Quantitative NMR Interpretation without Reference
As has been documented numerous times over the years, nuclear magnetic resonance (NMR) experiments are intrinsically quantitative. Still, quantitative NMR methods have not been widely adopted or largely introduced into pharmacopoeias. Here, we describe the quantitative interpretation of the 1D proton NMR experiment using only absolute signal intensities with the variation of common experimental parameters and their application.
Since its inception, NMR has always been considered inherently quantitative [1–6] and it has been used in teaching . As opposed to all other spectroscopic methods, the intensity of an NMR signal is directly proportional to the abundance of the nuclei causing it [6–8], which could even be in multiple molecules [9, 10]. In the case of simple mixtures, NMR allows for simultaneous quantification of the constituents based on one sole reference standard. The standard does not have to share its identity with any of the analytes of interest. This key feature makes quantitative NMR an extremely versatile technique, and numerous applications for the quantitative analysis of pharmaceutical compounds have been proposed over the decades [6, 11–23]. The majority of the described experiments are 1D liquid state, but 2D and CPMAS experiments have also been proposed. Also, most of the proposed quantitative methods are based on proton NMR experiments, but other nuclei have been used since the beginning: 31P [24, 25], 2H , and 13C [19, 27, 28]. In recent years, 23Na , 19F [30, 31], 35Cl [32, 33], 11B , 7Li , and quadrupolar nuclei like 27Al [36, 37] and 14N [38, 39] were added to the list. While some of the proposed methods are 2D experiments or CPMAS, mostly 1D liquid state experiments have been described.
Whichever method is chosen, the quantification by NMR is always based on the comparison of the signal intensity of reference material with the signal intensity of the analyte(s), as the intensities are proportional to the molar concentrations and the number of protons contributing to the signal. The reference signal can be provided by a reference material mixed with the analyte in one solution, internal referencing (IR) [18, 25, 29, 30, 32, 40–44], or by a separate solution, external reference (ER). Two methods for ER have been described; most commonly, two identical experiments are carried out, one time with the analyte and the other time with the reference material [6, 45, 46]. Alternatively, a solution with the reference is sealed into a capillary that is then added to the solution of the analyte . Hybrid methods like ERETIC [48–50] and PULCON [46, 51–56] have also been implemented, which combine ER and IR by an intermediate step. All these methods work with the best reliability when the reference used has a molar concentration that is close to the analyte’s concentration, thus requiring some previous knowledge about the analyte. The analysis of mixtures can also be restricted, as the quantification reliability might vary with the concentrations involved.
Several experimental parameters shown in Table 1 have influence on the NMR spectrum, and some of them are flexible depending on the chosen method. Here, we demonstrate a new hybrid method, flexible absolute intensity-based quantification by NMR (FAINT-NMR), which can be applied to the quantification of compounds, even with largely varying concentrations, without previous knowledge. The work presented demonstrates that the restrictions described for external referencing methods  are not necessary. The normalization of the absolute signal intensity by a receiver gain and the number of scans results in an Intensity Gain (IG) factor, based on which the quantification of every sample becomes possible, independent of the experimental parameters. As amplifiers are notoriously nonlinear, a manual linearization of the receiver gain values was performed, in order to verify if this would improve the quantification quality further.
The usability of FAINT-NMR was verified on a Bruker equipment AVANCE III 400 MHz equipped with a 5 mm BBO Prodigy probe and a sample changer, which was used with as much automation as possible for experiment acquisition, followed by partially automated interpretation. As the methods target small molecules, protons were chosen as the observed nucleus due to higher sensitivity and sufficient signal separation.
Samples were weighted on a calibrated Mettler Toledo AG245 balance and diluted with 0.6 ml of DMSO-d6 into 5 mm NMR tubes. After determining values for the fixed parameter (D1), the influence of the flexible parameters (NS, RG) was determined. The longest of the reference material was determined as 2.06 s by our own measurements in DMSO-d6, as 1.86 s in CDCl3  and 2.7 s in D2O ; thus, the inter-scan delay D1 was fixed as 16 s for all experiments.
Simple proton experiments with a 90° pulse and 16 k observe points were obtained at 25°C, varying the number of scans and receiver gain. Experiments with 2 to 64 scans (NS) and receiver gain (RG) from 25.4 to the highest RG value determined by the function automatic receiver gain (RGA) for the sample were carried out in duplicates. The RG values available on the equipment usually reach values above 4 K, which we could not observe for our samples for proton experiments. For proton experiments, we observe that the maximum RG value for low analyte concentrations is actually defined by the solvent “concentration” in the sample. When the analyte is in high concentration, it can decrease the RG value, as seen. Thus, the experiments use only a small slice of the possible RG values. All experiments were processed automatically (Fourier transformation and phase correction), followed by integration using intervals defined on one reference experiment. With this data set a constant IG (Intensity Gain, ) factor was determined, that allows the calculation of the concentration directly from the absolute intensity of a signal. Finally, a linearization of the RG values was carried out, and the improvement of the back-calculated values was verified.
FAINT-NMR was applied to a series of quinine samples, Figure 1, which was chosen due to its high molecular weight. Figure 2 shows the proton NMR spectrum of quinine in DMSO-d6 and the signals that were used for the quantification. Further signals were not used because they overlap or have complex multiplet patterns. In total, five samples diluted in 0.6 ml of DMSO-d6 were used, as shown in Table 2.
In Figure 3, the absolute signal intensities of 13 signals of quinine were averaged, normalized against their concentration, number of protons and scans, and scatter-plotted according to their respective RG. These signals were chosen because of their lack of overlap and the small number of observed couplings. The signal-to-noise ratio of all signals was always above 200 : 1.
The results from Figure 3 show that the per-scan signal intensity increment scatters around an average of 1650. Based on this, an IG factor of 1650 was defined for all intensity-based quantifications shown here. Furthermore, these results were used to carry out a manual linearization of the RG values, to further improve the results. The original and linearized RG values are shown in Table 3.
In Table 4, the 5 actual sample concentrations are compared to the back-calculated values (BC) and values back-calculated using a linearized RG (BC-l). Figure 4 shows the linear regression graph of the values in Table 4. The linear regression equations in Table 5 clearly show that the linearization of the RG improves the results, as the slope for the equation is very close to the optimum value of 1.0.
So far, a large-scale application of qNMR has been restricted by experimental conditions. In the case of internal reference methods, difficulties might arise because of signal overlap or interaction of the reference with the sample. In the case of external referencing, the fixed experimental conditions usually restrict the working range of the method. The results presented here show that some experimental parameters, like RG and NS, can be varied largely without affecting the quality of the quantification result. The linearization of the RG values further improves the accuracy of the method. By lifting these restrictions, FAINT-NMR can facilitate the quantification by NMR in general, including trace amounts in samples, as long as well-isolated signals are observed. One possibility to achieve theses isolated signals would be to combine Bayesian data analysis with FAINT-NMR, which would provide isolated signals and turn integration limits unneccessary.
All data (NMR data as raw, processed, and integrated; Spreadsheet with data interpretation) are available at https://doi.org/10.5281/zenodo.7221753.
Conflicts of Interest
The authors declare that there are no conflicts of interest.
This research was funded by the Fiocruz INOVA project and the Brazilian Agency Fundação de Amparo a Pesquisa do Estado do Rio de Janeiro (FAPERJ), (Grant no. E-26/201.470/2022(273626)).
N. Muller and J. Goldenson, “Rapid analysis of reaction mixtures by nuclear magnetic resonance spectroscopy,” Journal of the American Chemical Society, vol. 78, no. 20, pp. 5182-5183, 1956.View at: Google Scholar
L. W. Reeves, “Nuclear magnetic resonance measurements in solutions of acetylacetone: the effect of solvent interactions on the tautomeric equilibrium,” Canadian Journal of Chemistry, vol. 35, pp. 1351–1365, 1957.View at: Google Scholar
C. A. Reilly, “Nuclear magnetic resonance spectrometry,” Analytical Chemistry, vol. 30, pp. 839–848, 1958.View at: Google Scholar
R. B. Williams, “Quantitative determination of organic structures by nuclear magnetic resonance: intensity measurements,” Annals of the New York Academy of Sciences, vol. 70, no. 4, pp. 890–899, 1958.View at: Google Scholar
D. P. Hollis, “Quantitative analysis of aspirin, phenacetin, and caffeine mixtures by nuclear magnetic resonance spectrometry,” Analytical Chemistry, vol. 35, no. 11, pp. 1682–1684, 1963.View at: Google Scholar
W. B. Smith, “Quantitative analysis using NMR,” Journal of Chemical Education, vol. 41, p. 97, 1964.View at: Google Scholar
J. L. Jungnickel and J. W. Forbes, “Quantitative measurement of hydrogen types by intergrated nuclear magnetic resonance intensities,” Analytical Chemistry, vol. 35, no. 8, pp. 938–942, 1963.View at: Google Scholar
P. J. Paulsen and W. D. Cooke, “Quantitative determination of hydrogen and fluorine in organic compounds by nuclear magnetic resonance spectrometry,” Analytical Chemistry, vol. 36, no. 9, pp. 1713–1721, 1964.View at: Google Scholar
R. Kaplan and S. F. Laczynski, “NMR-A new instrumental tool for the analysis of cosmetic ingredients,” Journal of the Society of Cosmetic Chemists, vol. 25, pp. 507–514, 1974.View at: Google Scholar
U. Holzgrabe, B. Diehl, and I. E. Wawer, NMR Spectroscopy in Pharmaceutical Analysis, Elsevier, Amsterdam, Netherlands, 2008, https://www.sciencedirect.com/science/article/pii/B9780444531735000056.
U. Holzgrabe, “Quantitative NMR spectroscopy in pharmaceutical applications,” Progress in Nuclear Magnetic Resonance Spectroscopy, vol. 57, no. 2, pp. 229–240, 2010.View at: Google Scholar
R. Woodriff, B. R. Culver, D. Shrader, and A. B. Super, “Quantitative analysis by phosphorus-31 nuclear magnetic resonance spectrometry,” Analytical Chemistry, vol. 45, pp. 370-371, 1973.View at: Google Scholar
G. J. Martin, M. L. Martin, and F. Mabon, “A new method for the identification of the origin of natural products. Quantitative deuterium NMR at the natural abundance level applied to the characterization of anetholes,” Journal of the American Chemical Society, vol. 104, pp. 2658-2659, 1982.View at: Publisher Site | Google Scholar
T. H. Mareci and K. N. Scott, “Quantitative analysis of mixtures by carbon-13 nuclear magnetic resonance spectrometry,” Analytical Chemistry, vol. 49, no. 14, pp. 2130–2136, 1977.View at: Google Scholar
H. S. Lim, G. C. Han, and S. G. Lee, “Quantitative elemental analysis of sodium (23Na) by NMR spectroscopy,” Bulletin of the Korean Chemical Society, vol. 23, pp. 1507-1508, 2002.View at: Google Scholar
H. S. Lim and S. G. Lee, “Quantitative analysis of chloride by chlorine-35 NMR spectroscopy,” Bulletin of the Korean Chemical Society, vol. 27, pp. 972-973, 2006.View at: Google Scholar
S. A. Watson, A. J. Edwards, and J. A. Parkinson, “Standardless, automated determination of chlorine-35 by 35 Cl nuclear magnetic resonance,” Analytical Letters, vol. 50, pp. 161–172, 2017.View at: Google Scholar
L. M. Aguilera-Sáez, J. R. Belmonte-Sánchez, R. Romero-González et al., “Pushing the frontiers: boron-11 NMR as a method for quantitative boron analysis and its application to determine boric acid in commercial biocides,” Analyst, vol. 143, no. 19, pp. 4707–4714, 2018 10.View at: Publisher Site | Google Scholar
H. Maki, G. Sakata, and M. Mizuhata, “Quantitative NMR of quadrupolar nucleus as a novel analytical method: hydrolysis behaviour analysis of aluminum ion,” The Analyst, vol. 142, no. 10, pp. 1790–1799, 2017.View at: Google Scholar
R. Khatun, H. N. Hunter, Y. Sheng, B. W. Carpick, and M. D. Kirkitadze, “27Al and 31P NMR spectroscopy method development to quantify aluminum phosphate in adjuvanted vaccine formulations,” Journal of Pharmaceutical and Biomedical Analysis, vol. 159, pp. 166–172, 2018.View at: Publisher Site | Google Scholar
J. S. Salsbury and P. K. Isbester, “Quantitative1H NMR method for the routine spectroscopic determination of enantiomeric purity of active pharmaceutical ingredients fenfluramine, sertraline, and paroxetine,” Magnetic Resonance in Chemistry, vol. 43, pp. 910–917, 2005.View at: Google Scholar
C. Sterling, R. Crouch, D. J. Russell, and A. I. Calderõn, “1H-NMR quantification of major saccharides in açaí raw materials: a comparison of the internal standard methodology with the absolute intensity qNMR method,” Phytochemical Analysis, vol. 24, no. 6, pp. 631–637, 2013.View at: Publisher Site | Google Scholar
L. Chi, M. Huang, A. R. Pfaff, J. Huang, R. E. Gerald, and K. Woelk, “Capillary-tube package devices for the quantitative performance evaluation of nuclear magnetic resonance spectrometers and pulse sequences,” Review of Scientific Instruments, vol. 89, Article ID 123115, 2018.View at: Publisher Site | Google Scholar
Y. B. Monakhova, M. Kohl-Himmelseher, T. Kuballa, and D. W. Lachenmeier, “Determination of the purity of pharmaceutical reference materials by 1H NMR using the standardless PULCON methodology,” Journal of Pharmaceutical and Biomedical Analysis, vol. 100, pp. 381–386, 2014.View at: Publisher Site | Google Scholar
B. C. Garrido and L. J. de Carvalho, “Nuclear magnetic resonance using electronic referencing: method validation and evaluation of the measurement uncertainties for the quantification of benzoic acid in orange juice,” Magnetic Resonance in Chemistry, vol. 53, no. 2, pp. 135–141, 2015.View at: Publisher Site | Google Scholar