The extensive use of integration in proton NMR arises from the well-used doctrine that the area of an NMR resonance is proportional to the relative number of nuclei giving rise to it. In fact, this is only strictly true under well-defined experimen- tal conditions, and in routine proton spectra integrals may only be accurate to within 10–20% or so, for the reasons given earlier. Whilst this level of accuracy is usually sufficient for estimation of the relative proton count within a molecule, it is clearly inadequate for quantitative measurements where accuracy to within a few percent is required, and indeed this ac- curacy is possible provided appropriate parameters are employed. The fact that integrals are often reported to many decimal places by NMR software can draw one into believing such figures are significant, so inflating one’s expectations of what can be derived from routine spectra. Conversely, it is widely taught in introductory NMR lectures that it is not possible to integrate carbon-13 spectra. Whilst this is indeed inappropriate for routine acquisitions, not just for carbon-13 but also for many heteronuclei, it is nevertheless quite possible to obtain meaningful integrals when the appropriate protocols are employed, as described later.
In all these discussions it is important to be conscious of the fact that NMR measurements are always relative measures of signal intensities. There exist no NMR parameters equivalent to the extinction coefficients of ultraviolet spectroscopy, so ab- solute sample quantities cannot usually be determined directly. However, in the following sections two protocols will be intro- duced that do allow sample concentrations to be estimated without the need for an internal calibrant. These make use of either a synthetic electronic calibration signal ERETIC (electronic reference to in vivo concentrations) or a separate external calibration sample PULCON (pulse length–based concentration measurements) with which to determine sample concentrations.
4.1.2.1 Quantitative NMR—qNMR
Before considering the general practicalities pertinent to making quantitative measurements, we shall consider the use of NMR as a quantitative analytical method [7]. In this the typical aim is to define, with a high degree of accuracy, the relative levels of analytes present in a sample (such as when determining the percentage of an impurity present with a purity assay) or to determine the absolute concentrations of components in a sample. This approach is often referred to as quantitative NMR or simply qNMR, with the most common implementation employing proton spectroscopy termed qHNMR. This area has been reviewed in some comprehensive papers to which the interested reader is referred for extensive examples [8–10].
NMR is in fact very well suited as an analytical method, providing high precision and accuracy when properly validated, with the ability to simultaneously quantify multiple analytes within a sample without the need for identical standard com- pounds for calibration protocols, as are required for chromatographic assays.
The favoured use of proton NMR spectroscopy in qNMR arises from the greater sensitivity of proton detection, allow- ing an accuracy of 1% in measurements if appropriate experimental protocols are followed. In this, the optimum approach is to keep things simple and employ the single-pulse experiment of Fig. 4.1 (using parameters guided by the considerations discussed further), with an internal calibration standard added when absolute concentrations are to be determined. Herein the term calibration standard or calibrant refers to a material used to quantify an analyte, whilst the term reference stan- dard describes a chemical shift reference material such as tetramethylsilane (TMS) [9]. In some instances it may also be beneficial to employ 13C decoupling during proton acquisition to collapse the 13C satellites within the parent 12C proton resonance such that they do not overlap with neighbouring peaks. This is best achieved using the inverse-gated decoupling scheme of Section 4.2.3, to help attenuate sample heating that may be caused by carbon decoupling.
When assessing concentrations, the appropriate choice of calibrant is critical since its resonance(s) must not overlap those of the analyte(s) or solvent in the sample, meaning compounds with only a single resonance are favoured. The ma- terial should optimally be solid for accurate weighing (certainly not of high volatility), and highly soluble in the solvent used. It should also be available with high purity, stable, inert to the solvent and analytes studied, non-hygroscopic and, ideally, cheap. Many such compounds have been employed over the years and a number assessed specifically for use as calibration standards [11]. There is no absolute standard suitable for all studies, but some of the more useful compounds include maleic and fumaric acids, sodium acetate, dimethylsulfone, trimethylsilyl propionic acid (TSP; also a shift refer- ence standard), 1,3,5-trimethoxybenzene, 1,4-dinitrobenzene and 3,4,5-trichloropyridine. Relevant properties of these standards are summarised in Table 4.2. For assessment of the purity of standards themselves, highly pure acetanilide has been proposed as a suitable primary standard [12]. Analyte concentrations may then be determined by comparison of integrated peak intensities against those of the calibrant present at known concentration, taking account of the relative numbers of protons responsible for the integrated peaks. Alternative protocols derived from this procedure are described in Sections 4.1.3 and 4.1.4 and can avoid the need for an internal calibrant. Methods employing quantitative 2D NMR techniques that may be applicable to studies of more complex mixtures have also been reviewed [13], but are not con- sidered further here.
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138 High-Resolution NMR Techniques in Organic Chemistry
4.1.2.2 Data Collection
There are three features of specific importance to quantitative measurements, aside from the obvious need for adequate signal-to-noise in the spectrum. These are the avoidance of differential saturation effects, the need to characterise the NMR resonance lineshape properly and the need to avoid differential nuclear Overhauser effect (NOE) enhancements when decoupling is employed, a situation most significant for carbon-13 observation.
TABLE 4.2 Properties of Selected Calibration Standards
Solvent Solubility Calibration Standard Structure
Molecular Weight (g/mol)
1H d
(ppm) D2O DMSO–d6 CD3OD CDCl3
Maleic acid 116.07 6.0–6.3
✓ ✓ ✓ ✗
Fumaric acid 116.07 6.6–6.8
✓ ✓ ✓ ✗
Sodium acetate
O–
82.03 1.6–1.9
✓ ✓ ✓ ✗
Dimethyl sulfone 94.13 3.0
✓ ✓ ✓ ✓
TSP–d4 150.29 0.0
✓ ✓ ✓ ✗
1,3,5-
Trimethoxybenzene
168.19 6.1,
3.7–3.8
✗ ✓ ✓ ✓
1,4-Dinitrobenzene
O–
168.11 8.3–8.5
✗ ✓ ✓ ✓
3,4,5-
Trichloropyridine
182.43 8.5–8.8
✗ ✓ ✓ ✓
Acetanilide (primary standard)
135.17 2.0–2.2,
7.0–7.2, 7.2–7.3, 7.3–7.6, 7–10a
✓ ✓ ✓ ✓
1H shift ranges provide a guide but are solvent dependent within these ranges.
aThe amide NH shift of acetanilide varies greatly with solvent.
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One-Dimensional Techniques Chapter | 4 139
As mentioned in the previous section, acquiring data whilst pulsing rapidly relative to spin relaxation times leads to perturbation of the relative signal intensities in the spectrum, so to avoid this it is essential to wait for the spins to fully relax between pulses, demanding recycle times of at least 5T1 of the slowest relaxing nuclei. This allows the use of 90 degree observation pulses, thus providing the maximum possible signal per transient. Clearly, one requires some knowl- edge of the T1 values for the sample of interest which may be determined by the inversion recovery methods described in Section 2.4 or estimates made from prior knowledge of similar compounds. Whilst recycle times of the order of 5T1 are usually bearable for proton work, they can be tediously long in the study of heteronuclei which may demand many minutes between scans. Here relaxation reagents can be employed to reduce these periods to something more tolerable.
The second fundamental requirement is for the data to be sufficiently well digitised for the lineshape to be defined properly. To minimise intensity errors it is necessary to have at least four acquired data points covering the resonance line- width, although many more than this are preferable, so it is beneficial to use the minimum spectral width compatible with the sample and to adjust the acquisition times accordingly. For proton spectroscopy, acquisition times of 3–4 s are usually adequate. However, the spectral width should not be too narrow to ensure the receiver filters do not interfere with resonance intensities at the edges of the spectrum.
A further source of intensity distortions in heteronuclear spectra recorded with broadband proton decoupling arises from the NOE produced by proton saturation (see the chapter Correlations Through Space: The Nuclear Overhauser Effect). Clearly, differential enhancements will prevent the collection of meaningful intensity data, so it is necessary to take measures to suppress the NOE, yet it is still desirable to collect proton-decoupled spectra for optimum signal-to-noise and minimal resonance overlap. The solution to this apparent dichotomy is to employ the inverse-gated decoupling scheme described in the following section. The lack of the NOE and the need to pulse at a slow rate means quantitative measure- ments can take substantially longer than would routine observation of the same sample. The addition of a relaxation agent will again speed things along by reducing recycle delays and will also aid suppression of the NOE, as it will eliminate the dipolar relaxation responsible for this enhancement (Fig. 4.4).
4.1.2.3 Data Processing
Having taking the necessary precautions to ensure the acquired data genuinely reflects the relative ratios within the sample, appropriate processing can further enhance results. The spectra of heteronuclei, in particular, benefit from the application of an exponential function that broadens the lines. This helps to ensure the data are sufficiently well digitised in addition to improving the signal-to-noise ratio. For proton spectroscopy, achieving adequate sensitivity is not such a demanding problem, although the use of a matched exponential window will again help to ensure sufficient digitisation. The use of zero-filling will further assist with definition of the lineshape and is highly recommended, although this must not be used as a substitute for correct digitisation of the acquired FID. Careful phasing of the spectrum is also essential. Deviations from pure absorption-mode lineshapes will reduce integrated intensities with contributions from the negative-going components;
in the extreme case of a purely dispersive lineshape, the integrated intensity is zero! Another potential source of error arises from distortions of the spectrum baseline, which have their origins in spectrometer receiver stages. These errors mean the regions of the spectrum that should have zero intensity, that is, those that are free from signals, have a non-zero value, and make a positive or negative contribution to measurements. NMR software packages incorporate suitable baseline correction routines for this.
The final consideration when integrating is where the integral should start and finish. For a Lorentzian line, the tails extend a considerable distance from the centre and the integral should, ideally, cover 20 times the linewidth each side of the peak if it is to include 99% of it. For proton observation this is likely to be 10–20 Hz each side. In practice, it may not be possible to extend the integral over such distances before various other signals are met. These may arise from experimental imperfections (such as spinning sidebands), satellites from coupling to other nuclei or from other resonances in the sample.
Satellites can be particularly troublesome in some cases as they may constitute a large fraction of a total signal, owing to the high natural abundance of the second nuclide, and one must decide on whether to include them or exclude them for all measurements, or alternatively to collapse them entirely through use of the heteronuclear decoupling scheme described above. However, in some instances, satellites can be used to one’s advantage in quantitative measurements. One example is in the estimation of enantiomeric or diastereomeric excesses by proton NMR where the minor isomer is present at only a few percent of the major. In such cases, the ee or de measurement demands the comparison of a very large integral versus a very small one, a situation prone to error. Comparison of similar size integrals can be made if one considers only the car- bon-13 satellites of the major species (each present at 0.55%), and scales the calculation accordingly.
An alternative to resonance integration now commonplace in NMR processing software is to use direct lineshape fitting, or deconvolution, to determine peak areas. In this process resonances are decomposed into clusters of singlet peaks of either Lorentzian or Gaussian shape which have known linewidth and area. The sums of these lines should reproduce the original
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140 High-Resolution NMR Techniques in Organic Chemistry
resonance profile, as illustrated in Fig. 4.6. The experimental spectrum comprising an overlapping doublet and broad singlet have been deconvoluted to yield three Lorentizian singlets that represent the relative areas of each component. The use of deconvolution may reduce operator bias in integral definition and may prove to be more reliable in the presence of baseline noise or other low-level artefacts, or when resonances experience overlap with a neighbouring peak and are not sufficiently resolved for integration, as in this example.