The integration of NMR spectra is capable of being carried out with high accuracy, but this is only feasible if several error sources are appropriately handled. Accuracy of ±5% can be achieved easily on a modern spectrometer, given that relaxation issues are adequately handled. Several factors need to be kept in mind and optimized to achieve errors of less than 1%.
Signal to Noise
The spectrum needs to have sufficient signal to noise ratio to support the degree of accuracy required for the experiment. This means using more scans, if required.
NMR spectroscopy is thought of as unique among spectroscopic methods because the relaxation processes are relatively slow (on the order of seconds or tenths of seconds), in comparison to mass spectroscopy. In other words, as soon as the spectrometer has disturbed the equilibrium population of nuclei via pulsing at the resonance frequency, they come back to their original populations in 0.1 to 10s of seconds.
Typically, the T1 (spin-lattice relaxation time1) is measured to calculate a suitable relaxation delay. The spectra can become saturated if the pulse angle and repetition rates are very high. Integrations become less accurate because the relaxation rates of different protons in the sample are not the same. The effects of saturation are primarily severe for small molecules in mobile solvents because these typically have the longest T1 relaxation times.
To attain trustworthy integrations, the NMR spectrum has to be achieved in a way that avoids saturation. It is impossible to decide if a spectrum was operated correctly just by inspection, as it relies on the operator to take suitable precautions, such as putting in a 5-10 second relaxation delay between scans, if optimal integrations are required.
It is vital to recognize that integration errors as a result of saturation effects will depend on the relative relaxation rates of several protons in a molecule. Errors will be bigger when distinct kinds of protons are being evaluated, for instance aromatic CH to a methyl group, than when the protons are the same or similar (such as two methyl groups).
Line Shape Considerations
NMR signals in a perfectly tuned instrument are Lorenzian in shape, so the concentration covers some distance on both sides of the center of the peak. Integrations have to be carried out over an appropriately broad frequency range to catch enough of the peak for the favored level of accuracy.
Therefore, if the width of the peak at half height is 1 Hz, then an integration of ±2.3 Hz from the center of the peak is required to catch 90% of the area, ±5 Hz for 95%, ±11 Hz for 98%, and ±18 Hz for more than 99% of the area.
This means that carefully spaced peaks cannot be accurately combined via the standard method, but might need line-shape stimulations with a program like NUTS in order to measure relative peak areas accurately.
A peak has to be decided by an adequate number of points to attain an accurate integration. The errors produced are very small and can achieve 1% if a resonance with a width at half height of 0.5 Hz is sampled every 0.25 Hz.
All C-H signals have 13C satellites2 situated ±JC-H/2(usually 115-135 Hz, however, numbers above 250 Hz are known) from the center of the peak. Combined, these satellites constitute 1.1% of the area of the central peak (0.55% each). They need to be kept in mind if integration at the >99% level of accuracy is desired.
Bigger errors are presented if the satellites from an adjacent very strong peak fall under the signal being incorporated. The easiest technique to right this problem is by decoupling of 13C, which condenses the satellites into the central peak. A number of other elements have critical fractions of spin ½ nuclei at natural abundance, and these will also create satellites big enough to impede integrations. Most noteworthy are 117/119Sn, 29Si, and 77Se.
13C satellites have a positive side: they can be employed as internal standards to quantify small amounts of contaminants or isomers, because their size relative to the central peak is accurately identified.
Spinning sidebands can be seen at ± the spinning speed in Hz in spectra conducted on weakly tuned spectrometers and/or with samples in low-quality tubes. They absorb intensity coming from the central peak. SSBs are not often significant on modern spectrometers.
Baseline Slant and Curvature
Under particular circumstances, spectra can show substantial distortions of the baseline, which can obstruct the procurement of high-quality integrations. Conventional NMR work-up programs, like NUTS, have procedures for baseline adjustments.