V. Integration- I

This section will show you how to obtain good integrals. Examples of spectra of 0.1% ethylbenzene in CDCl₃ from the Unity+300 and VXR-S 400 NMR spectrometers are given in Figures V-1 and V-2 respectively. Both spectra were taken using the default parameters for acquiring ¹H spectra. If we assign an integral of 3.00 to the CH₃ triplet, then the phenyl region integrates to 4.52 protons, while the CH₂ qurtet integrates to 2.08 protons. Thus the integral for the phenyl protons is 9.6% too small, while the integral for the CH₂ quartet is off by 4.0%. The 9.6% error for the phenyl protons is not due to spectrometer error; it is because we have chosen parameters for acquiring the spectrum which guarentee we will get inaccurate integrals.

The accuracy of the integrals obtained for most routine spectra is usually about 10-20%. This accuracy is sometimes sufficient especially if you already know what the compound is. However, this accuracy is usually not adequate to determine the exact number of protons contributing to a given peak, nor is it sufficient for quantitative applications such as kinetic experiments or assays of product mixtures where one demands an accuracy of 1-2%. For example, 20% accuracy is not sufficient to decide whether two peaks have a relative ratio of 1:3 or 1:4. Obtaining 1-2% accuracy can be achieved but you need to be aware of the factors that affect integrations. These factors are discussed below.

1. There should be no nuclear Overhauser effect contributions or any other effects that selectively enhance certain peaks. This is a problem only with X nuclei such as ¹³C.

2. No peaks should be close to the ends of the spectrum. The spectral width should be large enough such that no peak is within 10% of the ends of the spectrum. This is because the spectrometer uses filters to filter out frequencies that are outside the spectral width. Unfortunately, the filters also tend to decrease the intensities of peaks near the ends of the spectrum. For example, at 299.96 MHz, if two peaks are separated by 7 ppm, a spectral width of atleast 2100 Hz is sufficient to get both peaks in the spectrum and prevent foldovers. However, to avoid distortion of the integral intensities because of filter effects, the spectral width should be set 10% larger on each side, 210 Hz, giving a total spectral width of about 2520 Hz (8.4 ppm). Although the standard setup parameters on the Unity+300 and VXR-S 400 should easily satisfy this criterion, you should be prepared to make the spectral width larger if necessary.

3. The pulse repetition (recycle) time should be atleast five T₁s. Data should be collected under conditions which ensure that all the nuclei can fully relax before the next FID is taken, i.e., if 90 degree pulse width are used, relaxation delays of 5xT₁ of the longest T₁ of interest are necessary. In the case of ethylbenzene, the longest T₁ of interest is 9.8 sec for the phenyl protons, so the relaxation delay when using 90⁰ pulse width should be at least 49 sec (5x9.8). In Figure V-3, is shown the spectrum of 0.1% ethylbenzene in CDCl₃, using a 90 degree pulse width, realaxation delay of 60 sec, taking 32 transients, and using a line broadening of 0.1 Hz ( for comparison, the default parameters on the Unity+300 use a 45 degree flip angle and a recycle delay of 5.1 sec). If we assign an integral of 3.00 to the CH₃ triplet, then the phenyl region integrates to 5.17 protons, while the CH₂ quartet integrates to 1.98 protons. Thus, the integral for the CH₂ quartet is off by only 1.0%, while the integral for the phenyl prtons is now 3.2% too high. The errors for both the phenyl protons and the CH₂ protons are now comparable; they reflect a good choice for the recycle delay for this sample. However, the 3.2% error for the phenyl protons is still higher than the 1-2% error range one needs for accurate quantitaive measurements. In this particular example, the signal from the residual proton (CHCl₃, 7.29 ppm) contributes to the integral of the phenyl region making it higher than the true value. This problem can be solved by measuring the spectrum in a solvent such as CD₂Cl₂ whose residual proton signal will not overlap with any of the ethylbenzene protons.