Basis on qNMR: Intramolecular vs Mixtures qNMR

A bit of historical background

NMR has won its reputation as a powerful tool for structure determination of organic molecules. In addition to the information provided by chemical shifts and coupling constants, the quantitative relationships existing between the peaks (or groups of peaks - multiplets) arising from the various nuclides in the sample has proven pivotal for the assignment and interpretation of NMR spectra.

Despite the fact that the concept of quantitative NMR (qNMR) has been coupled to NMR since the early 1950, shortly after the technique's inception, it seems as NMR, as an analytical tool for quantitative analysis was firstly mentioned in 1963 by Jungnickel and Forbes [Anal. Chem., 1963, 35 (8), pp 938–942] who determined the intramolecular proton ratios in 26 pure organic substances and Hollis [Anal. Chem., 1963, 35 (11), pp 1682–1684] who analyzed the amount fractions of aspirin, phenacetine and caffeine in respective mixtures.

From those pioneer works, many and varied studies on qNMR arose. As pointed out in J. Agric. Food Chem. 2002, 50, 3366-3374, qNMR is particularly suitable for the simultaneous determination of the percentage of active compounds and impurities in organic chemicals such as pharmaceuticals, agrochemicals and natural products, as well as vegetable oils, fuels and solvents, process monitoring, determination of enantiomeric excess, etc.

In what follows, I will use the term qNMR to refer to any quantitative measurement of NMR signals, regardless of whether the technique is employed as an analytical method (e.g. determination of the relative amounts of the components in a mixture) or as tool for structure determination or conformational analysis.

What’s the deal with qNMR?

The basic principle of qNMR assays is that, ideally, the integral of the set of all peaks which can be assigned to a particular nucleus is proportional to the molar concentration of that nucleus in the sample. Theoretically, this holds quite well, though there are deviations from the rule in strongly coupled systems. An important point to keep in mind is the word “ideally”; this includes, for example, perfectly relaxed samples.
Even so there remain a number of problems which can be first of all divided into two categories:

1. Sources of statistical assessment errors (scatter)
2. Sources of systematic assessment deviations (bias)

I will cover these points in detail in separate posts.

Intramolecular vs Intermolecular (mixtures) qNMR

The most important fundamental concept of qNMR is based on the fact that, the absorption coefficient for the absorption of electromagnetic energy is the same for all nuclides of the same species, regardless whether they belong to one or several molecules (e.g mixture). As a result, the NMR signal response (more precisely the integrated signal area) is directly proportional to the number of nuclides contributing to the signal.

For example, all organic chemists are very familiar with integrating the multiples of a 1H spectrum to elucidate or confirm a particular molecular structure (see figure below)


This application can be classified as Intramolecular qNMR. NOE spectra, where the intensity is related to the distance between spins and represents the main basis for NMR as a tool in structural molecular biology, is another application of Intramolecular qNMR (Note: In this context I’m not including Transfer-NOE used e.g. to study the structure of a ligand in a complex under conditions of fast exchange)

Let’s consider now another example, Intermolecular qNMR:
Purity determination of a compound using an internal standard (is) with known purity and assuming instrumental parameters properly set is given by the equation below (see for example, 10.1002/mrc.2464):

% purity by weight = W(is)/W(s) * A(s)/A(is)*MW(s)/MW(is)*H(is)/H(s)

where W(s) and W(is) are the weights of the sample and ISTD, A(s) and A(is) are the integrals (areas) of the sample and ISTD peaks, MW(s) and MW(is) are the molecular weights of the sample and ISTD, and H(s) and H(is) are the number of hydrogens represented by the integral for the sample and ISTD, respectively.

As a simple application, see Q-NMR for purity determination of macrolide antibiotic reference standards: Comparison with the mass balance method

Common to all qNMR studies is the calculation of NMR integrals. In my next post, I will cover the basic principles on NMR integration.