Improvements in the quantitation of NMR spectra by the use of statistical methods

Abstract

. Can. J. Chem. 69, 1189 (1991). In many applications of NMR spectroscopy to chemistry, quantitation plays a key role. This paper argues that peak heights not only can be used for quantitative work in NMR but that for careful work they should be used. Integrals are accurate, but because they depend on many subjective factors, their precision is suspect. Peak heights are very reproducible on modem spectrometers and so, given this precision, the accuracy can be obtained as well by using calibration methods. An example of the application of these methods is given in the case of a 13c labelling experiment that elucidates a photochemical transformation. Introduction NMR is certainly well known as one of the best methods for qualitative analysis: the identification of a molecule. Analysis of 13C and 'H spectra can often solve a structure completely, and the development of two-dimensional NMR methods has dramatically advanced this process (1, 2). These methods are based on spectral analysis, i.e., the positions of the lines in the spectrum, but quantitative analysis has also been an important part of NMR spectroscopy (3, 4). Counting protons using integrals is a very familiar part of proton NMR. Theory says that in the absence of saturation, the integral over a spectral line is directly proportional to the number of spins and the proportionality is the same for all lines in the spectrum. This simple quantitation can be extended and applied so that accurate and precise integration of NMR spectra is important in many fields (5-10). Measurements of enantiomeric and diastereomeric excess are crucial in the design of chiral synthesis. Particularly in isotopic labelling studies, such as the one described in this work, NMR is one of the few methods than can give a detailed picture of the mechanism of the reactions. The important data in this case are relative enrichments at different sites in the molecule (6, 7), so separations are impossible, and mass spectrometry is not selective enough to identify individual sites. However, the validity of these results depends crucially on the precision and accuracy of the quantitation of the NMR data.Normal methods of quantitation using integration are not without problems (3,4,11,12). In practice, the process involves several subjective decisions on the part of the operator. The choice of integration region, the phasing of the spectrum, and the correction of the baseline are all under the control of the operator, and each may profoundly affect the value of the integral. Careful work with good signal-to-noise ratios and standard conditions can minimize the variation of the results, but there will still be a random component due to the operator's particular choices as well as possible biases between operators (12). Typical estimates of the reliability of an integral are 3-5%

Regulating Competing Supramolecular Interactions Using Ligand Concentration

“…The fraction of monomeric cycles was calculated by dividing the area of the peak assigned to MC by the total peak area corresponding to the specific proton. Considering the errors on weighing (1%), 42 pipetting (1%) 43 and NMR integration/ deconvolution (5%), 44 As shown in Figure 6B, the addition of NaPy first leads to the appearance of signal d, which is converted into signal e upon further addition of NaPy. This behavior strongly suggests that signal d originates from an A−N contact connected to a B−B cycle, while signal e originates from an A−N contact in a tritopic UPy with all UPys bound to NaPy.…”

“…The fraction of monomeric cycles was calculated by dividing the area of the peak assigned to MC by the total peak area corresponding to the specific proton. Considering the errors on weighing (1%), 42 pipetting (1%)43 and NMR integration/ deconvolution (5%),44 we used standard error propagation techniques to determine the standard deviation to be ≈5%.The errors bars depicted two times the standard deviation, i.e., 10%. The solid line is used to guide the eye.…”

Supramolecular Buffering by Ring–Chain Competition

“…To quantify the effect of those errors on the calculated C NaPy free , we employ relative standard deviations based on instrumental specifications and reported accuracies of NMR integrals. 26 As such, the plotted error bars are not based on multiple measurements of samples at the same total concentration, but are calculated based on a single measurement. The 95% confidence interval on C NaPy free is calculated by standard error propagation techniques (see ESI).…”

Techniques and applications of far-UV photochemistry in solution. The photochemistry of the C3H4 and C4H6 hydrocarbons

“…the distribution of the label in both the allene and alkyne products by 13C NMR spectroscopy (eq 15),21 using a technique developed to improve the precision associated with 13C NMR integrations. 42 The distribution of the label in alkyne 28* is such that at least 40% of this product must arise via the alkenylidene pathway, assuming equal migratory aptitudes for methyl and isopropyl groups in the alkenylidene intermediate (eq 16). It should be noted that the predominant isotopomer of the alkyne can also be formed via [1,2]-H migration in vinylcarbene 39.…”