ShimNetV2‐RM Neural Network for Post‐Acquisition Correction of Spectral Lineshapes in NMR Reaction Monitoring

ABSTRACT

NMR can be used to monitor reactions in situ, typically by acquiring a series of standard one‐dimensional spectra at regular intervals. However, the experimental setup is more demanding than for stable, nonreacting samples. For example, the usual pre‐acquisition correction of magnetic field homogeneity, known as shimming, can sometimes be too time‐consuming to be repeated before each spectrum in a series. This results in a gradual increase in spectral lineshape distortions during the reaction. Fortunately, the spectra can be improved to some extent by applying post‐acquisition corrections. We propose replacing the standard semi‐manual reference deconvolution method with a neural network called ShimNetV2‐RM. Our method, previously developed under the name ShimNet for standard nonreacting samples, can be tailored for reaction monitoring by constraining training parameters using well‐shimmed pre‐ and post‐monitoring spectra. To demonstrate the applicability of the proposed approach under realistic and demanding conditions, we applied ShimNetV2‐RM to two representative copper‐catalyzed azide‐alkyne cycloaddition (CuAAC) reactions.

Use ShimNetV2‐RM neural network to correct distorted lineshapes in the in situ reaction monitoring data! During long reactions, the magnetic field homogeneity can degrade. The proposed approach effectively addresses this problem, restoring narrow lineshapes.

1. Introduction

Among the many applications of nuclear magnetic resonance (NMR) spectroscopy, in situ reaction monitoring is the area in which the technique's strengths are most evident [1, 2]. First, under relevant measurement conditions [3, 4], the NMR signal is directly proportional to the amount of material present. Thus, no calibration is required to determine concentrations. Secondly, because NMR is a noninvasive method, the determined reaction time profile can be relied upon. Furthermore, chemical shifts and multiplicities are directly related to structure, enabling the identification of substrates, products, and intermediates.

The most straightforward approach to NMR reaction monitoring is to acquire a series of one‐dimensional spectra and use the integrals to determine the reaction progress [2, 5]. If an extraordinary resolution is required, two‐dimensional (2D) spectra can be used, in which nonuniform sampling (NUS) is particularly beneficial (see, for example, [6]). The 1D signals and 2D increments can be collected interleaved [7], allowing corrections for effects such as relatively rapid changes in chemical shifts [8]. Ultrafast techniques can further accelerate experiments, providing precise snapshots of the reaction [9].

However, time‐resolved NMR experiments can be more demanding than “stationary” ones, since sample properties may change between consecutive spectra in a series. In particular, the sample's magnetic susceptibility may be affected by the concentration and temperature gradients. These effects degrade the magnetic field homogeneity, leading to distorted lineshapes. Moreover, in longer experiments, the natural drift of the field generated by the spectrometer magnet and shim coils degrades spectral resolution. The latter effect depends on hardware stability and is also problematic for nonreacting samples.

The usual remedy for the problem is to compensate for inhomogeneity with a set of correction coils (“shims”). However, it involves adjusting the electric currents for several minutes (even when automated, e.g., by gradient shimming [10, 11, 12]). Therefore, it might be too impractical to update shims between consecutive spectra in a time‐resolved experiment, if dense sampling of the reaction progress is necessary. Consequently, the spectral resolution may be compromised, potentially leading to biased kinetic profiles determined from integrals of overlapping peaks.

Various solutions to the problem of degrading field homogeneity have been proposed. Firstly, the data acquisition can be improved. For example, the effect of magnetic field inhomogeneity can be alleviated by the spatially‐selective and frequency‐shifted acquisition [13, 14] as inhomogeneities are less pronounced in smaller volumes [15]. Alternatively, the use of the echo‐based MR‐SHARPER pulse sequence enables removing even residual inhomogeneities and approaching natural linewidths [16].

If the collected spectra exhibit distorted lineshapes, dedicated spectral analysis methods can be used to address resolution issues. For example, the Wasserstein metric is particularly useful in this context, enabling a quantitative decomposition of a mixture spectrum into component spectra [17]. The method can also be applied to reacting mixtures, allowing the determination of kinetic profiles from spectra heavily distorted by a lack of shimming, locking, or temperature instabilities [18].

Finally, spectral lineshape distortions can be removed using dedicated post‐acquisition signal processing. The simplest approach is a reference deconvolution (RD), in which distortion is determined from a manually selected, well‐separated peak whose theoretical, “perfect” lineshape is assumed [19, 20, 21, 22]. The method is effective if the signal‐to‐noise ratio is sufficient, and the peak's “ideal” parameters are properly guessed. Otherwise, RD may even introduce further distortions, such as baseline artifacts. The approach to RD exploiting an internal standard with known lineshape parameters allows for alleviating this problem [23]. It is also noteworthy that the reference signal used for RD need not be a singlet [24]. The concept of RD can be improved and automatized using machine learning (ML) methods, such as RH‐Unet, which requires peak‐picking but not strict parameter guessing [25]. Another ML‐based approach, developed in our group, is a neural network called ShimNet [26]. It is trained using experimental lineshape distortions measured on a given spectrometer, which are then convolved with the simulated spectra to train the network.

In this paper, we demonstrate how to improve the architecture of ShimNet (the upgraded version is called ShimNetV2) and adapt the neural network training to enhance the correction quality of typical spectra in NMR reaction monitoring (ShimNetV2‐RM). We exploit the fact that peak parameters can be estimated from well‐shimmed spectra acquired before and after the reaction. Then, we train a dedicated network for each series of spectra (i.e., each reaction). We tested our approach in two representative copper‐catalyzed azide‐alkyne cycloaddition (CuAAC) reactions. These are examples of prototypical click chemistry, which is often used in modern organic synthesis to prepare 1,4‐disubstituted 1,2,3‐triazoles with high yield and regioselectivity. This class of reactions requires complex kinetic analysis and mechanistic interpretation because reactive intermediates form rapidly and depend strongly on the copper catalyst [27, 28]. CuAAC reactions are also the basis of a wide range of applications in analytical chemistry [29, 30], bioorthogonal chemistry [31, 32], and materials science [33, 34], in which precise reaction monitoring is very important for reliable kinetic characterization, understanding structure–property relationships, and optimizing functionalization strategies.

2. Methods

2.1. Sample Preparation for CuAAC Reaction Monitoring

The effectiveness of ShimNetV2 and ShimNetV2‐RM was verified on spectra from in situ monitoring of two CuAAC reactions. The first one involved benzyl azide A and a phenylacetylene B, yielding a compound with a single triazole ring C. The second reaction was between the same azide A and an octa‐1,7‐diyne D, yielding a product with two triazole rings E (Figure 1).

FIGURE 1.

Schemes of the copper(I)‐catalyzed azide‐alkyne cycloaddition (CuAAC) reactions used in this study. The upper left panel shows the scheme of reaction between benzyl azide A and phenylacetylene B, which yields 1‐benzyl‐4‐phenyl‐1H‐1,2,3‐triazole C. Upper right, the scheme of reaction between benzyl azide A and octa‐1,7‐diyne D, resulting in the formation of 1,4‐bis(1‐benzyl‐1H‐1,2,3‐triazol‐4‐yl)butane E. Below H NMR spectra recorded before and after reaction monitoring. The concentration was reduced tenfold for samples before the reaction (upper spectra) and fivefold for samples after the reaction monitoring (bottom spectra). All spectra were measured on a 600‐MHz Agilent NMR spectrometer.

The reaction yielding compound C is well described in the literature and has been studied by NMR [28, 35, 36]. For the second reaction, octa‐1,7‐diyne D was chosen for its easy availability, good stability, and the few NMR‐based studies on the reaction products reported in the literature (see SI in [37]). The reaction with a diyne is expected to proceed in two steps: the formation of a mono‐addition azide product, followed by reaction at the second alkyne group. This sequential process may therefore yield particularly rich, dynamically evolving data [38].

CuAAC reactions can be initiated by adding Cu(I) ions, e.g., obtained by reducing the Cu(II) ions from CuSO 5H O with L‐ascorbate. In our case, the reduction was carried out in D O, at room temperature. The Cu(I) solution and samples were prepared and measured in an argon atmosphere. The anaerobic conditions were necessary to prevent the oxidation of Cu(I) ion.

The mixtures of substrates, prepared in DMSO‐d , were also deoxygenated under argon. Then, they were transferred to 5 mm screw‐cap NMR tubes and kept under argon. The initial concentrations of both reagents were 20 mM in the azide‐phenylacetylene reaction. In the reaction between azide and octa‐1,7‐diyne, the initial concentrations were 40 and 20 mM, respectively.

Our reactions were initiated by adding $20\mathrm{\mu }\text{L}$ of a Cu(I) D O solution to a DMSO‐d substrate mixture, giving a total Cu(I) ion concentration of 1.6 mM in the sample.

To obtain reference spectra with well‐resolved peaks, we also prepared diluted versions of the pre‐ and post‐reaction mixtures, diluted tenfold and fivefold, respectively. The dilution led to longer $T_2^{\ast }$ relaxation times, resulting in spectra with narrower lines. This helped identify the correct signal pattern, perform reliable peak assignment, and clearly identify the reaction products (Figure 1, compounds C and E). However, performing a reaction at such low concentrations was not feasible on a reasonable timescale.

2.2. NMR Experiments

The reactions were monitored using an array of H NMR experiments, each with a single scan, acquired every 5 s for 5 h (reaction between azide and phenylacetylene) and every 20 s for 13 h (reaction between azide and octa‐1,7‐diyne). All NMR experiments were recorded on an Agilent 600 MHz with a DirectDrive 2 console and a room temperature HCN probe. The spectral width was 9615.38 Hz, the pulse width was $9.1\mathrm{\mu }\text{s}$, and the acquisition time was 1.70 s.

Before initiating each reaction, the well‐shimmed spectrum of the reaction mixture has been acquired. Similarly, after the reaction, the sample was shimmed, and the data were acquired. The measurements were repeated for the diluted samples.

The data processing in Mnova 16.0.0 (Mestrelab Research, S. L., Spain) before reconstruction followed the recommendations from our original work on ShimNet [26], i.e., no apodization was applied, automatic phase correction and zero‐filling to 64k points were used, and the baseline correction was performed using Bernstein polynomial fitting (third order). For the benzyl azide and phenylacetylene reaction, the spectrum was truncated to the region from 8.24 to 4.0 ppm. In the case of the benzyl azide and octa‐1,7‐diyne reaction, the spectrum was truncated to the region from 8.2 to 0.5 ppm. Solvent regions from 3.69 to 3.45 ppm and from 2.54 to 2.40 ppm were zeroed to improve the correction by reducing the intensity range (see [26] for detailed discussions).

To compare the results of our method with the state‐of‐the‐art approach, we additionally processed the spectra with the RD. We used basic deconvolution implemented in MNova 17.0 software with “Suppress zero‐crossing artifacts” option (threshold: 0.50%). The use of this variant was necessary to avoid very strong baseline distortions. The parameters (half‐width and intensity) of the reference peak were obtained by performing Lorentzian line fitting in Mnova using a well‐resolved singlet signal in the well‐shimmed spectra of a mixture of substrates. In the case of the reaction of benzyl azide with phenylacetylene, deconvolution was performed on the signal in the 4.36–4.40‐ppm range, which had an intensity of 14.42 and a linewidth of 2.2 Hz. For the reaction of benzyl azide with octa‐1,7‐diene, deconvolution was performed on the signal in the range of 4.36–4.42 ppm with an intensity of 17.82, a linewidth of 2.3 Hz. The fitted reference peaks are shown in Figure S3.

2.3. ShimNetV2

In this work, we use an enhanced version of ShimNet [26], referred to as ShimNetV2 (Figure 2). The modifications with respect to the original ShimNet are concentrated in the middle block, where local spectral representations in the latent space are transformed into global features that jointly contribute to the input tensor of the decoder. The encoder, decoder, and representation head remain largely unchanged with respect to the previous version. Figure S1 and Table S1 show a comparison of ShimNet and ShimNetV2 performance on an example spectrum, as well as the reconstruction loss on synthetic data, where the “ground truth” is known.

FIGURE 2.

The architecture of the ShimNetV2 and ShimNetV2‐RM neural networks used in this study. The numbers indicate the dimensionality of tensors for a spectrum of length N and a response function length R. MLP stands for multilayer perceptron, conv for convolutional block.

The most important modifications introduced in the middle block are as follows:

• addition of a local feature processor,

• inclusion of learnable key and value projections in the attention block,

• replacement of single‐head attention with multi‐ head attention,

• addition of a global feature processor.

Beyond these major architectural changes, ReLU activations were replaced with GELU, the bottleneck dimensionality was increased from 64 to 128, and the bias term in the final decoder layer was removed to mitigate large training gradients. As a consequence of these changes, the total number of model parameters increased from approximately 220k to 1.6M. Despite this substantial increase in model size, both training and inference times remain manageable: Training speed is limited primarily by the data generator, while inference takes approximately 1 s on a CPU‐only setup.

For clarity, we now describe the information flow through the network step by step.

1. The distorted spectrum is processed by a convolutional encoder using local sliding‐window operations, lifting the input into a latent space. For an input spectrum of length N, the resulting representation has shape (N‐24,L), where L denotes the latent dimensionality, in our case 128. This latent representation encodes both local spectral structure and information about the distorting response function.

2. The attention block acts as a learnable weighting mechanism that aggregates the latent representation into a single global feature vector.

3. An auxiliary response head is trained to reconstruct the distortion response function, which is known during training. Applying this head to the global feature vector encourages the encoder and attention modules to encode relevant global information.

4. The global feature vector and the local features are further processed and concatenated to form the input to the decoder. The global feature vector is broadcast along the spectral dimension so that, at each spectral position, the decoder receives both spatially varying local features and spatially invariant global features.

5. The convolutional decoder reconstructs the clean spectrum by jointly exploiting local and global information.

In addition to the architectural modifications, several training‐related enhancements were introduced. First, the response functions were smoothed using moving‐average filters with multiple weighting schemes (1‐1‐1, 1‐2‐1, 1‐4‐1, and 1‐3‐3‐1). All smoothed variants were included to form an ensemble of response functions used during training. Second, the response functions were temporally stretched by varying their length from $-$20% to +50%. Beyond these major changes, the mean squared error loss was replaced with mean absolute error to increase sensitivity to small deviations, which are critical for accurate peak shape reconstruction. All input spectra were normalized to a fixed scale during training, and the batch size was reduced to meet GPU memory constraints. Other aspects of the training remain the same as in [26], including clean synthetic spectra generation and the collection of shim coil response functions.

From a software perspective, several minor improvements were also implemented in ShimNet, including support for installation via pip, improved modularity of model and data generation, an added training data visualization tool, and other utility features. Github code is available at https://github.com/center4ml/shimnet/tree/reaction‐monitoring‐shimnet‐v2 and ready to use webservice at https://huggingface.co/spaces/NMR‐CeNT‐UW/ShimNet.

Overall, the resulting ShimNetV2 model is substantially more capable than its predecessor. It not only achieves improved performance on the training data but also demonstrates significantly better generalization. In particular, targeted fine‐tuning or de novo training for reaction monitoring yields unsatisfactory results with the original ShimNet, whereas ShimNetV2 performs robustly under these protocols.

2.4. Training for Reaction Monitoring (ShimNetV2‐RM)

Although ShimNetV2 performs reasonably well in the reaction monitoring task, its performance can be further improved through dedicated fine‐tuning (Figure 3). This short training procedure (approximately 1 h) uses the ShimnetV2 model weights, trained on a wide range of spectra, as the starting point (Figure S2 shows the comparison of short and long training results). In the fine‐tuning, we leverage prior knowledge of correct (well‐shimmed) spectra of substrates and/or the final reaction mixture to generate training data that closely resemble the distorted spectra encountered during reaction monitoring. This version of ShimNetV2, tailored for reaction monitoring, will be referred to as ShimNetV2‐RM.

FIGURE 3.

Training data generation scheme for ShimNetV2‐RM. Signals for data training were generated from auto line fitting performed in MNova 16.0.0 (Mestrelab Research, S. L., Spain).

In the first step, peak lists are extracted from clean reference spectra using MNova 16.0.0 auto line fitting. In our case, spectra of both individual substrates and the final mixture are used. To avoid artifacts, broad peaks (> 3.5 Hz) are filtered out. To accelerate training, the effective spectral window is reduced by compressing inter‐peak distances to a maximum of 20 Hz. The corresponding processing script is included in the code base. Each training spectrum contains all peaks from the extracted list, with their parameters randomly perturbed as follows: peak positions by $\pm$5 Hz, peak heights by $-$20% to +30%, peak widths by $-$10% to +20%, and Gaussian fraction by $-$30% to +30%.

Spectral distortions are simulated as described in the original ShimNet paper [26]. Specifically, using the augmented database of 69k recorded shim coil response functions (Section 2), each clean spectrum is convolved with a randomly selected response function, and a small amount of Gaussian noise is added. The model is trained for 7500 iterations with a batch size of 256, corresponding to approximately 2 million spectra processed during training.

3. Results and Discussion

This study presents two reactions that exemplify fairly difficult cases involving the overlap of complex multiplet patterns. On the other hand, their kinetics are slow enough not to affect the lineshapes, i.e., the sample is practically stable on the timescale of a single FID acquisition (1.7 s). However, the linewidths are affected by field inhomogeneity, which continuously increases during the reaction. Thus, the reactions represent cases when spectral resolution degrades due to environmental factors (magnetic field drift) rather than changes in the properties of the sample's ingredients. Figure 4 shows these effects. Panel (a) shows the spectra of the post‐reaction mixture (first reaction)—before and after reshimming, and the well‐shimmed spectrum of the fivefold diluted sample. The latter shows that magnetic field inhomogeneity is not the only reason for line broadening. The full width at half maximum (FWHM) decreases by about 18% after the dilution. Panel (b) shows that the worsening of the magnetic field homogeneity occurs gradually.

FIGURE 4.

The line broadening for the H”(C) signal marked in green in Figure 1 (reaction of azide with phenylacetylene). Peak heights are normalized. Panel (a) shows the peak right after the reaction (FWHM = 2.85 Hz), after reshimming (FWHM = 2.33 Hz), and after fivefold dilution and shimming (FWHM = 1.91 Hz). Panel (b) shows how the linewidth changes during the reaction.

Figure 5 shows the spectra from in situ monitoring of both reactions. Panels (a) and (b) present the well‐shimmed spectra of substrate mixtures and post‐reaction mixtures. These spectra have been fitted as described above in Section 2 to obtain the chemical shifts, peak heights and widths, as well as Gaussian‐to‐Lorentzian proportions. Panels (c) and (d) show that the time scale of the reaction is in the range of hours. Importantly for our tests, the multiplet patterns, especially in the aromatic region, are very complex. In fact, we cannot assume a spectrum to be a combination of specific multiplets, since they cannot be deconvolved from any of these spectra. As described in Section 2, it is better to assume that the spectrum is a superposition of independent singlets. Notably, some peaks move in time (in particular, the resonance at ca. 4.10–4.05 ppm in reaction with phenylacetylene). This motivates randomizing chemical shifts to some extent during the generation of synthetic training data.

FIGURE 5.

H NMR spectra of mixtures before and after the CuAAC reactions: (a) between benzyl azide and phenylacetylene; (b) between benzyl azide and octa‐1,7‐diyne. On the right, Panels (c) and (d) show respective series of spectra collected during reaction monitoring—every 200th spectrum is shown in Panel (c) and every 50th in Panel (d).

The line broadening shown in Figure 4 leads to the loss of subtle multiplet structures and may hamper the interpretation of the spectra, in particular the resonance assignment and identification of the products. Figure 6a,b shows this effect and demonstrates that it can be alleviated using ShimNetV2 and ShimNetV2‐RM. The latter approach is particularly effective, leading to the appearance of peaks marked with arrows. We confirmed their validity by comparing the spectra with those of the diluted post‐reaction mixtures (see Figure 1). All peaks marked with arrows are true resonances, not artifacts. Figures S4 and S5 show kinetic curves for other peaks.

FIGURE 6.

Performance of ShimNetV2 and ShimNetV2‐RM compared to reference deconvolution. (a) Comparison of the raw spectrum corresponding to approximately halfway through the CuAAC reaction of benzyl azide with phenylacethylene with the results of reference deconvolution, ShimNetV2, and ShimNetV2‐RM processing. (b) Similar comparison for the reaction of benzyl azide with octa‐1,7‐diyne. Peaks revealed by the reconstruction are marked with arrows. (c) Peaks' integrals vs. reaction time for the reaction from Panel (a). (d) Peaks' integrals vs. reaction time for the reaction from Panel (b). The integrals were normalized by dividing by the highest integral.

It is interesting to compare the proposed approach with the RD. In the case of studied reactions, RD can be very effective, since the parameters of the reference peak can be obtained from well‐shimmed spectra of substrate mixtures. Indeed, as Figure 6a,b shows, the reference deconvolution narrows the linewidths almost as effectively as ShimNetV2. However, RD is known to introduce baseline artifacts, which are also visible in Figure 6a,b.

Usually, the main goal of in situ monitoring is to determine reaction kinetics, i.e., how the concentrations of substrates and products change over time. These can be determined from the peak integrals. The relative integrals are not significantly affected by line broadening, except in particularly unlucky cases of peak overlap or when integration regions are narrow. Thus, a well‐performing, numerically stable correction method should yield kinetic curves that overlap with those obtained from the raw data. As can be seen from Figure 6c,d, both ShimNetV2 and ShimNetV2‐RM fulfill this requirement. The peak integrals are superimposable with those obtained from the “raw” spectra, with correlation coefficients close to one. Moreover, the peak integrals for both substrates are consistent with their relative concentrations.

Compared to ShimNetV2 and ShimNetV2‐RM, the kinetic curves obtained from spectra processed with RD are less consistent with those obtained from the “raw” spectra. In particular, the difference revealed for the well‐separated signal (first, blue panel in Figure 6c and second, red panel in Figure 6d) suggests that RD distorts kinetic profiles. Indeed, we observed some residual zero‐crossing artifacts, even though we used a regularized version of RD (see Figure S6).

It should be emphasized that applying ShimNetV2‐RM requires training a dedicated neural network for each serial dataset (each reaction). As described in Section 2, the well‐shimmed spectra before and after the reaction must be peak‐picked to generate the training data parameters. However, training time can be significantly reduced (to 1 h in our case) by using weights of ShimNetV2 as a starting point. Moreover, this training scheme yields better reconstruction quality than training from scratch using only the substrates' and products' peak parameters (Figure S2 compares relevant spectra).

4. Conclusions

A homogeneous magnetic field is a prerequisite for obtaining well‐resolved NMR spectra with optimal sensitivity. Updating the correction for magnetic field inhomogeneity during long measurements is necessary, but often too time‐consuming to be feasible. We propose applying post‐acquisition signal processing with a ShimNetV2‐RM neural network to solve this problem. The version of ShimNet presented in this work enables post‐acquisition correction of spectra distorted by magnetic field inhomogeneity that builds up during the reaction, either due to varying sample composition or natural drifts of the spectrometer's magnet. The corrected spectra exhibit better‐resolved peaks still revealing proper reaction kinetics.

Author Contributions

Conceptualization and writing – original draft: K.K., S.J., and M.B. Supervision: K.K. Funding acquisition and project administration: K.K. Methodology: S.J. and M.B. Data curation and analysis: S.J. and M.B. Writing – review and editing: K.K., S.J., and M.B.

Conflicts of Interest

The authors declare no conflicts of interest.

Supporting information

The Supporting Information includes a comparison of ShimNet and ShimNetV2 performance, a comparison of two neural network training strategies for reaction monitoring, additional kinetic plots for both reactions, and a detailed view of RD artifacts.

Data Availability Statement

The raw H NMR datasets from studied reactions are available at https://zenodo.org/records/18474776.

The Code is available on GitHub: https://github.com/center4ml/shimnet/tree/reaction‐monitoring‐shimnet‐v2.