# Clean ¹H NMR Spectra of Products Directly from Batch and Flow Reaction Mixtures

Yuliia Horbenko, Martin Jaudronnet, Nour El Sabbagh, Margherita Bazzoni, Aurélie Bernard, Mathias Nilsson, Patrick Giraudeau, François-xavier Felpin, Jean-nicolas Dumez

► To cite this version:

Yuliia Horbenko, Martin Jaudronnet, Nour El Sabbagh, Margherita Bazzoni, Aurélie Bernard, et al. Clean ¹H NMR Spectra of Products Directly from Batch and Flow Reaction Mixtures. ChemistryEurope, 2025, 3 (3), pp.e202500038. 10.1002/ceur.202500038. hal-05117346

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# Clean ¹H NMR Spectra of Products Directly from Batch and Flow Reaction Mixtures

Yuliia Horbenko, Martin Jaudronnet, Nour El Sabbagh, Margherita Bazzoni, Aurélie Bernard, Mathias Nilsson, Patrick Giraudeau, François-Xavier Felpin,* and Jean-Nicolas Dumez*

Nuclear magnetic resonance (NMR) spectroscopy is widely used for the monitoring of chemical reactions. Flow NMR methods are being increasingly used to monitor reactions carried out in either batch or flow synthesis mode. Kinetic information is commonly obtained by integration of assigned peaks across a series of spectra. However, the complexity of NMR spectra in reaction mixtures can result in peak overlap and assignment issues, which make it difficult to recover the clean complete spectrum of compounds involved in the reaction. Multiway analysis methods can in principle be used to separate information on compounds in a mixture, but they are demanding on the quality and form of the input data.

Herein, it is shown how the multiway analysis of time-resolved diffusion NMR data can yield the clean spectrum of newly formed compounds, for a selection of click reactions carried out in batch and in flow, when monitored by flow NMR. The use of a fast and robust diffusion NMR approach, together with careful processing, yields high-quality data, even for continuously flowing samples, which was previously inaccessible. Multiway analysis then yields 1D ¹H spectra together with concentration changes. The proposed approach is expected to be particularly useful for reaction monitoring applications.

## 1. Introduction

Reaction monitoring is an essential aspect of chemical synthesis, which provides insight into reaction mechanisms, and helps to optimize reaction conditions and control reaction outcomes. An array of analytical methods are available for reaction monitoring, including high-performance liquid chromatography (HPLC),[1-4] Fourier-transform infrared spectroscopy (FTIR),[5-7] and nuclear magnetic resonance (NMR) spectroscopy.[8] NMR spectroscopy is one of the most robust and widely used approaches, as it provides structural information about compounds in solution, as well as quantitative measurements of concentrations that yield kinetic information.

The monitoring of a chemical reaction or process by NMR spectroscopy can be implemented in several ways. For the real-time monitoring of batch reactions, the first and simplest

approach is to carry out a reaction directly in an NMR tube. For reaction timescales of several minutes or more, this requires no special equipment. However, the absence of stirring means that the reaction conditions are not the same as in classical batch synthesis, which may lead to different results.[9] Also, some common steps such as progressive addition or illumination are complicated to implement. Online monitoring by flow NMR is an alternative approach that provides real-time monitoring of a reaction carried out in a batch reactor that enables stirring, temperature control, etc.[4,10-12] In this approach, the reaction mixture is continuously pumped to and from the spectrometer through capillaries. Flow NMR has, for example, proved useful for the analysis of diverse catalytic reactions.[13-19] Together with supervised chemometric methods, it can provide quantitative data from complex mixtures.[20]

Reaction monitoring is also essential in the emerging field of flow synthesis, which provides improved reaction control and straightforward automation.[21,22] Flow NMR can be very helpful for the in-line monitoring of such flow reactions.[12] In this approach, the flow transfer line is connected to the reactor outlet and the crude mixture continuously flows to the NMR flow cell. NMR spectra are then recorded, and peak volumes are used to track the concentration of a compound of interest. This approach ultimately offers the possibility to develop autonomous flow reactors, for which data are processed and used in a feedback loop. For instance, both benchtop and high-field NMR spectrometers have been integrated as an in-line analytical tool into self-optimizing reactors.[23,24]

NMR spectroscopy is also the workhorse method for structure verification in chemical synthesis, and such verification typically relies on NMR spectra of relatively pure compounds. This is in contrast to the mixture spectra that are obtained through reaction monitoring. Consider, for example, 1D ¹H NMR experiments,

Y. Horbenko, M. Jaudronnet, N. El Sabbagh, M. Bazzoni, A. Bernard,

P. Giraudeau, F.-X. Felpin, J.-N. Dumez

Nantes Université

CNRS

CEISAM UMR 6230

F-44000 Nantes, France

E-mail: Francois-Xavier.Felpin@univ-nantes.fr

Jean-Nicolas.Dumez@univ-nantes.fr

M. Nilsson

Department of Chemistry

University of Manchester

Oxford Road, Manchester M13 9PL, UK

<figure><img src="image_3.png" /></figure>

Supporting information for this article is available on the WWW under https://doi.org/10.1002/ceur.202500038

<figure><img src="image_4.png" /></figure>

© 2025 The Author(s). ChemistryEurope published by Chemistry Europe and Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
<figure><img src="image_5.png" /></figure>

the most commonly used NMR experiments for reaction monitoring applications. For most reaction mixtures, these spectra almost always display some degree of overlap between spectra from different compounds. While the presence of a single resolved peak for a given compound makes it possible to quantify that compound, spectrum overlap is an obstacle to the recovery of full clean spectra (as if from pure compounds).

Several unsupervised chemometric tools are available that can yield, from reaction monitoring data, the spectra and kinetic curve (i.e., concentration changes) of the compounds involved in the reaction.[25] For example, multivariate curve resolution (MCR) has been applied to decompose chromatographic data.[26] However, MCR and other bilinear methods feature a rotational ambiguity problem, meaning that there exists an infinite number of mathematically valid solutions to the unmixing problem, which prevents finding the one that has chemical meaning.[27] While the use of constraints may help to address this ambiguity, an alternative consists of using approaches that yield a unique solution.

Multiway analysis, which relies on higher-dimensional data sets (3 dimensions or more) to avoid rotational ambiguity, and provide a unique solution, has led to many applications in chemistry. For example, parallel factor analysis (PARAFAC) that was first introduced in phonetics and psychometrics,[28,29] and popularized by Bro and co-workers for chemometrics, is now used to interpret the fluorescence of natural organic matter.[25,30] A formally equivalent canonical polyadic decomposition (CPD) algorithm, commonly used for signal processing,[31] was successfully applied to the fluorescence signal processing.[32] The Manchester NMR methodology group has shown that PARAFAC/CPD can be used to decompose a variety NMR data sets that have three dimensions.[33-38] In particular, they showed that for time-series of sets of diffusion-weighted NMR spectra obtained for sugar hydrolysis reactions, due to its trilinear structure, can be decomposed into 1D spectra, kinetic curves and diffusion decays.[35,36]

In NMR spectroscopy, diffusion weighting is achieved by applying a pair of pulsed magnetic-field gradients separated by a delay. A key feature of this approach is that signals that originate from the same molecule experience the same degree of attenuation. This is exploited in univariate[39] and multivariate[40] analysis of diffusion NMR data, It is also central to the use of PARAFAC/CPD. Therefore, multiway analysis of diffusion NMR data can be a powerful method to obtain clean NMR spectra from a reaction mixture. There are, however, severe obstacles to its use for flowing samples.

For the algorithmic decomposition of reaction components to be successful, the monitoring data must satisfy the trilinearity hypothesis, otherwise PARAFAC yields a chemically meaningless solution. For time-resolved diffusion NMR, this mainly means that, for each component, the (rescaled) NMR spectrum and the diffusion coefficient must remain the same across the entire series of diffusion-weighted spectra. Also, for each component, the diffusion attenuation and the kinetics must remain the same across the entire spectrum, but these conditions are virtually always verified and form the motivation to use PARAFAC to analyze time-resolved NMR data. In practice, a number of contributions that include field instability, flow effects, and the use of non-deuterated solvent, can act to break the trilinearity hypothesis.

Herein, we show how multiway analysis of time-resolved diffusion NMR data can yield the 1D ¹H spectra of compounds formed in the reaction, for several batch and flow click reactions that were monitored using flow NMR. The resulting clean spectra are obtained directly from the reaction mixtures, for a variety of diverse and demanding experimental conditions. First, we explain how the approach is implemented, including the selection of an appropriate NMR pulse sequence, the processing steps that are required for multiway analysis, and the model employed to retrieve pure spectra. Then, we describe three applications to the analysis of click reactions, monitored with different setups. In each case, multiway analysis provides the 1D ¹H spectrum of the product of the click reactions along with its diffusion attenuation curve, and concentration profile. For the online monitoring of batch reactions, kinetic curves are also obtained from the multiway analysis, with good time resolution. In the case of in-line monitoring of flow reactions, a minimum number of 2 runs was found to yield a clean separation of the mixture spectra. These results illustrate the potential of time-resolved diffusion NMR data and multiway analysis to yield clean spectra directly from reactions carried out in conditions that are relevant but that also make NMR acquisition challenging. This approach may notably serve to advance automated and autonomous batch and flow synthesis.

## 2. Results and Discussion

### 2.1. General Strategy

In this work we selected Copper-Alkyne-Azide-Cycloaddition (CuAAC) reactions (Scheme 1) as benchmark transformations due to their prevalence in research fields such as chemical-biology and material sciences.[41,42] The cycloaddition of organic azides on alkynes, leading to triazole heterocycles, was monitored by time-resolved diffusion NMR. The main objective was to recover the 1D ¹H spectrum of the newly formed heterocycles, directly from the reaction mixture.

The general procedure is described in Figure 1. It consists of first carrying out a reaction and collecting time-resolved diffusion NMR data—the number of time points will depend on how the reaction is carried out and monitored. A data “cuboid” (a rank 3 tensor) is then constructed with three dimensions: reaction time, chemical shift, and gradient amplitude. The data are then carefully processed and a number of components are chosen. Finally, the data is fed to the PARAFAC algorithm to obtain 1D spectra of reactants and a product, concentration profiles, and diffusion profiles.

Formally, PARAFAC consists of decomposing the data X into the three loading matrices (A, B, and C), which minimize the sum of squares of the residuals $e_{ijk}$

$$x_{ijk} = \sum_{f=1}^{F} a_{if}b_{jf}c_{kf} + e_{ijk} \quad (1)$$

where F is the number of components, $x_{ijk}$ is an element of X, and X has size ($l \times m \times n$), $a_{if}$ is an element of A, and A has size ($l \times F$), $b_{jf}$ is an element of B, and B has size ($m \times F$), $c_{kf}$ is an element of C,
<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /><figcaption>**Scheme 1.** The Copper-Alkyne-Azide-Cycloaddition reactions, noted A–C), carried out in the experiments.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>**Figure 1.** General strategy: real-time diffusion NMR and multiway analysis yields product spectrum, concentration profiles, and diffusion decays.</figcaption></figure>

and C has size ($n \times F$). If X consists of time-resolved diffusion NMR data, then ideally the loading matrix A (or respectively B and C) contains the 1D spectra (or respectively the concentration profiles and diffusion profiles) of the different compounds in solution. However, while the PARAFAC algorithm virtually always yields some output, that output only has chemical meaning if the time-resolved NMR data meets specific conditions. The ways in which these conditions were met here are described in the following three sections.

The PARAFAC decomposition can be facilitated by applying constraints to the model, such as enforcing non-negativity on one or more modes. As for spectral data, we could assume that

spectra should contain positive peaks. Therefore, the non-negative constraint could be applied on the spectral mode.[43]

## 2.2. Choice of Diffusion NMR Pulse Sequence

Multiway analysis of time-resolved diffusion NMR data relies on the fact that the translational diffusion coefficients of compounds in solution are accurately encoded in the data. However, there are a number of factors that can result in significant systematic or random errors in the measurement. Notably, convection or flow causes the sample to move, leading to errors, and this breaks the
<figure><img src="image_9.png" /></figure>

assumption that the estimated diffusion coefficient does not
change as a function of time for a given compounds. Herein, we
chose to work with the one-shot double-stimulated echo (DSTE)
pulse sequence shown in Figure S1, Supporting Information,
using an encoding gradient that is orthogonal to the main direc-
tion of the flow (the relevance or using a probe with triple-axis
gradients for flow NMR has been demonstrated for several
applications).[44-46] This pulse sequence combines two approaches
to mitigate the effect of sample flow, and was recently shown to be
effective for flow rates of up to 3 mL min⁻¹.[45]

The one-shot DSTE pulse sequence also makes it possible to
collect full diffusion decay curves in 2 min. This is achieved thanks
to the use of orthogonal coherence transfer pathway (CTP) selec-
tion gradients, which make CTP selection possible in only 1 scan
per diffusion increment.[45] Such short experimental time is key to
the use of multiway analysis in this investigation. Indeed, if sam-
ple composition changes significantly between two gradient
increments in a diffusion data set, then the trilinearity hypothesis
is also broken. The results shown in Section 2.5–2.7 show that the
one-shot DSTE pulse sequence yields data of high enough quality
for multi-way analysis, even in the challenging case of a continu-
ously flowing sample.

**2.3. Data Processing**

Multiway analysis of time-resolved diffusion NMR data is also
highly sensitive to spectral quality. This includes the peak shapes,
as well as their phase and position. Any change in shape, phase or
position results in a deviation from the trilinearity hypothesis, and
thus reduces the quality of the spectral separation. These issues
were relatively small in the work of Nilsson et al.[35,36] which con-
sidered reactions carried out in an NMR tube, using a deuterated
solvent, and with compounds that yield peaks in a narrow spec-
tral band and without frequency shifts; though even so the data
benefited by the use of reference deconvolution[47] to correct for
small changes during the reaction. On the contrary, the click reac-
tions shown in Scheme 1 display all three types of errors more
strongly. This is especially true in flow NMR conditions, because
of the use of non-deuterated solvents. While solvent signals can
be efficiently suppressed, for example, with a water suppression
enhanced by T₁ effects (WET) block that can be incorporated into
the one-shot DSTE sequence,[48,49] the absence of deuterium
means that field-frequency locking as well as automated shim
tuning cannot be used.

The different types of errors that are observed in time-resolved
diffusion NMR data are shown in **Figure 2**. First, as can be seen in
panel b, there is a gradient-dependent phase distortion. While this
would often be innocuous in a DOSY-type analysis of the data, it is
detrimental in multiway analyses and can be corrected by individ-
ual (rather than global) phasing of the 1D spectra. This procedure
was automated here by defining the phase correction for each dif-
fusion increment and then applying the phase correction array to
all diffusion data sets. Second, peak shapes can change as a func-
tion of time, because of uncompensated changes in field inhomo-
geneity (Figure 2c). This can be corrected by the reference
deconvolution procedure.[47] The only requirement is the presence

of a reference singlet signal, which is present at a sufficient ampli-
tude in all spectra, including highest gradient amplitude. Herein,
we chose to work with 1,3,5-trimethoxybenzene (TMB) because
it is inert in the reaction studied and has a well separated peak.
Reference deconvolution also compensates for global spectral
shifts, which are common when not using field-frequency lock.

Finally, some peaks tend to shift within the data set because
of the possible temperature drift or chemical reaction itself

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /></figure>

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /><figcaption>**Figure 2.** a) Experimental diffusion dataset of flow NMR data; b) spectral region showing phase distortions; c) spectral region showing a line shape distortion; d) spectral region showing a peak shift.</figcaption></figure>
<figure><img src="image_14.png" /></figure>

(Figure 2d). The interval correlation optimized shifting (ICO-Shift) algorithm permits to efficiently align peaks in large datasets.[50] ICO-Shift is based on splitting spectra into intervals and shifting each vector to be as close as possible to a reference spectrum.

Data processing and analysis were mostly performed using the GNAT software. The compiled version, which does not require a license, is available on the website of the Manchester NMR methodology team.

## 2.4. Choice of a Two-Component Model

Besides the cuboid of time-resolved diffusion NMR monitoring data, PARAFAC requires as an input a single number, corresponding to the number of components F in the decomposition given in Equation (1). For the click reactions studied here, three organic molecules (2 reactants and 1 product) take part in the reaction and one may in principle aim for three-component PARAFAC (the reference compound is excluded from the analysis, since its peaks appear in known and otherwise empty regions of the spectrum). However, the two reactants have identical kinetic profiles, as they have the same starting concentration and very similar diffusion coefficients, and are therefore well described by a single PARAFAC component, making it easier to obtain the desired data from the product with a two-component PARAFAC model. With this approach, previously used for the hydrolysis of sucrose,[36] decomposition is successful if one of the two components combines the spectra of the two reactants, while the other component provides information on the product.

## 2.5. Monitoring in an NMR Tube

Monitoring in a tube is usually the first step in studying a new reaction by NMR. It helps to get an idea of how a reaction is progressing and to evaluate the quality of NMR data for specific needs. To test the performance of PARAFAC on the monitoring data of the click reactions, we started with reactions carried out in an NMR tube. Reactions were carried out in either 3 or 5 mm tubes, and the results were found to be comparable in both cases (see Figure S4, Supporting Information). The temperature needed to be stabilized to minimize any temperature drift.

The monitoring data shows that the concentration curve of the product from reaction A almost reached a plateau in 2 h, reaction B in 3 h and reaction C in 30 min. In comparison, the time needed to acquire a complete diffusion NMR data set was approximately two minutes, thus providing good time resolution. Even for such favorable conditions, with field-frequency locking and automated shimming, the acquired diffusion datasets required separate 1D spectra processing for phase and baseline correction. Alignment was also found to be necessary, and the ICO-Shift algorithm was run for either automatically or manually defined regions (based on visual inspection). For reference deconvolution, one of the peaks of TMB, at 3.65 ppm, was used, with a line-width chosen to avoid wiggles after deconvolution. The spectral regions containing the solvent and internal reference peaks and the edges of the spectra were not included in the analysis.

The results of multiway analysis of time-resolved diffusion NMR data for reaction A carried out in an NMR tube are shown in **Figure 3**. One can see in Figure 3a that the analysis resulted in

<figure><img src="image_15.png" /><figcaption>**Figure 3.** Two-component PARAFAC decomposition of data from reaction A (see Scheme 1) directly in an NMR tube (products – blue, reactants - orange). a) Spectra b) concentration profiles (compared to 1Ds ¹H integrals), c) diffusion decays.</figcaption></figure>
<figure><img src="image_16.png" /></figure>

clean spectra, for the product in one component, and for the two reactants in the other component. In particular, the region around 7.4 ppm that contains overlapping peaks is well separated. The intensity of the cross-talks (found, e.g., at 2.8 and 4.3 ppm) does not exceed 5% of the highest peak in the spectra.

Multiway analysis also yields the concentration time curves, which in this case can be compared against peak integrals from a time series of 1D ¹H experiments (these were interleaved with diffusion NMR experiments). When they are scaled to their maximum value, the two are found to be in virtually perfect agreement. Diffusion NMR thus yields relative concentrations, which then require calibration to obtain absolute concentrations. The diffusion decay curves are also obtained from the analysis. When fitting that of the product with the Stejskal–Tanner equation, a value of $14.6 \times 10^{-10} \text{ m}^2 \text{ s}^{-1}$ is obtained, which is within 3% of a reference value obtained from separate diffusion-ordered spectroscopy (DOSY) analysis. The difference in the diffusion coefficients of the reactants and the product was sufficient to

give satisfactory results. This further validates the success of the multiway analysis in this case.

Comparable results were obtained with reactions B and C, and are shown in the Supporting Information.

## 2.6. Online Monitoring of Batch Reactions

Online monitoring by flow NMR makes it possible to carry out the synthesis in a flask while continuously sending a portion of the crude mixture to the NMR spectrometer for data acquisition. The NMR pulse sequence used in the experiment plays a major role to mitigate flow effects and its implementation is greatly facilitated by the use of a triple-axis gradient probe. However, accurate results can still be obtained with a single-axis gradient probe using low-pulsation pumps and convection compensation, as reported by Thomlinson and co-workers.[51]

Each of the click reactions shown in Scheme 1 was performed in a flask with continuous stirring of the reaction mixture. The

<figure><img src="image_17.png" /><figcaption>**Figure 4.** Two-component PARAFAC decomposition of data from reaction B (see Scheme 1) in a flask and monitored by flow NMR (products - blue, reactants - orange). a) The experimental setup consisted of the flask in which the reaction took place, the pump that delivered the reaction mixture to the spectrometer for analysis, b) spectra, c) concentration profiles (compared to 1Ds ¹H integrals), and d) diffusion decays.</figcaption></figure>
<figure><img src="image_18.png" /></figure>

sample was pumped using a peristaltic pump to the NMR spectrometer and the data were acquired in continuous flow. Particular attention was paid to data processing as this case is the most demanding in terms of data correction. Data processing included all of the above steps, that is, individual phasing and baseline correction, alignment and reference deconvolution.

The results of PARAFAC analysis of time-resolved diffusion NMR data for reaction B carried out in flask and monitored by flow NMR are shown in **Figure 4**. Also, in this case very good separation was achieved between the product and the two reactants. The intensity of the cross-talk does not exceed 8% of the highest peak in the spectra. This is in spite of the factors (non-deuterated solvent, flowing sample) that are particularly difficult for diffusion experiments, and which were counteracted through careful pulse sequence design and data processing.

The region around 2 ppm displays some baseline distortion, which originate from imperfect solvent signal suppression. Another detrimental consequence, in this case, of working with

non-deuterated solvents, is the suppression of signals that are close to the solvent signal. In Figure 4b, one can note that proton *d* is absent in the product spectrum. The same consequence can be seen for the reaction C in Figure S7, Supporting Information.

The kinetic curves obtained with multiway analysis, in the case of online monitoring by flow NMR are also here in good agreement with those obtained from 1D ¹H experiments. For reaction B, fitting of the diffusion decays obtained from the multi-way analysis yielded a coefficient of 12.0 × 10⁻¹⁰ m² s⁻¹ which differs by less than 1% from the reference value obtained with DOSY analysis. Overall, provided that the data are suitably processed, excellent separation is obtained also in the case of online monitoring by flow NMR.

## 2.7. In-Line Monitoring of Flow Reactions

In flow synthesis, chemical reactions occur while the sample is transported through capillaries. In-line analysis, meaning that

<figure><img src="image_19.png" /><figcaption>**Figure 5.** Two-component PARAFAC decomposition of data from the reaction C (see Scheme 1) from a flow synthesis (products - blue, reactants - orange). a) The experimental setup consisted of two stock solutions of reactants, two pumps, the mixing point, a flow reactor and the spectrometer, b) spectra, and c) diffusion decays.</figcaption></figure>
<figure><img src="image_20.png" /></figure>

the entirety of the reactor output traverses the detector, is well suited to monitor the outcome of a flow reaction. Here we used the setup schematized in **Figure 5**, in which the two reactants (one of them already mixed with the catalyst) are pumped continuously at a fixed flow rate through the reactor and the detector. In this approach, the composition of the sample in the detector does not change in time. Different residence times, corresponding to different flow rates, are thus obtained with different, independent runs. Data acquisition is possible either in continuous flow, or by interrupting the flow if the acquisition is fast compared to the reaction kinetics.

Flow synthesis typically involves a sequence of multiple runs to, for example, probe the influence of a reaction parameter such as the residence time. Here we sought to determine the minimum number of time points needed to achieve spectrum separation with multiway analysis. In this case, we found that two diffusion data sets, obtained at different residence times were sufficient to obtain the product spectrum. The resulting spectra and diffusion decays are shown in Figure 5 for reaction C (Scheme 1), using data sets obtained for 7- and 14-min residence times. Again, the quality of the resulting spectra is very high, with a level of cross-talk which was only 3% of the highest peak in the spectra. While the residence times had to be chosen to be sufficiently different, one can observe, by picking pairs of data sets from the online monitoring data, that there is a broad tolerance on the choice of reaction times.

Interestingly, in the case of reaction C, the diffusion decays that are obtained with PARAFAC are not smooth. This is particularly evident in the tube and online cases for this reaction (see Supporting Information). There are several possible explanations for this. The two reactants have significantly different diffusion coefficients and therefore decay at different rates, partly violating the multilinearity hypothesis. The resulting diffusion curve can therefore be expected to be a compromise between the two diffusion decays of the reactants. In addition, the diffusion decay of the product is also not smooth, which is also to be expected as the PARAFAC components are not independent. Another possibility is that in this case the change in concentration that occurs during the diffusion NMR experiment also plays a role. In fact, the fitting of the diffusion decays obtained with PARAFAC gives an estimated diffusion coefficient of $13.6 \times 10^{-10} \text{ m}^2 \text{ s}^{-1}$ for the product, which differs by 5% from the reference value obtained by DOSY analysis. In spite of these limitations, very good separation of the spectra is achieved suggesting that the method is reasonably robust toward some partial violations of the multilinear requirement of the PARAFAC mode.

## 3. Conclusion

We have shown that multiway analysis of time-resolved diffusion NMR data makes it possible to obtain clean 1D 1H spectra of newly formed compound, directly from a reaction mixture, for several click reactions monitored in diverse and challenging experimental conditions. Examples were shown for batch reactions carried out in an NMR tube, for batch reactions carried out in a flask and monitored by flow NMR, and for flow reactions

monitored by flow NMR. The approach relies on fast and robust diffusion NMR experiments, together with processing steps to account for experimental deviations of spectral parameters. In the case of batch reactions, the analysis also yields accurate concentration time curves. For flow synthesis, it was found that two runs at two different reaction times were sufficient to achieve spectral separation, making the method efficient. The proposed approach to obtain clean spectra of newly formed product is thus applicable to a diverse range of experimental setup, and has significant potential for applications in reaction monitoring and autonomous chemical synthesis.

## Acknowledgements

This work has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (grant agreements no 801774/DINAMIX and 814747/SUMMIT) the Region Pays de la Loire (Connect Talent HP NMR), the Agence Nationale de la Recherche (ANR-21-CE07-0056-02), the I-SITE NexT (iChem4.0) and a Royal Society International Exchange Scheme (IES/R1/221028). The NExT initiative is supported by Nantes Université, the Région des Pays de la Loire and Nantes Métropole in the frame of the Programme d'Investissement d'Avenir (PIA). The authors also acknowledge the French National Infrastructure for Metabolomics and Fluxomics MetaboHUB-ANR-11-INBS-0010 (www.metabohub.fr) and the Corsaire metabolomics core facility (Biogenouest). This work includes NMR experiments carried out on the CEISAM NMR platform.

## Conflict of Interest

The author declare no conflict of interest.

## Author Contributions

**Yuliia Horbenko:** conceptualisation; software; data curation; investigation, validation; formal analysis, visualization; writing—original draft. **Mathias Nilsson:** conceptualisation. **Patrick Giraudeau:** conceptualisation; Supervision. **François-Xavier Felpin:** conceptualisation; Supervision; project administration. **Jean-Nicolas Dumez:** conceptualisation; project administration; Supervision; writing—original draft. **Martin Jaudronnet:** investigation, validation. **Nour El Sabbagh:** investigation, validation; software. **Margherita Bazzoni:** investigation, validation. **Aurélie Bernard:** resources. All authors: writing—review and editing.

## Data Availability Statement

The data is available on Zenodo: https://doi.org/10.5281/zenodo.14281507.

**Keywords:** click chemistry · diffusion nuclear magnetic resonance · multiway analysis · nuclear magnetic resonance spectroscopy · parallel factor analysis
<figure><img src="image_21.png" /></figure>

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Manuscript received: February 18, 2025

Revised manuscript received: March 24, 2025

Version of record online: April 24, 2025