below, the only practical way to separate the two is to use a perpendicular to the minimum point as the dividing line, as shown in red. However, this excludes some of the area from each peak, as can be seen when your mouse is positioned over the figure:

Whenever feasible, you should avoid using such overlapping peaks in calculations. While the peak resolution can sometimes be improved by changing the experimental conditions, this is not always possible. In many cases, the integrated areas of other peaks in the spectrum can be substituted.
 
Baseline artifacts can have significant adverse effects on the reliability of integral values. A baseline which rises linearly across the spectrum, for example, causes a severely sloping integral baseline, a shown below. Note that the right side of the spectrum is only slightly displaced above the gray baseline, but that the integral slopes steeply upward. Computerized integration procedures always include a routine for correcting sloping baselines.
 
Similarly, curved spectral baselines, like those discussed earlier, cause distortions in the integration as well. This is seen as curvature in the integral baseline. Like a sloping baseline, it can be adjusted by computer:
 

In many cases, both kinds of integral baseline artifacts are present. They can sometimes be corrected automatically, but more commonly, some user intervention is required. The best way to reduce the need for such adjustments is to insure that your spectrum has a properly corrected baseline before any integration is performed.

 

HELPFUL HINT!

If you find that you do need to make integral baseline corrections, do the first-order (curved) adjustments first, followed by the zero-order (linear). Remove any curvature, leaving both side of the integral slanting in the same direction, with the same slope. Then make linear corrections to flatten the integral. If necessary, repeat this procedure until the integral baselines are acceptable.

 

END OF SOFTWARE-INDEPENDENT TUTORIAL