Quantum Mechanical Quantitative Nuclear Magnetic Resonance Enables Digital Reference Standards at All Magnetic Fields and Enhances qNMR Sustainability

Abstract

Quantum mechanics (QM)-driven ¹Hiterative functionalized spin analysis produces HifSA profiles, which encode the complete ¹H spin parameters (“nuclear genotype”) of analytes of interest. HifSA profiles enable the establishment of digital reference standards (dRS) that are portable, FAIR (findable - accessible - interoperable - reusable), and fit for the purpose of quantitative ¹H NMR (qHNMR) analysis at any magnetic field. This approach enhances the sustainability of analytical standards. Moreover, the analyte-specific complete chemical shift and J-coupling information in HifSA-based dRS enable computational quantitation of substances in mixtures via QM-total-line-shape fitting (QM-qHNMR). We present the proof of concept for HifSA-based dRS by resolving the highly overlapping NMR resonances in the experimental spectra (“nuclear phenotypes”) of the diastereomeric mixture of (2RS, 4RS)- and (2RS, 4SR)-difenoconazole (DFZ), a widely used antifouling food additive. The underlying ¹H spin parameters are highly conserved in various solvents, are robust against variation in measurement temperature, and work across a wide range of magnetic fields. QM-qHNMR analysis of DFZ samples at 80, 400, 600, and 800 MHz showed high congruence with metrological reference values. Furthermore, this study introduces QM-qHNMR combined with chiral shift reagents for the analysis of all four DFZ stereoisomers: (2R, 4R)-, (2S, 4S)-, (2R, 4S)-, and (2S, 4R)-DFZ to perform chiral qHNMR measurements.

As ¹H NMR spectra are widely construed as peak patterns with visually derived multiplicities, the underlying accurate NMR parameters, namely, the chemical shifts and coupling constants, are typically assigned by simplistic rules, which are known to not hold true for strongly coupled and overlapping signals. The abundance of “multiplet” annotations in the literature indicates the approximate and relatively incomplete nature of most reported ¹H NMR data. However, since its early conception as part of quantum mechanical (QM) theory and subsequent implementation for chemical analysis by NMR pioneers such as Anderson, Arnold, and Shoolery, as well as other NMR pioneers such as Bloch, Bloom, Packard, and Varian, nuclear magnetic resonance (NMR) spectroscopy has been recognized as a simultaneously qualitative and quantitative analytical method.¹ Considering the established QM foundation of NMR spectroscopy, accurate and comprehensive spin parameter sets are independent of the magnetic field. This provides a superior foundation for digital reference standards (dRS) that are portable from benchtop to ultrahigh field NMR instruments, fully explain even severe overlap and higher order effects in NMR spectra, and can fulfill FAIR (findable, accessible, interoperable, and reusable) principles for the dissemination of analytical and metrological knowledge.²

In the simplistic and most widely practiced 1D ¹H NMR experiment, proper selection of acquisition (AQ) and delay (D₁) times establishes quantitative conditions. This yields ¹H NMR (qHNMR) spectra in which all hydrogens in a sample produce a unity response according to their molarity.³ As direct proportionality holds true even across substances in mixtures, their qHNMR spectra strictly reflect the molar ratios of the chemical species present. This allows the determination of the absolute purity and/or concentration of analytes by comparing their qHNMR responses with those of certified reference materials (CRM) as calibrants with metrological traceability. In qNMR, calibration can be internal⁴ (IC) or external (EC)^5,6 and does not need to be identical with the target analyte(s).

Both the most widely practiced IC- and the less common EC-based methods of absolute qNMR quantitation rely on integration as the quantitative measure (INT-qHNMR).⁷ Accordingly, peak patterns of interest must be sufficiently separated in the spectrum to achieve accurate results. This requirement explains why high magnetic field strengths are widely considered essential for qHNMR. At the same time, it makes it evident why INT-qHNMR methods are more readily implemented for pure, single chemical entities and relatively simple mixtures, whereas assessing complex mixtures is tied to access to ultrahigh field NMR instruments and often still limited in scope. Overcoming these limitations, taking advantage of the unity response and nonidentical calibrant advantage, and fostering a wider adoption of qHNMR as an analytical technique, thus, call for a superior means of separating peak patterns quantitatively.

Moreover, the ideal advanced toolset will also be independent of magnetic field strength while retaining the high specificity and strict quantitative nature of NMR analysis. While existing peak-fitting (PF; see ref (7) and references therein) methods are useful in addressing peak overlap, they depend on empirical deconvolution methods that ignore the underlying QM reality by default.

Founded in QM theory, ¹H NMR resonances are commonly visualized by humans as more or less interpretable peak patterns that are substance-specific and encode the hydrogens in the molecules. Depending on both the molecular spin–spin coupling network and magnetic field strength, individual or overlapping peak patterns result in single or (more often) multiple lines. The relative line frequencies and intensities determine the degree of overlap in the resulting peak patterns, thereby explaining how well the patterns are resolved vs remaining indistinguishable.⁸ In addition to having frequencies and intensities, lines comprise a certain shape and width, collectively referred to as “line shape”. Each nucleus has an intrinsic line shape, and the observed resonance is also affected by magnetic strength and field homogeneity, temperature, molecular dynamic properties, and data processing (apodization). Thus, a typical ¹H NMR spectrum represents the convolution of numerous underlying lines and shapes, forming variably resolved peaks and patterns (see ref (8) for terminology), which are commonly designated as doublets (d), triplets (t), etc., or very frequently as multiplets (m) when too complex.

Fortunately, these convoluted NMR spectroscopic properties can be explained in a much more concise and universal format, i.e., the NMR parameters of the underlying ¹H spin system: the chemical shifts (δ), coupling constants (J), and line shapes (w_1/2, Lorentzian–Gaussian ratio). In their entirety, these parameters describe the spectrum much more accurately and explicitly than the commonly used peak and multiplicity pattern annotations because the parameter sets are intrinsic to the substance and portable across magnetic fields.

Representing what could be termed the “nuclear DNA of a molecule”, NMR parameters describe the “nuclear genotype” of a molecule unambiguously under the given experimental conditions (solvent, temperature, and concentration). Notably, this highly characteristic information can be readily extracted from experimental (q)HNMR spectra (by analogy: “nuclear phenotypes”) by means of QM-based spin analysis (QMSA). Implemented as ¹H iterative functionalized spin analysis (HifSA), a state-of-the-art toolset and workflow for this process has recently been described in detail.⁷ In addition to providing the essential NMR spin parameters, HifSA enables the establishment of digital reference standards (dRS) for both identity and quantity (purity) via QM-based computational methods.

We selected a globally used fungicide, difenoconazole (DFZ), as the model compound for this study (Figure 1). Meeting the additional challenge from the four stereoisomers of DFZ, this study demonstrates how QM-qHNMR can resolve complex peak patterns with severe peak overlap qualitatively and quantitatively, thereby pushing qHNMR analysis beyond the boundaries of INT and PF qNMR methods. The presented workflow involves the step-by-step implementation of HifSA profiles, initially for the diastereomers and subsequently for the enantiomers via a chiral shift reagent as well as QM-qHNMR procedures for the precise quantitation of the stereochemical composition. Furthermore, using the universal ¹H spin parameters of DFZ, we evaluated the accuracy of QM-qHNMR at different magnetic fields. In light of the results, the final discussion addresses the prospects of implementing QM-qHNMR in regulatory science and to build dRS libraries.

Figure 1.

Structures of difenoconazole (DFZ) and Chirabite-AR. Asterisk (*) indicates chiral centers that produce four stereoisomers: (2R, 4R)-, (2S, 4S)-, (2R, 4S)-, and (2S, 4R)-DFZ.

Experimental Section

Materials

Dimethyl sulfone (DMSO₂; cat. no. 048-33271, 99.9% mass fraction), 1,4-BTMSB-d₄ (cat. no. 024-17031, 100.0% mass fraction), acetone-d₆ (cat. no. 012-26681, 99.9% D), and chloroform-d (cat. no. 031-25531, 99.8% D) were from FUJIFILM Wako Pure Chemical Corp. Chirabite-AR (cat. no. C2184) was from Tokyo Chemical Industry Co., Ltd. Three commercial batches of DFZ (FA255-257) were obtained from the Japan Food Additives Association. DFZ reference materials were from Hayashi Pure Chemical Ind., Ltd. (cat. no. 99053174; RM001) and FUJIFILM Wako Pure Chemical Corp. (cat. no. 042-25241; RM002).

General Sample Preparation

The samples were prepared at 20–25 °C and 40–80% relative humidity. Materials stored at 4 °C were first equilibrated to room temperature (RT) using a desiccator with drying silica gel and then left in the sample preparation area for at least 30 min. The weights in milligrams were measured to five decimal places with precision using an ultramicrobalance (XP2U; Mettler Toledo). Volumetric measurements used a calibrated electronic autopipette (Multipette Xstream; Eppendorf). Suitable quantities of DFZ and the IC were placed into a weighing dish (cat. no. W1126-100EA, Sigma-Aldrich), which collectively (dish w/DFZ and IC) was transferred to an empty vial, where 1.0 mL of the deuterated solvent was added, ensuring complete dissolution of the analyte and IC. A precise aliquot (600 μL) of the solution was transferred to an NMR tube and flame-sealed. Table S1 summarizes the sample information.

General NMR Instrumentation

The qualitative NMR experiments were performed on a JEOL JNM-ECZL600G (600.17 MHz for ¹H) equipped with an RT (HFX) probe, regulated at 25 °C, and operated using JEOL Delta v6.1 software. For QM-qHNMR at different magnetic fields, the following instruments were used: for high-field NMR, JNM-ECZL400S (399.78 MHz), JNM-ECZ600R/S1 (600.67 MHz), and JNM-ECZ800R (800.14 MHz), all equipped with RT (HFX) cryogenic UltraCOOL (TH) or UltraCOOL (CH) probes; for benchtop NMR, a Bruker Fourier 80 (80.15 MHz), regulated at 25.0 °C and operated with TopSpin software. Acquisition times (AQ) and the relaxation delays (D₁) were set to at least 4 and 60 s, respectively. Depending on the sample concentration and magnetic field, the number of scans (NS) was 8, 32, or 64 to ensure that the signal-to-noise ratio (SNR) was >1,000. For INT-qHNMR, ¹³C decoupling without sample spinning was applied to collapse the ¹³C satellite signals and avoid spinning sidebands. Conversely, for HifSA and QM-qHNMR, no ¹³C decoupling was applied and samples were spun at 15 Hz for the high-field measurements (see also the Supporting Information).

FID Processing

All FIDs were processed using MestReNova software, v14.2.1 (Mestrelab Research). No window functions were used for INT-qHNMR and the generation of the HifSA profiles. For QM-qHNMR analysis, mild Lorentz-to-Gauss (LG) transformation was employed as the apodization function, with modest line broadening (LB) and Gaussian (GB) parameters, both entered in Hz, avoiding dispersive peaks. Further processing involved the following: zero filling to 512 K data points and manual phase adjustment followed by fifth-order polynomial baseline correction. Chemical shifts were referenced to the residual solvent resonance (δ_H 2.050 ppm for acetone-d₅, 7.260 ppm for CHCl₃).

INT-qHNMR

Precisely weighed (Table S1), about 10 mg of DFZ and 1 mg of 1,4-BTMSB-d₄ (IC) were dissolved in 1.0 mL of acetone-d₆ and then analyzed using a 600 MHz spectrometer. INT-qHNMR measurements used the integral values of the DFZ H-7 peak pattern, relative to those of the Me groups of 1,4-BTMSB-d₄ (Figure S1). The SNR for the DFZ H-7 and Me groups of 1,4-BTMSB-d₄ were greater than 4000 and 40,000, respectively, with no window functions applied. Calculations of the sum of all four DFZ stereoisomers followed eq 1:

1

where the subscripts denote the analyte, the IC, and the sample; Cont, content; A, area; H, number of hydrogens; M, molar mass; m, mass; and P, purity.

HifSA Processing

Precisely weighed, about 40 mg of DFZ (RM002) was dissolved in 1.0 mL of the deuterated solvent (acetone-d₆ or chloroform-d). HifSA was conducted using Cosmic Truth (CT; NMR Solutions Ltd.), a client server-based application (ct.nmrsolutions.io) for iterative functionalized spin analysis of NMR spectra. Upon submission of the JCAMP spectrum and structures of the relevant DFZ stereoisomers in MOL format, CT predicted a set of initial ¹H spin parameters. Subsequent semiautomatic iterative optimization of all δ, J, and line shape parameters was continued until all local root-mean-square (RMS) differences were <0.10. The resulting HifSA profiles explained all overlapping signals and higher-order spin-coupling effects in the spectra. Heteronuclear couplings, ¹J_C,H, were not included in the iterative analysis process.

QM-qHNMR

Precisely weighed, about 40 mg of DFZ and 1 mg of DMSO₂ (IC) were dissolved in 1.0 mL of acetone-d₆ or chloroform-d. FID processing used LG apodization (LB/GB of 0.11/0 Hz for high-field spectra; −0.1/1.0 Hz for low-field) and trapezoidal (80%) window functions. The spectra in JCAMP format and the MOL files of the two DFZ diastereomers and the IC were submitted to CT. The starting values for δ, J, and line widths were taken from the HifSA profiles, and the J values were fixed during the iterations. As the employed qHNMR pulse sequence involved an ample relaxation delay of 60 s, the individual response coefficients of all resonances were fixed at 100% (“FULL”) during the iteration. Finally, the quantitative results were calculated from the population outcomes of the iteration, following eq 2.

2

where the subscripts denote the DFZ diastereomers, DMSO₂ (IC), and the sample (S); Po is the population (molar ratio).

Chiral Chromatography

The four stereoisomers were resolved by high-performance liquid chromatography (LC), carried out on a Shimadzu Prominence HPLC system with an SPD-M20A photodiode array detector. The LC conditions followed previous work.^9,10 The column was a CHIRALCELL OJ-H (4.6 × 250 mm, 3 μm, Daicel Chemical Industries; maintained at 30 °C), and the eluent was n-hexane/ethanol (9:1, v/v), with a 0.8 mL/min flow rate. Precisely weighed, about 5 mg of DFZ was dissolved in 50 mL of EtOH in a volumetric flask, and 10 μL was injected. Diastereomer and enantiomer fractions (DF and EF, respectively) were calculated using the peak area (A) following eqs 3–5.

3

4

5

Reference standards of the four stereoisomers (2 mg each) were isolated and prepared from FA255 using the HPLC conditions described above (Figure S2).

Results and Discussion

Stereochemical Composition of the DFZ Samples

Reference values for the diastereomeric and enantiomeric composition of the five DFZ samples were determined by INT-qHNMR and chiral LC. Nonchiral NMR analysis at high field distinguished the resonances of the two diastereomers. Using the resonances of H-7, the content of DFZ was determined as the sum of both diastereomers (Figure S1). Both the diastereomeric and enantiomeric fractions (DF and EF, respectively) were determined by chiral LC, exhibiting favorable separation performance (Figure S3). The results are consistent with the observed zero specific rotation values (Table S2) and indicate that all DFZ samples were racemic mixtures, making them particularly useful for the verification of QM-qHNMR accuracy (Table 1).

Table 1. Investigated DFZ Samples.

sample	DFZ contenta	DFb	EFAb	EFBb
FA255	95.8%	0.412	0.500	0.501
FA256	95.4%	0.428	0.501	0.501
FA257	95.7%	0.411	0.501	0.501
RM001	99.0%	0.544	0.500	0.501
RM002	99.7%	0.448	0.500	0.501

^aResults from INT-qHNMR.

^bResults from chiral chromatography. All values are the average of three experiments, with an RSD of less than 0.1%.

HifSA of Diastereomers

While the ¹H chemical shifts of DFZ in chloroform-d have been assigned previously,¹¹ the accurate J_H,H coupling constants remain unknown. The essential ¹H spin parameters were determined in two solvents, chloroform-d and acetone-d₆, using the sample with the highest purity (RM002; Table 1). This study confirmed the importance of proper shimming as a prerequisite of high-quality spectra with optimum line shapes. Sample spinning facilitated shimming and access to quality spectra. Moreover, single-pulse acquisition eliminated temperature effects from the ¹³C decoupling and/or other factors from multipulse schemes that frequently affect spectra acquired with cold probes at high fields. Spectra for HifSA were acquired without ¹³C decoupling.

Confirming prior experience, it was important to consider the presence of long-range couplings (LRCs) before starting the HifSA iteration. LRCs can typically be detected and extracted visually in good approximation from the resolution-enhanced spectrum using LB/GB apodization. Figure 2 shows the H-3″ resonance of (2RS, 4RS)-DFZ in acetone-d₆ as an example: resolution enhancement reveals ⁴J, ⁵J, and ⁵J LRCs with H-5″, H-7A, and H-7B, respectively. Such LRCs are easily overlooked when working with nonapodized spectra. Including these “hidden” LRCs in the iterative calculation was instrumental in achieving full documentation of the DFZ spin system as well as reliable magnetic field independence. Efforts aimed at acquiring high-quality spectra from high-field NMR instruments and recognizing and measuring LRCs should be recognized as essential, and awareness for this requirement should be built among analysts. In theory, HifSA is not limited by the size of the spin system and calculational constraints. However, it should be noted that establishing HifSA profiles for significantly larger spin systems clearly requires increasing degrees of spectral understanding and/or operator time investment. Rather than the underlying theory, the limitation of HifSA lies in the amount of information that can be extracted unambiguously from the NMR spectra. High-quality spectra from high-resolution NMR instruments are crucial as increased spectral dispersion and resolution both maximize the amount of accessible information. However, once a HifSA profile of an analyte is established, it can be applied to other samples in full automation.

Figure 2.

Applying strong Lorentzian-to-Gaussian (LG) transformation aids in visualizing small splittings caused by minor LRCs. This facilitates access to J-coupling information for the building of HifSA profiles. Demonstrated here for H-3″ of (2RS, 4SR)-DFZ in acetone-d₆, LB/GB resolution enhancement reveals splitting patterns due to couplings with H-5″, H-7A, and H-7B that are essential for understanding the coupling network and subsequent QM-qHNMR analysis.

Tables S3 and S4 summarize the ¹H spin parameters for acetone-d₆ and chloroform-d solutions, respectively. Multiplicities are reported in first-order annotation based on the true coupling constants derived from the HifSA profiles rather than based on the visual appearance of the resonances. The listed NMR parameters permitted the calculation of separate spectra for the two diastereomers. Their sum spectra agreed exactly with the experimental data in acetone-d₆ and chloroform-d (Figure 3).

Figure 3.

Experimental ¹H spectra of the two DFZ diastereomers in two solvents and their calculated spectra (HifSA fingerprints). The full numerical ¹H parameters (HifSA profiles) are shown in Tables S3 and S4.

Robustness of ¹H Spin Parameters

To assess the feasibility of QM-qHNMR, the robustness of the ¹H spin parameters for DFZ was evaluated. It is known that NMR spectra vary depending on solvent, temperature, and other factors such as pH. The DFZ spectra showed marked differences in the chemical shift and multiplicity patterns (but not the J values) between the acetone-d₆ and CDCl₃ solutions. In CDCl₃, H-3′ resonated at a frequency between that of H-10′/14′ and H-11′/13′, whereas in acetone-d₆, it appeared at lower frequency than H-10′/14′ (Figure 3). Crucially, as expected, the coupling networks and J values were highly conserved between solvents and much less variable than the chemical shift patterns (Figure S4). The largest observed difference was just 0.259 Hz for J_H-4,H-5B in (2RS, 4RS)-DFZ (J values: 8.104 Hz in acetone-d₆ vs 8.363 Hz in CDCl₃).

Regarding line shape, CDCl₃ gave rise to marginally broader lines compared to acetone-d₆, attributed to solvent viscosity. However, the relative line widths across the various peak patterns were similar. This indicated that ¹H spin parameters can be deduced from one solvent and adopted as a template to readily determine HifSA profiles for other solvents.

Evaluating temperature dependence (25.0 °C vs 26.5 °C) revealed only very small differences in both solvents (Figure S5). While the NMR probe sample temperature can generally be unified, such as to 25.0 °C for the present study, the actual temperatures may still differ slightly between NMR instruments, depending on calibration status. The higher operation temperature (e.g., 26.5 or 37.0 °C) of some benchtop instruments with permanent magnets should still be kept in mind. The observed negligible temperature dependence of J values is reassuring for QM-qHNMR. Despite the small impact, proper consideration of temperature dependencies can be addressed by including a QM fitting process for the chemical shifts as relative chemical shifts also affect the peak patterns, often even substantially. Collectively, this study fixed the J-coupling network values during the iterations, thereby reducing the analysis time.

QM-qHNMR of DFZ Diastereomers in Two Solvents

Using the HifSA spin parameters of the pure DFZ diastereomers as templates (acetone-d₆ and CDCl₃; Tables S3 and S4, respectively), QM-qHNMR was performed for five commercial DFZ samples. DMSO₂ was selected as a CRM IC, showing only a singlet resonance, the line shape of which was also used as an indicator for the quality of the spectra. For both QM-qHNMR and HifSA as described above, single-pulse acquisition with sample spinning was performed. FID processing applied exponential multiplication with an LB of 0.11 Hz, which broadened the spectral lines by the amount corresponding to the inverse of twice the acquisition time (4.5 s). LG transformation with an LB/GB of −0.7/0.3 Hz was employed to enhance resolution and confirm the presence of LRCs (Figure 2). As DMSO₂ showed symmetrical and sharp lines in all spectra, with line widths in the range of 0.3–0.4 Hz in both acetone-d₆ and CDCl₃, all spectra were of high quality. QM-qHNMR processing of these spectra using the CT software showed good accuracy and precision in both solvents (Figure S6) and accurate diastereomeric distinction (Table 2).

Table 2. Accuracy of the QM-qHNMR Quantitation of the Diastereomeric Composition of DFZ in Two Solvents at 600 MHz^a.

	acetone-d6
sample	DFZ content	DF
FA255	100.9 ± 0.3%	99.8 ± 0.3%
FA256	100.5 ± 0.1%	99.3 ± 0.4%
FA257	100.6 ± 0.0%	98.3 ± 0.4%
RM001	100.3 ± 0.2%	100.0 ± 0.2%
RM002	100.2 ± 0.4%	101.3 ± 0.3%

	chloroform-d
sample	DFZ content	DF
FA255	100.8 ± 0.8%	99.0 ± 0.2%
FA256	101.0 ± 0.5%	99.4 ± 0.1%
FA257	101.1 ± 0.3%	101.3 ± 0.5%
RM001	100.3 ± 0.2%	99.2 ± 0.1%
RM002	101.2 ± 0.3%	101.5 ± 0.0%

^aAll experiments were conducted in triplicate.

In addition, a ¹³C decoupled spectrum of the purest sample (RM002) acquired without spinning was subjected to QM-qHNMR. The resulting accuracy and precision were equivalent to those of ¹³C-coupled spectra with spinning: the DFZ content and diastereomeric ratio were 100.1 ± 0.2 and 100.8 ± 0.2%, respectively (n = 3 in acetone-d₆). This showed that the occurrence of ¹³C satellites and even spinning sidebands did not distract the QM-qHNMR determinations. In other words, the small isotopic peak patterns as well as the residual spinning sidebands were recognized as impurities by the CT software. However, if the goal was to use QM-qHNMR to quantitate a component with very low abundance to the ¹³C satellites, then it would be advisable to apply ¹³C decoupling and avoid sample rotation.

Effects of Lorentz-to-Gauss Transformations on QM-qHNMR

By default, the spectra subjected to QM-qHNMR analysis applied 0.11 Hz LB and trapezoidal window functions for postacquisition processing. The trapezoid was necessary due to the digital filtering characteristics of the acquisition scheme in the high-field spectrometers. As the use of window functions with nonunity values at time zero has been subject to debate in the qNMR community, this study also evaluated the impact of LG apodization on QM-qHNMR accuracy. Table 3 shows the accuracy of QM-qHNMR upon performing 12 types of LB/GB processing schemes with the same FID from RM002. While increasing(ly negative) LB values intensify GB resolution enhancement, QM-qHNMR accuracy degrades when resolution is emphasized too much. The threshold becomes readily visible as dispersive line shapes (down-wiggles) appear in the spectrum (Figure S7). Interestingly, the resolution benefits of LG apodization are still compatible with accurate quantitation: employing 0.3–1.0 Hz GB in combination with −0.1 Hz or lower LB values yielded accurate results.

Table 3. Robustness of the Accuracy of QM-Quantitation as a Function of Lorentzian-to-Gaussian (LG) Transformations with Various LB/GB Parameters (600 MHz, ¹H; RM002 in Acetone-d₆).

LB/GB [Hz]	DFZ content	DF
0/0.3	99.8%	100.8%
–0.1/0.3	100.4%	100.6%
–0.3/0.3	83.6%	100.9%
0/0.5	100.4%	100.5%
–0.1/0.5	100.6%	100.7%
–0.3/0.5	90.7%	100.4%
–0.5/0.5	77.7%	100.4%
0/1.0	101.2%	100.3%
–0.1/1.0	100.4%	100.1%
–0.3/1.0	95.8%	99.9%
–0.5/1.0	89.9%	100.1%
–1.0/1.0	77.9%	99.3%

Robustness of QM-qHNMR in Suboptimal Spectra

Our collective observations support the conclusion that even spectra with compromised quality can be successfully subjected to QM-qHNMR. Figure S8 shows an example of such a compromised spectrum, exhibiting an inhomogeneous magnetic field. Applying LG processing with an LB/GB of −0.1/1.0 Hz not only covered up this imperfection visually, by yielding apparently symmetric lines, but also did not obfuscate the total-line-shape fitting process of QM-qHNMR. The accuracies of the DFZ content and DF determinations were still acceptable at 99.3 and 98.5%, respectively. This means that QM-qHNMR can utilize spectra processed with certain levels of apodization for imperfection, e.g., when magnetic field homogeneity is compromised and/or measurements cannot be repeated as long as accurate ¹H spin parameters of the analyte are known.

QM-qHNMR across a Range of Magnetic Field Strengths

HifSA profiles are a new form of a dRS as they encode fully assigned ¹H resonances, explain all observed ¹H splitting patterns, and capture all non first-/higher-order effects that occur—even those often ignored at higher magnetic field strengths. Importantly, as QM parameters are portable between different magnetic fields, they can be readily applied for analysis with cryogen-free NMR instruments, thus enhancing the sustainability of NMR in chemical and pharmaceutical analysis.

To establish an example for QM-qHNMR analysis across various NMR instruments, sample RM002 was analyzed across a range of magnetic field strength equivalent to 80–800 MHz ¹H. In the iterative calculations of the 80 MHz spectra, the regions of interest (ROIs) were restricted to ranges where peak patterns were visually distinguishable, for more reliable results (Figure S9). Both the DFZ content and the DF were confirmed to be in good agreement with the reference values, showing less than 2.0 and 0.9% errors, respectively (Table 4).

Table 4. Comparison of the Accuracy of the QM-qHNMR Determination of the DFZ Diastereomer Fraction (DF), for NMR Instruments with Different Magnetic Field Strengths^a.

1H freq	DFZ content	DF
80 MHz	100.5 ± 0.1%	100.9 ± 0.5%
400 MHz	101.7 ± 0.5%	100.3 ± 0.0%
600 MHz	100.4 ± 0.1%	100.9 ± 0.3%
800 MHz	102.0 ± 0.2%	100.1 ± 0.1%

^aSample: RM002 in acetone-d₆; triplicate determinations. HifSA profiles from a separate 600 MHz instrument; J values set as constant.

The remaining four commercial DFZ samples were also examined at 80 MHz. The resulting DFZ content and DF values showed errors below 1.3 and 0.9%, respectively (Table S5). Collectively, these results strongly support the feasibility of developing more sustainable QM-qHNMR assays as well as dRS for molecules with known ¹H spin parameters. This reemphasizes the value of HifSA profiles and raw NMR data sharing as a means of FAIR principles.¹²

QM-qHNMR Combination with the Chiral Shift Reagent

The impact of chirality on the chemistry and biological activity of molecules is well established. In NMR spectroscopy, enantiomers are by default indistinguishable as the corresponding nuclei in both enantiomeric environments have identical electronic surroundings, resulting in the same chemical shifts, J couplings, and line shapes. However, chiral shift reagents can produce enantiomeric dispersion via the generation of diastereomeric adducts (complexes and covalent bonds).¹³ Among available chiral shift reagents, Chirabite-AR contains no paramagnetic metals, which can cause line broadening, and has been reported to work well in CDCl₃.¹⁴ Applied to DFZ, Chirabite-AR addition caused significant enantiomeric dispersion (Figure 4). Accordingly, the chemical shifts of all four stereoisomers could be identified by comparing the spectra of each pure reference standard (1 mg/mL) containing Chirabite-AR (2 mg/mL) in CDCl₃. This led to ¹H spin parameters for (2RS, 4RS)- and (2RS, 4SR)-DFZ, which could be used as templates for the enantiomeric mixtures as follows: (2RS, 4RS) for the set of (2R, 4R) and (2S, 4S) and (2RS, 4SR) for the set of (2R, 4S) and (2S, 4R). Tables S6 and S7 summarize the NMR parameters of Chirabite-AR in the presence of DFZ and the enantiomeric dispersion for (2RS, 4RS)- and (2RS, 4SR)-DFZ in the RM002 sample.

Figure 4.

QM foundation of HifSA combined with chiral analysis enables the resolution of all four DFZ stereoisomers: shown is the experimental ¹H NMR spectrum of high-purity DFZ aligned with the HifSA fingerprints of the individual hydrogens (calculated spectra) of its stereoisomers. The sample was 19.9657 mg/mL DFZ (RM002) containing 10.0664 mg/mL Chirabite-AR in CDCl₃. The full ¹H spin parameters (HifSA profiles) are shown in Table S6 (Chirabite-AR) and Table S7 (DFZ stereoisomers).

Using the iteration results achieved with this template, chiral QM-qHNMR was performed for five DFZ samples at 600 MHz. To minimize analysis time, the ROIs for the iteration were restricted to the ranges where the peak patterns of the stereoisomers were visually distinguishable (Figure S10). The accuracy of the determined DFZ contents and stereoisomeric ratios showed good agreement with the LC- and INT-qHNMR-based reference values, exhibiting differences below 0.9 and 1.0% errors, respectively (Table 5).

Table 5. Accuracy of the QM-qHNMR Quantitation of the Four DFZ Stereoisomers in CDCl₃ with Chirabite-AR as the Chiral Selector^a.

samples	DFZ content	DF	EFA	EFB
FA255	100.9 ± 0.6%	100.0 ± 0.1%	99.6 ± 0.6%	99.4 ± 0.3%
FA256	99.9 ± 0.2%	100.8 ± 0.1%	99.9 ± 0.7%	99.0 ± 0.6%
FA257	100.1 ± 0.1%	101.0 ± 0.3%	99.8 ± 0.5%	99.6 ± 0.2%
RM001	99.7 ± 0.4%	100.0 ± 0.1%	99.9 ± 0.8%	100.1 ± 0.2%
RM002	99.8 ± 0.6%	100.7 ± 0.2%	99.8 ± 1.0%	99.5 ± 0.4%

^aAll experiments were conducted in triplicate.

Conclusions

Accuracy and Validation of QM-qHNMR

This study validated the accuracy of QM-qHNMR using a sample containing all four stereoisomers of DFZ. Achieving total-line-shape fitting of the experimental spectra, QM-qHNMR utilizes the full, compound-specific ¹H spin parameters of the target analyte(s). The process is driven by a software tool capable of iterative calculations involved in quantum mechanical spin analysis (QMSA). This study commenced with the determination of the ¹H spin parameters of the DFZ diastereomers in acetone-d₆ and chloroform-d, using CT as an iterative QMSA tool. Reproducible control of the sample makeup including solvent, measurement temperature, and use of mild LG apodization enabled both highly specific qualitative assignments and highly accurate quantitative analysis. The HifSA profiles developed for DFZ are fit to serve as FAIR digital reference standards (dRS), and their portable nature enhances the sustainable profile of qualitative and quantitative NMR analyses. Therefore, efforts to generate HifSA profiles from a high-quality spectrum obtained from high-resolution NMR instruments are justified. Note that HifSA profiles determined from low-field or excessively broadened spectra may compromise the accuracy and essential portability of dRS.

Throughout the nonchiral validation experiments with DFZ, QM-qHNMR successfully discerned the two DFZ diastereomers with significantly overlapping ¹H NMR spectra and quantified them with a deviation of less than 2% relative to the LC- and INT-qHNMR-based reference values. This level of consistency was achieved across varying magnetic fields, ranging from 80 to 800 MHz. Furthermore, QM-qHNMR effectively separated and quantified all four DFZ stereoisomers without compromising the accuracy of the quantitation. Notably, QM-qHNMR achieved this despite the unavoidable resonance overlap upon addition of the chiral shift reagent, Chirabite-AR.

In this study, chiral composition reference values of the DFZ samples were derived from INT-qHNMR (for absolute content) and chiral LC (for DF/EF_A/EF_B). Expectedly, the results of QM-qHNMR were consistent with INT-qHNMR: both quantitation methods utilized CRMs (DMSO₂/1,4-BTMSB-d₄) as IC, and the content of DFZ was based on the molar ratio relative to the IC. For chiral LC, the reference values, DF/EF_A/EF_B, assume that the response factors of the four stereoisomers are equivalent, which remains a source of uncertainty of the LC-based determination. The DF/EF_A/EF_B results from QM-qHNMR still aligned well with those of chiral LC. Explanation of the observed small deviations will require metrological validation of both QM-qHNMR and the response factors of DFZ in chiral LC, which were beyond the scope of the present study.

Enhancing Analytical Sustainability

Considering the present outcomes as well as the digital and portable nature of HifSA-based dRS, QM-qHNMR has major potential to enhance the sustainability of qualitative and quantitative spectroscopic analyses for both common and rare substances. The sharing of ¹H spin parameters of key analytes via FAIR dissemination practices increases sustainability further and should, therefore, be encouraged widely.

Considering the breadth of applicable health- and food-related products, the impact of QM-qHNMR on sustainability is potentially high as it is directly amenable to the quality control (QC) of food additives, pharmaceuticals, natural products, and herbal medicines. Another advantage of this approach is that, unlike most other analytical methods, it eliminates the necessity to develop, supply, and control (identical) physical reference materials.

As the SNR determines the achievable uncertainly level of both INT- and QM-qHNMR measurements, the sample concentration and NS values yielding relatively high-SNR spectra are conducive to metrology-level analysis, as presented here (see also the Supporting Information). While a systematic comparison of the validation requirements is a topic for future studies, the QM approach has the advantage of deriving quantitative information from multiple resonances. This resolves peak overlap known to limit INT-qNMR and reduces the SNR requirements of QM-qHNMR workflows.

QM-qHNMR in Regulatory Science

As qHNMR is a molar-based SI traceable method, QM-qHNMR could further advance the proper definition of products and scientific outcomes globally. Being a relatively new method, the uncertainty budget of the QM component in QM-qHNMR has not been verified metrologically. However, the presented results indicate that it is fit for adoption as a standard method in regulatory science.

Studying DFZ also offered an opportunity to examine the feasibility of QM-qHNMR as an official test method. In Japan, when DFZ is used after the harvest of agricultural products, the substance is classified as an anti-mold agent rather than a pesticide. Thus, relevant QC methods are described in an official compilation of food additive specifications and standards under the Food Sanitation Act (i.e., Japan’s Specifications and Standards for Food Additives [JSFA]). The DFZ monograph prescribes the use of infrared spectroscopy (IR) and GC/FID for qualitative and quantitative tests and presupposes a food additive of relatively high purity as the DFZ content is specified to be 94% or higher. As demonstrated in this study, QM-qHNMR could serve as an attractive alternative to the existing IR and GC/FID methods. The ¹H spin parameters can be shared in text format to readily serve as a dRS. Therefore, any properly operating NMR instrument in the world can instantly conduct qualitative and quantitative tests following standardized methodology as outlined herein.

QM-qHNMR Advances Benchtop NMR Analysis

Recently, low-field NMR spectrometers have become available at costs comparable to those of HPLC and GC chromatographs. The proliferation of more affordable NMR instruments undoubtedly enhances the value of ¹H spin parameters, compiled as HifSA profiles. Thus, it is advantageous to develop and encourage means of disseminating ¹H spin parameters. A QM-driven approach has recently been used to establish a pharmacopoeial ad hoc standard for the qualitative analysis of the antiviral drug, remdesivir.¹⁵ While reference spectra at various magnetic fields are helpful for the “phenotypical” interpretation of NMR spectra, HifSA profiles containing the actual ¹H spin parameters are the definitive data: they encode the “nuclear genotype” of an analyte and establish a highly reproducible connection between the molecular structure and NMR spectroscopic properties with the superior stringency of quantum mechanical theory. As ¹H spin parameters of more substances become available, ideally via FAIR repositories, the growth of simultaneously qualitative and quantitative QM-qHNMR analyses can be predicted.

Data Availability Statement

The raw NMR data as well as calculation and information spreadsheets are shared at DOI: 10.7910/DVN/HXRZIY.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.analchem.3c05267.

• Chromatograms of four DFZ stereoisomers; qHNMR spectra used for INT-qHNMR and LB/GB processing; details of the ¹H spin parameters/HifSA profiles (PDF)

Author Present Address

^⊥ Toyo University, Saitama 351-8510, Japan

The authors declare the following competing financial interest(s): T.M. is an employee of FUJIFILM Wako; K.A. and T.S. of JEOL Ltd.; J.L. of NMR Solutions; S.P.K. and M.N. are co-owners of NMR Solutions. The other authors declare no competing financial interest.