Reducing Quantitative Evaluation Errors in NMR

The incorporation of NMR spectra can be performed with great accuracy, but this is only possible if a number of sources of error are correctly handled. On a modern spectrometer, accuracy of ±5% can be attained effortlessly if relaxation issues are properly handled. A number of factors have to be considered and optimized in order to get errors of <1%.

Signal to Noise

It is necessary for the spectrum to have adequate signal to noise in order to support the level of accuracy needed for the experiment. This means using more scans if needed.

Saturation Effects

NMR spectroscopy is considered to be unique among spectroscopic methods in that the relaxation processes are comparatively slow (on the order of seconds or tenths of seconds), compared to ms, us and pico-seconds for UV and IR. In other words, once the spectrometer has perturbed the equilibrium population of nuclei by pulsing at the resonance frequency, it takes from 0.1 to 10s of seconds for them to come back to their original populations.

Usually, one measures the T₁ (spin-lattice relaxation time¹) in order to calculate an appropriate relaxation delay. If the pulse angle and repetition rates are very high then spectra can become saturated. Because the relaxation rates of different protons in the sample are different, integrations become less accurate. Saturation effects are mainly severe for tiny molecules in mobile solvents, because these normally have the longest T₁ relaxation times.

To get reliable integrations, the NMR spectrum must be attained in a way that saturation is avoided. It is not possible to tell whether a spectrum was operated appropriately just by inspection, it depends upon the operator to take appropriate precautions, for instance putting in a 5-10 second relaxation delay between scans, if optimal integrations are needed. Luckily, even a proton spectrum acquired without pulse delays will typically give reasonably good integrations (say within 3%). It is crucial to identify that integration errors caused by saturation effects will rely on the relative relaxation rates of numerous protons in a molecule. Errors will be larger when diverse kinds of protons are being compared, such as aromatic CH to a methyl group, than when the protons are identical or similar in type (for example two methyl groups).

Line Shape Considerations

NMR signals in a perfectly tuned instrument are Lorenzian in shape, so the intensity covers some distance on either sides of the center of the peak. Integrations must be performed over an adequately extensive frequency range to capture enough of the peak for the preferred level of accuracy. Thus, if the peak width at half height is 1 Hz, then an integration of ±2.3 Hz from the center of the peak is needed to capture 90% of the area, ±5.5 Hz for 95%, ±11 Hz for 98% and ±18 Hz for >99% of the area. This means that peaks that are carefully spaced cannot be accurately combined by the usual technique, but may require line-shape simulations with a program like NUTS to accurately measure relative peak areas.

Digital Resolution

A peak must be determined by a sufficient number of points if an accurate integration is to be acquired. The errors introduced are remarkably small, and can accomplish 1% 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 ± J_C-H/2 from the center of the peak (J_C-H/2 is commonly 115-135 Hz, although numbers above 250 Hz are known). Together these satellites make up 1.1% of the area of the central peak (0.55% each). They have to be accounted for if integration at the >99% level of accuracy is wanted. Larger errors are introduced if the satellites from a neighboring very intense peak fall under the signal being incorporated. The simplest technique to correct this issue is by ¹³C decoupling, which compresses the satellites into the central peak. Several other elements have important fractions of spin ½ nuclei at natural abundance, and these will also produce satellites large enough to interfere with integrations. Most notable are ^117/119Sn, ²⁹Si, and ⁷⁷Se.

There is a bright side to 13C satellites: they can be used as internal standards for the quantitation of very small quantities of contaminants or isomers, since their size compared to the central peak is accurately identified.

Spinning Sidebands

These can appear at ± the spinning speed in Hz in spectra operated on weakly tuned spectrometers and/or with samples in low-quality tubes. They absorb intensity from the central peak. SSBs are rarely significant on modern spectrometers.

Baseline Slant and Curvature

Under certain conditions spectra can display considerable distortions of the baseline, which can interfere with obtaining high-quality integrations. Standard NMR work-up programs (like NUTS) have routines for baseline adjustment.

References

1. Reich, Hans J. “8.1 Relaxation in NMR Spectroscopy.” 8.1 Relaxation in NMR Spectroscopy, University
   of Wisconsin, 7^th Aug. 2017, www.chem.wisc.edu/areas/reich/nmr/08-tech-01-relax.htm.
2. Reich, Hans J. “5-HMR-3 Spin-Spin Splitting: J-Coupling.” 5-HMR-3 Spin-Spin Splitting: J-Coupling, University of Wisconsin, 10^th Aug. 2017, www.chem.wisc.edu/areas/reich/nmr/05-hmr-03-jcoupl.htm#05-hmr-03-jcoupl-c13satellite.

This information has been sourced, reviewed and adapted from materials provided by Anasazi Instruments.

For more information on this source, please visit Anasazi Instruments.