NMR spectroscopy can be performed with great accuracy, but can only be achieved if a number of sources of error are handled correctly. Using a modern spectrometer, an accuracy of ±5% can be easily attained so long as relaxation issues are properly handled. A number of factors must be considered and optimized in order to achieve errors of <1%.
Signal to Noise
The spectrum must have adequate signal to noise to support the level of accuracy required by the experiment, which means using more scans if required.
Saturation Effects
NMR spectroscopy is considered to be relatively unique among spectroscopic methods because of the relatively slow relaxation processes involved, which are on the order of seconds or tenths of seconds. This is significantly slower than UV or IR measurements, where relaxation times of ms, µs and pico-seconds are more common.
In other words, after the spectrometer has perturbed the equilibrium population of nuclei following a pulse at the resonance frequency, it takes between 0.1 and 10s of seconds for them to return to their original populations.
Normally, T1, the spin-lattice relaxation time1, is measured in order to calculate an appropriate relaxation delay. If a very high pulse angle and repetition rates are used, spectra can become saturated. As the relaxation rates of different protons in the sample can vary, integrations become less accurate. Saturation effects are generally more severe for small molecules in mobile solvents, as these have the longest T1 relaxation times.
To achieve reliable integrations, NMR spectra must be obtained in a way that prevents saturation from occurring. Inspection alone is insufficient to tell whether a spectrum was operated appropriately, and so the operator must take appropriate precautions, for instance putting in a small relaxation delay between scans (5-10 s), if optimal integrations are required.
Fortunately, even a proton spectrum acquired without pulse delays will usually give reasonably good integrations (with an error of around 3%). It is important to note that integration errors caused by saturation effects will rely on the relative relaxation rates of numerous protons in a molecule.
These errors will be larger when comparing diverse kinds of protons, such as aromatic CH to a methyl group, than when the protons are similar in type, for example in the case of two methyl groups.
Line Shape Considerations
In a perfectly tuned instrument, NMR signals are Lorenzian in shape, so the intensity is spread a certain distance on either side of the peak center. As a result, integrations must be performed over an extensive frequency range in order to capture enough of the peak for a high level of accuracy to be obtained.
For example, if the peak width at half height is 1 Hz, then an integration of ±2.3 Hz from the peak center is required to capture 90% of the area, while ±5.5 Hz is needed to achieve 95%, ±11 Hz for 98% and ±18 Hz for >99% of the area. As such, peaks that are carefully spaced cannot be accurately combined by the usual technique and may instead require line-shape simulations, using a program such as NUTS to measure relative peak areas accurately.
Digital Resolution
In order to acquire an accurate integration, a peak must be determined by a sufficient number of points. The errors introduced are small and an error of 1% can be accomplished if a resonance with a width at half height of 0.5 Hz is sampled every 0.25 Hz.
Isotopic Satellites
All C-H signals have 13C satellites2 located at a position ± JC-H/2 from the peak center (JC-H/2 is typically 115-135 Hz, but numbers above 250 Hz are known). Together these satellites can make up 1.1% of the area of the central peak (0.55% each). Because of this, their effect has to be considered if integration at the >99% level of accuracy is required.
Larger errors can be introduced if the satellites from an intense neighboring peak fall under the signal being incorporated. The easiest technique to correct this issue is known as 13C decoupling, in which the satellites are compressed into the central peak.
Several other elements have a high fraction of spin ½ nuclei at natural abundance, and these can also produce large enough satellites to interfere with integrations. The most notable of these are 117/119Sn, 29Si, and 77Se.
There is a bright side to 13C satellites however: they can be used as internal standards for the quantitation of tiny quantities of isomers or contaminants, as their size compared to the central peak is well understood.
Spinning Sidebands
Sidebands can appear at ± the spinning speed (in Hz) in spectra operated on weakly tuned spectrometers and/or with samples contained in low-quality tubes. They can absorb intensity from the central peak. These are rarely significant on modern spectrometers.
Baseline Slant and Curvature
Under certain conditions spectra can display significant baseline distortions, which can interfere with obtaining high-quality integrations. Standard NMR work-up programs, such as NUTS have routines for baseline adjustment.
References
- Reich, Hans J. “8.1 Relaxation in NMR Spectroscopy.” 8.1 Relaxation in NMR Spectroscopy, University of Wisconsin, 7th Aug. 2017, www.chem.wisc.edu/areas/reich/nmr/08-tech-01-relax.htm.
- Reich, Hans J. “5-HMR-3 Spin-Spin Splitting: J-Coupling.” 5-HMR-3 Spin-Spin Splitting: J-Coupling, University of Wisconsin, 10th Aug. 2017, www.chem.wisc.edu/areas/reich/nmr/05-hmr-03-jcoupl.htm#05-hmr-03-jcoupl-c13satellite.
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