Accurate and Precise External Calibration Enhances the Versatility of Quantitative NMR (qNMR)

Abstract

Quantitative ¹H NMR (qHNMR) is a highly regarded analytical methodology for purity determination as it balances metrological rigor, practicality, and versatility well. While ideal for intrinsically mass-limited samples, external calibration (EC) qHNMR is overshadowed by the prevalence of internal calibration and perceived rather than real practical limitations. To overcome this hurdle, this study applied the principle of reciprocity, certified reference materials (caffeine as analyte, dimethyl sulfone as calibrant), and a systematic evaluation of data acquisition workflows to extract key factors for the achievement of accuracy and precision in EC-qHNMR. Automatic calibration of the 90° pulse width (90PW) formed the foundation for the principle of reciprocity and used optimized nutation experiments, showing good agreement with values derived from manual high-precision measurement of 360PW. Employing the automatic 90PW calibration, EC-qHNMR with automatic vs. manual tuning and matching (T&M) yielded the certified purity value within 1% error. The timing of T&M (before vs. after shimming) turned out to be critically important: sufficient time is required to achieve full temperature equilibrium relative to thermal gradients in the air inside the probe and the sample. Achievable accuracy across different NMR solvents varies with differences in thermal conductivity and leads to 2% or greater errors. With matching solvents, the demonstrated accuracy of ~1.0% underscores the feasibility of EC-qHNMR as a highly practical research tool.

Graphical Abstract

In the biomedical or chemical context, an integrity description of chemical constitution must cover both structure and purity. This concerns all substances of interest, regardless of their discovery or production stage and source (natural or synthetic). Purity assessment is of importance whenever chemistry is linked with biological and/or quantitative evaluation. Typically, the target compounds are isolated or synthesized in limited quantities during early stage work. The frequent unavailability of matching metrological reference materials (RMs) precludes their conventional purity assessments by hyphenated LC or GC. Alternatives involve subtraction of the content of all impurities:^1,2 while recognized as compound-independent methodology, mass balance approach still measure impurities by compound-dependent methods. Moreover, they require larger quantities of sample (e.g., Karl-Fischer titration for water content). Preparing RMs for each target compound or attempting a mass balance approach requires considerable effort that rapidly overtaxes early stage discovery programs.

Quantitative NMR (qNMR) has multiple qualities to help solve this challenge: (a) favorable accuracy, precision, and near universal detection capabilities (¹H or other nuclei);³ (b) a plethora of established ¹H qNMR (qHNMR) protocols that utilize the mostly routine and sensitive of NMR experiments and (c) availability of comprehensively evaluated acquisition and processing parameters;^3–8 (d) flexibility of using various quantitative measures including peak height, integration, fitting, and quantum mechanics;⁹ (e) independence from identical RMs and ability to employ any (metrological) RM for calibration. (f) Unlike absorbance- or ionization-based methods, qNMR features a unity response factor, simplifying quantitative calibration even further: instead of being required for each individual analyte, calibration can cover an entire qNMR method for an given instrument. (f) One striking feature for mass limited samples is the ability to recover them, provided that data acquisition uses external calibration (EC) to avoid sample contamination.

The 100% qNMR method achieves this readily, but is limited to relative quantitation (ref³ discusses the advantages). Whereas EC can determine absolute purity, internal calibration (IC) qHNMR predominates current qNMR practice: it innately compensates for errors associated with NMR tubes, analyte and calibrant weighing, volumetrics, and sample handling. IC-qHNMR has become prevalent despite known issues with the choice of an appropriate calibrant, signal overlap, and peak purity challenges in the already narrow ¹H chemical shift window. However, in early-stage discovery and other research programs, spiking a precious sample with a calibrant is most undesirable.

This is where EC comes in: regardless of magnetic field strength, any NMR spectrometer can be calibrated as a tool for absolute purity determination throughout a project. Furthermore, by applying the principle of reciprocity,^10,11 EC-qHNMR can achieve universality that allows anyone to analyze ¹H spectra quantitatively without depending on proprietary tools or software¹² that are processing-focused and agnostic to data acquisition. The principle of reciprocity relates to the variation of the signal intensity (or probe quality factor, Q) as being inversely proportional to the value of the 90° pulse width (90PW).

Practiced long by Burton, Quilliam and Walter,¹² the principle of reciprocity is the core of all EC-qNMR methodology that compensates for differences in signal response between analyte and EC samples (PULCON,¹³ ERETIC-2¹⁴). Essential elements of such EC experiments are: (i) radiofrequency (rf) tuning to the Larmor frequency; (ii) transmission line matching to 50 Ω; and (iii) precise determination and application of the 90PW.

Considerably more studies have been dedicated to IC vs. EC, earning IC acceptance in metrology, regulatory, and legal systems.^3–7 Despite EC’s theoretical validity^12–24 and demonstrated utility in IC/EC comparison studies,^{15,16,19–21, 23} EC is regarded as less accurate and IC the first choice of most qNMR practitioners. This study establishes experimental conditions that close the (perceived) IC-to-EC qNMR reliability gap and advances EC-qHNMR as fully viable and practical.

Applying identical processing parameters to both EC- and IC-qHNMR, the present study examined six qNMR data acquisition workflow patterns systematically (Figure 1; patterns 2-5 manual operation) and identified those factors that are most critical to quantitative accuracy and precision. The outcomes enable the automation of high-accuracy EC-qHNMR methodology, thereby fostering projects that can benefit the most from a lack of sample contamination and greater flexibility and speed of EC vs. IC. Caffeine (CAF), dimethyl sulfone (DMSO₂), and maleic acid (MA) were used as analyte, EC, and IC, respectively. DMSO₂ and MA have already been validated as qHNMR calibrants in deuterated solvents.²⁵ To ensure accuracy, all analytes were certified reference materials (CRMs), and their certified purities are reflected in the sample concentrations (Table 1).

Figure 1.

Systematic evaluation of qNMR acquisition workflow patterns identified the most critical factors for quantitative accuracy and precision. When gradient shimming (axials Z1…Z6) gave inadequate line shape, manual adjustments (radials X/XZ/Y/YZ) were performed.

Table 1.

Investigated samples^a

No	Sample	Solvent	IC or additive
1	0.255 mg/mL DMSO2	DMSO-d6	0.704 mg/mL MA
2	0.482 mg/mL DMSO2	DMSO-d6	0.652 mg/mL MA
3	0.948 mg/mL DMSO2	DMSO-d6	0.713 mg/mL MA
4	1.679 mg/mL CAF	DMSO-d6	0.714 mg/mL MA
5	0.766 mg/mL DMSO2	DMSO-d6	2.111 mg/mL MA
6	1.446 mg/mL DMSO2	DMSO-d6	1.955 mg/mL MA
7	2.843 mg/mL DMSO2	DMSO-d6	2.138 mg/mL MA
8	5.038 mg/mL CAF	DMSO-d6	2.143 mg/mL MA
9	1.787 mg/mL CAF	D2O
10	1.787 mg/mL CAF	D2O
11	1.787 mg/mL CAF	D2O	200 mM NaClb
12	1.065 mg/mL DMSO2	DMSO-d6
13	0.863 mg/mL DMSO2	CD3OD
14	0.955 mg/mL DMSO2	Acetone-d6
15	0.927 mg/mL DMSO2	CDCl3
16	1.172 mg/mL DMSO2	D2O

^aConcentrations are corrected by the certified purity values. Samples 5 to 8 were in 3-mm, all others in 5-mm tubes. Samples 1–8, 9–11, and 12–16 were prepared on Mar 29, Aug 9, and Aug 13 in 2019, respectively.

^bAdded to produce the highly conductive sample.

EXPERIMENTAL SECTION

Analytes.

Maleic acid (MA; Cat No 135-17951, 99.9% mass fraction), DMSO₂ (Cat No 048-33271, 99.9% mass fraction), 1,4-BTMSB-d₄ (Cat No 024-17031, 99.9% mass fraction), and DSS-d₆ (Cat No 044-31671, 92.4% mass fraction) were from Fujifilm Wako Pure Chemical Corp. (Osaka, Japan); caffeine (CAF; Cat No 56396, 99.9% mass fraction) from Sigma-Aldrich (St. Louis, MO, USA); DMSO-d₆ (Cat No DLM-10-10×0.75, 99.9% D), D₂O (Cat No DLM-6-10×0.75, 99.96% D), and CD₃OD (Cat No DLM-24-10×0.75, 99.8% D) from Cambridge Isotope Laboratories (Tewksbury, MA, USA); acetone-d₆ (Cat No 444855, 99.9% D) and CDCl₃ (Cat No 416754, 99.8% D) from Sigma-Aldrich; rifampicin (RMP, Cat No 195490) and isoniazid (INH, Cat No I3377–50G) from MP Biomedicals (Irvine, CA, USA) and Sigma-Aldrich, respectively.

NMR Tubes.

While designed for 5-mm NMR tubes, the NMR probe employed in this study also accommodates 3-mm NMR tube samples, allowing for reduced solvent volumes without negative impact on S/N. As described previously,^12,17 the precision of the inner diameter (ID) of NMR tubes is critical for eliminating errors from the differences between the analyte and the EC sample volumes detected by the probe. The 5-mm (ID = 4.20 ± 0.025 mm; Cat No XR-55-7) and 3-mm (ID = 2.41 ± 0.015 mm; Cat No, C-S-3-500-7) NMR tubes from Norell Inc (Morganton, NC, USA) had nearly identical relative standard deviations (RSDs) in their sample volumes (1.19% vs. 1.24%, respectively).

Sample Preparation.

Weights and volumes were measured at 20–25ºC using an ultra-microbalance (XP6; Mettler Toledo) and a recently calibrated electronic auto-pipette (Multipette Xstream; Eppendorf), respectively. Materials stored at −20 ºC were first equilibrated to RT using a desiccator with drying silica gel, and then left in the sample preparation area for at least 30 min. A suitable quantity of material was placed into a weighing dish (Cat No W1126-100EA, Sigma-Aldrich), then everything (material and dish) transferred to an empty vial and the appropriate deuterated solvent added, ensuring complete dissolution. Precise aliquots of the solution (600 μL for 5-mm, 200 μL for 3-mm) were transferred to the NMR tubes and the tube flame-sealed. Table 1 summarized additional essential sample information.

NMR Instrumentation.

This study was performed on a JEOL 400 MHz instrument (JNM-ECZ400S/L1; 399.7822 MHz for ¹H), equipped with 5-mm cryogenic (SuperCOOL) and RT (Royal) probes, regulated at 25 ºC (298 K), operated with JEOL Delta v5.3.1 software.

qHNMR Experiments.

Basic, single-pulse acquisition employed ¹³C decoupling to collapsed the ¹³C satellite signals for simplified assignments, enhance determination of low-level impurities, and increase integration accuracy. MPF8 ¹³C decoupling modulation was selected due to its wider linear decoupling range compared to GARP.

To minimize heating effects arising from the decoupling duty cycle, MPF8 was applied only during acquisition time (AQ). The number of scans (NS) was 16 or 32, and 4 for dummy scans (DS). The relaxation delay (D₁) was set at 20 or 60 s to maintain a pulse repetition time (T_r) [AQ + D₁] at least 10× the longest T₁ for all signals of interested. By setting the number of data points to 65,536, for a spectral width of 7,494 Hz, AQ became 8.75 s. Segments of 749.4 Hz were clipped at both ends of the spectra, and the remaining 5,995.2 Hz subjected to further processing: zero filling (4×) to 262,144 points, no additional window functions were applied. The phase was adjusted manually, followed by baseline correction (Akima fitting). The processed spectra were saved separately from the original FIDs.

Quantification.

All acquired spectra were processed with the “Quantitative Analysis” module of the Delta software. The quantitative results were calculated automatically following eqn. 1 using the integral values from automatic integration, the determined 90PW values, and the sample concentrations.

$$\mathrm{Molar}{\mathrm{Conc.}}_{\text{A}}=\mathrm{Molar}{\mathrm{Conc.}}_{\text{C}}\times {\text{S}}_{\text{A}}/{\text{S}}_{\text{C}}\times {\text{H}}_{\text{C}}/{\text{H}}_{\text{A}}\times 90{\mathrm{PW}}_{\text{A}}/90{\mathrm{PW}}_{\text{C}}\times {\text{T}}_{\text{C}}/{\text{T}}_{\text{A}}$$ (1)

where the subscripts denote analyte (A) vs. calibrant (C); Molar conc., concentration; S, absolute integral value; H, number of hydrogens; 90PW, 90° pulse width; T, temperature (in K).

Receiver Gain (RG).

RG optimization utilized 3.323 mg/mL DMSO₂ in DMSO-d₆ (5-mm) as it exhibited the most intense signals of all studied samples, examining an RG range from 10 to 70 under otherwise identical qHNMR conditions. FID processing used with EM (0.2 Hz) to unify the signal shape of each measurement, followed by zero-filling (4×). Plotting the absolute integral values and S/N ratios of all measurements yielded 30 as the optimal RG value (Figure S1, Supporting Information).

Spin-lattice Relaxation Time (T₁) Experiments.

The T₁ values of all hydrogens were determined by using Delta’s default inversion recovery pulse sequence (“double_pulse.jxp”). The τ interval was set to 10 exponentially spaced data points between 60 and 0.1 s, with NS set to 1 for each interval. D₁ was set to 60 s, and 16,384 data points were acquired at a spectral width of 7494 Hz (clipped: 5995.2 Hz). FID processing with exponential multiplication (0.2 Hz broadening factor) and trapezoidal window functions. From the processed spectra, T₁ was calculated using the “Non-linear Inversion Recovery algorithm in JEOL Delta software.

Nutation Experiment.

To determine the on-resonance 90PW values of the target signals, standard ¹H experiments were first performed to determine the chemical shift of the signals of interest. These chemical shift values became the transmitter offset position for the subsequent nutation experiments at 1249.5 Hz spectral width (999.6 Hz after 20% clipping), acquiring 1,024 data points for a range of PW values (1, 5, 9, 13, 17, 21, 25, 29, 33, 37 μs). NS was 1, D₁ 10 or 20 s (depending on sample T₁ values). The FID of each nutation array was processed with the same window functions as the T₁ experiments. For calculation of 90PW, the curves built from the processed spectra were subjected to the “Nutation Analysis” module in Delta.

RESULTS AND DISCUSSION

Optimization of 90° Pulse Width Measurement.

As employing the principle of reciprocity is the foundation of EC-qHNMR methodology, sample-specific calibration and application of precise 90PWs are essential. Traditional methods for obtaining 90PW rely on nutation measurements that consist of a set of arrayed experiments with varying PWs.²⁶ To reduce unfavorable effects introduced by T₁, it is common to determine 360PW by seeking this null point manual and calculating 90PW as 360PW/4. Additional measurements with a smaller ΔPW steps around 360PW enhance the accuracy of this form of 90PW determination. For accurate yet automatic 90PW determination, this study employed the classical nutation experiment after optimizing an established non-linear curve fitting method.²⁷ Sample 4 (Table 1) exhibiting one signal from MA, four signals from CAF, and the residual solvent signal (DMSO-d₅), was used to determine the 90PW of each signal on-resonance as summarized in Table 2. A comparison with the manual, small step 360PW null-based method showed good agreement of the resulting 90PWs across both the intramolecular (four in CAF) and intermolecular signals (CAF, MA, and DMSO-d₅). With the non-linear curve fitting method, accuracy of the 90PW values depended on the symmetry of the sinusoid that represented the signal intensity at various PWs. Whenever the relaxation delay, D₁, was short compared to T₁ of the target signal, the sinusoid was skewed (Figure S2, Supporting Information). To further determine the 90PW precisely within 1% error via the curve fitting method, D₁ must be set to at least 2×T₁ of the target signal. All presented EC-qHNMR measurements used a 90PW calibrated by the non-linear curve fitting method, with D₁ set to 10 or 20 s, and avoiding hydrogens with unsuitably long T₁.

Table 2.

Consistency of the 90PW values determined under various conditions over 3 days using sample 4.

	D1	Measurement	MA	CAF_H1	CAF_H3	CAF_H7	CAF_H8	DMSO-d5
Method	[s]	time [min]	T1, 2.6 s	T1, 1.9 s	T1, 2.4 s	T1, 1.7 s	T1, 6.4 s	T1, 15 s
Manual null pointa	30	7	reference valueb	100.0 ± 0.2%	100.1 ± 0.2%	100.1 ± 0.2%	100.6 ± 0.2%	100.7 ± 0.0%
Automatic non-linear curve fitting	1	1	99.8 ± 0.6%	98.9 ± 0.1%	99.6 ± 0.8%	99.5 ± 0.3%	96.8 ± 0.1%	95.1 ± 0.1%
	5	2	99.6 ± 0.2%	99.9 ± 0.3%	100.2 ± 0.3%	99.9 ± 0.1%	99.8 ± 1.5%	98.4 ± 0.1%
	10	3	99.9 ± 0.1%	99.8 ± 0.3%	100.0 ± 0.4%	99.9 ± 0.1%	100.3 ± 0.3%	99.4 ± 0.2%
	20	4	99.8 ± 0.2%	99.7 ± 0.5%	99.8 ± 0.4%	99.9 ± 0.3%	100.3 ± 0.5%	100.6 ± 0.5%
	30	6	99.9 ± 0.4%	99.8 ± 0.6%	99.8 ± 0.6%	99.9 ± 0.3%	100.3 ± 0.5%	100.7 ± 0.4%
	60	11	99.9 ± 0.1%	99.7 ± 0.3%	99.9 ± 0.5%	100.0 ± 0.2%	100.5 ± 0.4%	100.6 ± 0.1%
	120	21	99.6 ± 0.2%	99.7 ± 0.0%	99.6 ± 0.1%	99.9 ± 0.1%	100.4 ± 0.4%	100.7 ± 0.1%

^aDetermine the 90PW via manual analysis of the 360PW null point.

^b7.374 μs (day 1), 7.363 μs (days 2 and 3), all other 90PW given as relative values.

Systematic Evaluation of Six EC-qHNMR Workflow Patterns.

Figure 1 shows the workflows of six systematically altered series of EC-qHNMR experiments. Each procedure was performed over a 6-day period using CAF and DMSO₂ as the analyte and EC, respectively. As samples 1-4 were in 5-mm vs. samples 5-8 in 3-mm tubes, the sample volumes differed markedly. To achieve closely matching S/N ratios from the different tube sizes, samples 1-4 were prepared by 3-fold dilution of samples 5-8. As MA was added to them as an IC, quantitative values by IC-qHNMR methodology were also plotted (Figure 2). Finally, to confirm the validity of the principle of reciprocity for highly conductive samples, EC-qHNMR was applied to samples 9 to 11 as an additional set of experiments (Table 3).

Figure 2.

A comparison of the quantitative values obtained for EC- and IC-qHNMR under the six different workflow procedures. For the EC-qHNMR, quantitative results for CAF (Analyte) are plotted relative to its certified value. The values are based on DMSO₂ at three different concentrations (EC1-3). For IC-qHNMR, using MA as IC, quantitative values of CAF and DMSO₂ (EC1-3) are plotted relative to their certified values. Samples 1-4 in 5-mm NMR tubes and 5-8 in 3-mm NMR tubes were used for the analysis (Table 1). The D₁ and NS were set to 20 s and 32, respectively.

Table 3.

EC-qHNMR for highly conductive samples.

	Sample 10 a	Sample 11 (200mM NaCl)
Pattern 1	100.4 ± 0.2%	86.4 ± 0.1%
Pattern 2	101.2 ± 1.1%	94.6 ± 0.3%
Pattern 4	100.2 ± 1.5%	100.1 ± 1.4%

^aQuant. values with standard deviations (n = 3) relative to the certified value of CAF. Sample 9 served as EC. Data acquired on Aug 9, 2019.

Based on previous reports,^15,18 accurate EC-qHNMR is achievable even if the solvent differs between samples by applying the principle of reciprocity. This cancellation of solvent differences was examined using samples 12 to 16 (Figure 4). In the case of IC-qHNMR, good accuracy and precision were observed for all patterns (Figure 2). This confirmed that all samples were prepared accurately, and that sample decomposition was not significant factor for the chosen samples pertaining to the accuracy and precision of the EC-qHNMR method.

Figure 4.

Effects of a panel of widely used deuterated solvents on EC-qHNMR, using workflow pattern 4 and sample 12 as EC. Quantitative values for DMSO₂ in samples 13-16 (NS=16) are plotted relative to their certified values. The experiments were conducted in triplicate on Aug 15 and 17, 2019.

The Impact of the Principle of Reciprocity on EC-qHNMR.

Optimum probe conditions can differ between samples depending on their conductivity and ionic strength. Therefore, adjustment of tuning and matching (T&M) is a basic tenet of qNMR and conducted to unify rf transmission to the samples. Optimized probe conditions hold true to the principle of reciprocity between analyte and EC.

However, even EC-qHNMR measurements which were not based on the principle of reciprocity, such as patterns 1 and 2, showed good agreement between the quantitative values of CAF and its certified value. The same applied to both 5-mm and 3-mm NMR tubes (Figure 2). These results indicated that the conductivities (ionic strengths) of the samples were (near) identical. Furthermore, 90PW calibration also work across tube sizes as the precision resulting from patterns 1 and 2 were also highly congruent. Accordingly, the results of EC-qHNMR patterns 3 and 4, both based on the principle of reciprocity, showed good accuracy and precision (99.4 ± 0.86% and 99.8 ± 0.89% for 5-mm; 99.9 ± 1.14% and 99.6 ± 0.94% for 3-mm). The observation that pattern 2 (99.4 ± 0.54%) is slightly superior to patterns 3 and 4 (5-mm tubes), both of which are based on the principle of reciprocity, indicates that these small differences are due to residual factors related to instrumentation. This includes instrument factors related to extended time periods (pattern 2 acquired in March/April vs. patterns 3 and 4 in July/August. Notably, comparison of the RSD values of patterns 2-4 for IC-qHNMR (0.38%, 0.59%, and 0.57%, respectively) indicated that variations were small and on par with metrological methods.

While the observed precision of IC-qHNMR was still (yet marginally) better than that of EC-qHNMR, the accuracies of EC-qHNMR, as determined via three calibrants (EC1-3), were still within 1% or better error. This is fully acceptable for most (IC-)qHNMR applications.

Precision with 3-mm tubes inferior to what was observed with 5-mm. A plausible explanation is that RF coil excitation differs sufficiently between 5-mm vs. 3-mm tubes to cause this outcome. While EC works for both 5-mm and 3-mm tubes, it apparently cannot be transferred between the two, at least with certain probe configurations, possibly due to reduced RF homogeneity of 3-mm tubes in certain 5-mm probes. However, the outcomes of 3-mm samples were still favorable, with errors that are negligible for applications, e.g., at early discovery stages.

Highly Conductive Samples.

The existence of an inverse correlation between the probe quality factor (Q factor) and 90PW will be evident from the results of EC-qHNMR for highly conductive sample. Table 3 shows a comparison of quantitative values from a non-ionic vs. ionic samples (10 and 11, resp.) under workflow patterns 1, 2, and 4 with ¹³C decoupled acquisition. Predictably, EC-qHNMR accuracy of sample 11 degraded without the principle of reciprocity in patterns 1 and 2. The details of the inverse correlation between the Q factor and 90PW under pattern 4 is summarized in Table S1, Supporting Information. The NaCl in sample 11 dampened the Q factor yielding uncorrected quantitative results with an accuracy of around 92%, whereas 90PW-based correction resulted in good accuracy (100.1%; Table 3).

Automatic vs. Manual Tuning & Matching (T&M).

Manual T&M monitored the wobble curve, for tuning to the Larmor frequency, and reflection level adjustment to zero for impedance matching for each sample. In the case of auto T&M, achievable reflection levels were in the range of 10-30. Interestingly, no significant differences were observed between patterns 3 and 4 (Figure 2). Thus, it can be concluded that the use of auto T&M is sufficiently reliable with EC-qHNMR, and further indicates that EC-qHNMR data acquisition can be automated.

The Sequence of Shimming and T&M.

When sufficient integral range is guaranteed, spectral resolution (magnetic field homogeneity) does not affect the value of signal areas. Therefore, shimming can be done before and/or after T&M. However, the accuracies in patterns 5 and 6 were clearly lower than those in patterns 3 and 4 (Figure 2). Another factor relates to the probe heater, which serves to heating the (typically cooler) air sent into the probe inside where the sample is exposed. During the pattern 3 and 4 experiment, the probe heater had been set to be turned off at the time of sample ejection (sample changer). Patterns 5 and 6 performed T&M two minutes after the probe heater was turned on. In contrast, as gradient shimming takes about 3 minutes, T&M in patterns 3 and 4 occurred ca. 5 min after the probe heater was turned on.

These observations nurtured the hypothesis that the temperature of the air inside the probe was inhomogeneous (non-equilibrated), as indicated by the results of patterns 5 and 6. This is supported by the fact that the accuracy was relatively worst for the 3-mm NMR tubes, which leave the largest gap of circulating air around the tube inside the probe. To test this hypothesis, additional experiments were performed (Figure 3). For example, implementing the T&M procedure more than 5 min. after triggering probe heating resulted in the same precision for both patterns, “shimming first” and “T&M first.” The enhanced accuracy and precision in pattern 6 vs. pattern 5 first appeared to be counterintuitive, but can be explained as an indirect result of manual T&M: as it takes longer than its automated equivalent, temperature gradients can declined farther or are even eliminated during the prolonged manual T&M process time.

Figure 3.

Pre-optimized workflows (A) with alternating order of shimming and T&M and resulting EC- and IC-qHNMR results for CAF (B). EC-qHNMR values are based on DMSO₂ at three different concentrations (EC 1-3), and the quantitative results for CAF are plotted relative to its certified value. IC-qHNMR used MA as IC, and the quantitative results for CAF and DMSO₂ (EC1-3) are plotted relative to their certified values. Samples 5-8 in 3-mm NMR tubes were employed used for the analysis (Table 1). As these measurements used the RT probe, the S/N ratio was reduced by ca. 3-fold relative to the cryo-probe. The D₁ and NS values were 20 s and 32, respectively.

In summary, it became clear that the timing of T&M is critically important. Although T&M can be done before or after shimming, allowing sufficient time for temperature gradients of the air inside the probe and the sample to reach full equilibrium at the set temperature is crucial. If the room temperatures in the instrument’s location and the temperature of the air (or N₂) flowing into the probe can be kept stable, turning off the probe heater during EC-qHNMR is a viable approach for obtaining accurate and precise quantitation. The presented data also indicate that basic, non-3D forms of ²D-based gradient shimming yields sufficient consistency for EC-qHNMR.

Different Solvents.

To evaluate the validity of EC-qHNMR, quantitation across five different commonly used NMR solvents, via the principle of reciprocity, DMSO₂ certified reference material was chosen and dissolved in DMSO-d₆, CDCl₃, CD₃OD, D₂O, and acetone-d₆ (samples 12-16) to establish the test materials. The T₁ values of the DMSO₂ hydrogens in these solvents were 2.8, 3.5, 5.3, 6.0, and 6.3 s respectively. Sample 12 (in DMSO-d₆) was selected as EC, and the D₁ set to 20 or 60 s to maintain the targeted quantitative conditions (AQ [8.75 s] + D₁ ≥ 10×T₁ for the target hydrogen). For other analytes, D₁ was conservatively unified to 60 s. Applying workflow pattern 4, Figure 4 plots the quantitative results for DMSO₂ with and without ¹³C decoupling. With ¹³C decoupled acquisition, when the EC signal was obtained with a D₁ of 20 s, the observed error in acetone-d₆ and CDCl₃ was of ≥4%. Such undesirable error levels could be removed by standardizing D₁ at 60 s for all samples. On the other hand, without ¹³C decoupling, no significant difference resulted in the quantitative values regardless whether D₁ for the EC was set to 20 or 60 s. In fact, with ¹³C decoupled acquisition and a D1 of 20 s, signal intensity was decreased by 2.4–2.9% relative to longer-D1 conditions. This explains the initially observed 4+% error (Table S2, Supporting Information). These results confirmed that certain heating effects from ¹³C decoupling (here: MPF8) on quantification do exist. Under conditions where D₁ is 20 s, the duration of heating from decoupling is greater relative to the entire duty cycle time than when D₁ is 60 s. In other words, D₁ can be regarded as cooling time that counter-balances heating from the relatively high-power ¹³C radio frequency composite decoupling, thereby eliminating interferences during AQ. As a result of the heating effect, 90PW values calibrated before the measurement in coupled mode can shift slightly when employing ¹³C decoupling, resulting in smaller than expected signal intensities.

Unless factors that correct for the thermal conductivity during the measurement are introduced into the principle of reciprocity, the use of matching solvents for the EC and the analyte sample will ensure the most accurate quantitative results. However, EC-qHNMR with non-matching solvents still yield useful results, as long as the associated error levels are considered.

Probe-related Robustness of the Principle of Reciprocity.

Using data from samples 1–4, obtained under pattern 3 in 5-mm NMR tubes (Figure 2), and MA as target analyte, both the Q factor and 90PW were monitored for more than one month (Jul 11 to Aug 18, 2019). Both Q factor and 90PW showed good consistency over the observation period (Figure 5). While EC-qHNMR without T&M and 90PW calibration yield practically acceptable result only when the conductivity of the EC and analyte samples are matched (Figure 2, patterns 1 and 2), these results indicate that implementation of both T&M and 90PW calibration in EC-qHNMR is highly recommended for enhanced accuracy. This data also support the conclusion that the value of the 90PW itself, measured after T&M, can serve as an indicator of whether the probe is working properly.

Figure 5.

Evaluation of the impact of the Q factor, 90PW, and Q factor × 90PW utilized the spectra of MA in 5-mm NMR tubes (samples 1-4) from EC-qHNMR workflow pattern 3 (Figure 2). The Q factor represents the integral per hydrogen over the molar concentration. Data are represented as values relative to sample 1, were acquired on Jul 11, 2019, and calculated with a Q factor of 20.989 (90PW [7.3632 μs]); Q factor × 90PW = 154.55).

Application to “Real” Samples: Rifampicin and Isoniazid.

The finally validated EC-qHNMR method was applied to commercially available reference materials (RMs) of the anti-TB drugs, INH and RMP, which are widely used as bioassay positive control and calibrants in our tuberculosis drug discovery program. As the investigated INH and RMP RMs used in this study are not CRMs, the accuracy of EC-qHNMR was evaluated by comparing the results with those obtained by IC-qHNMR. Figure 6 shows the ¹H spectra containing the ICs: BTMSB for INH, and DSS-d₆ for RMP. The aromatic hydrogens in INH and the hydrogen attached to C-1ʹ in RMP²⁸ were selected for the quantitative determinations. Both instances yielded good agreement in the determined absolute purity values between the IC- and the EC-qHNMR method (Table 4).

Figure 6.

EC-qHNMR spectra of INH and RMP, containing BTMSB and DSS-d₆ as ICs, respectively. Solid red dots indicate the resonances targeted for quantitation.

Table 4.

IC- and EC-qHNMR results for INH and RMP.

Analyte	Solvent	IC-qHNMR a	EC-qHNMR b
INH	CD3OD	99.9%	101.0%
RMP	DMSO-d6	87.0%	86.5%

^aBTMSB and DSS-d₆ were used as IC for INH and RMP, respectively.

^bSamples 12 and 13 were used as EC for INH and RMP, respectively.

D₁ and NS were set to 60 s and 16, respectively.

CONCLUSIONS

This study determined the key factors in qNMR data acquisition that effect variations of quantitation outcomes of EC-qHNMR measurements employing the principle of reciprocity: T&M, 90PW calibration, and the particular sequence and timing of the involved steps (shimming, tuning, matching, 90PW, FID acquisition) all contribute to the trueness of the quantitation and are prerequisites of any software-based qNMR data evaluation tool.

Systematic performance evaluation of EC-qHNMR following the six acquisition workflow patterns (Figure 1) revealed that the instrument’s automatic T&M function was sufficiently reliable for accurate quantitation. Notably, sufficient time for probe and sample temperature equilibration should precede T&M. T&M can be performed before and/or after shimming. Due to limited equilibration time, patterns 5 and 6 were associated with a certain degree of temperature gradient and, thus, residual field inhomogeneity in the active volume during T&M. Such a gradient could potentially be studied further via monitoring of the exact chemical shift of the temperature-sensitive H₂O signal. However, as sample preparation only employed high purity compounds and deuterated solvents, the lack of H₂O is actually obvious from samples 1-8, and the absence of temperature gradient is evident for patterns 1-6 due to no visible differences in signal line shape and chemical shift for CAF, DMSO₂, and MA.

When measuring 90PW via automated nutation, D₁ should be ≥2×T₁ of the target nuclei. When increasing the number of arrayed PW data points to yield better defined nutation sinusoids, long T₁s can cause unfavorable effects, and D₁ may need to be increased well beyond 2×T₁. Confirming congruence between 90PWs of both intramolecular and intermolecular signals in the same sample validates the 90PW measurements. This is generally supported by the fact that analyte and IC are excited with the same PW, which is the basis for accuracy in IC-qHNMR.

EC-qHNMR with the presented optimized settings and workflow exhibits a low ~1.0% error, including for highly conductive samples, and enables automation of EC-qNMR acquisition. Observed EC accuracy was nearly the same as for IC-qHNMR performed in parallel. The presented EC outcomes were independent of NMR processing software and can be implemented on any instrument. No significant differences occurred in accuracy and precision of the quantitative values from MestReNova 12.0 (Mestrelab Research) vs. JEOL Delta 5.3.1 software (Figure S3 and Figure 2, respectively).

Additional factors impacting EC-qHNMR accuracy emerge when the analyte and EC samples use different solvents. This relates to heating effects the sample experiences during the time composite ¹³C decoupling pulses are applied. While details of these temperature fluctuations will require separate investigation, thermal conductivity varies between solvents and temperature effects become more pronounced as NS increases. Thus, identical solvents for analyte and EC should be used for high accuracy EC-qHNMR.

Collectively, the present findings reveal the data acquisition conditions (workflow patterns 6–8; Figures 1–3) that make EC-qHNMR sufficiently reliable for many applications. The accuracy demonstrated here (~1.0%) clearly exceeds the general perception of EC performing with “a few to several %” error.

The presented result can inspire the development and implementation of protocols as well as acquisition and matching processing software that automate EC-qNMR measurements using optimized workflow patterns. This will facilitate the wider implementation of EC-qHNMR as an attractive tool for valuable, mass-limited samples, and expedite further systematic studies of other factors that affect the quantitative outcomes in qNMR (e.g., NMR tubes and sample preparation).