Connecting the Practice of Modern Qualitative and Quantitative NMR Analysis with Its Theoretical Foundation

Abstract

This Perspective seeks to reconnect the current practice of nuclear magnetic resonance (NMR) spectroscopy in chemical structure and quantitative (qNMR) analysis with its roots in classical physics and quantum mechanics (QM). Rationales for this approach are derived from various angles, including focused reviews of the key parameters of the nuclear resonance phenomenon, the structural information richness of NMR spectra, and significant progress in both computational and spectrometer hardware. This provides collective reasoning for the reintegration of computational quantum mechanical spectral analysis (QMSA) into the contemporary practice of NMR spectral interpretation. Retethering operator-dependent visual phenotypic with QM-driven computational genotypic analysis yields more objective and accurate information by taking advantage of QM as the foundational reference point for NMR. Powerful computational tools for compound genotyping are available and evolve rapidly toward automation. In addition to enhancing the rigor and reproducibility of structure elucidation of new and the dereplication of known compounds, QM anchoring enables competent resolution of peak overlap, with resulting benefits in qNMR and low-field/benchtop NMR analysis. Furthermore, examination of common definitions and documentation practices shows that an evolutionary reconciliation of NMR terminology helps resolve ambiguities: shifting from phenotypic peak focus to genotypic QM-based pattern analysis is not only the logical next step when communicating structures of natural products and other molecules reproducibly but also a timely approach, as it yields QMSA-verified data for evolving knowledge bases for molecules of biomedical relevance.

General Introduction and Perspective Goals

Fundamental Considerations

NMR spectroscopy is indispensable in natural product (NP) chemistry and related disciplines including foods, biochemistry, biomedicine, and pharmacy. General quantum mechanics (QM) connects NMR spectra with the underlying fundamental NMR theory. The QM-NMR relationship has been strong since the very outset of NMR spectroscopy,¹ as the proper interpretation of spectra has depended on QM-based spectral analysis (QMSA), which the NMR pioneers used to validate experimental findings.

In fact, QM theory forms the physical framework for much of our understanding of the universe. This makes QMSA the natural Gold Standard for NMR spectroscopy and anchors it in both the SI system and metrology.^2,3 Nearly eight decades after Anderson, Bloch, Hansen, Packard, Varian, and their co-workers recognized the NMR phenomenon and built the first high-resolution spectrometers (see ref (4) and references cited therein), it is important to remember the QM theoretical foundation of NMR spectroscopy.

One key advantage of a theory-based interpretation of spectra is the dramatic reduction of both the number of variables and the degrees of freedom for finding a definitive and highly specific structural solution. While reduction of a complex NMR spectrum to a chemical structure through human interpretation of complex peak patterns demands advanced expertise, available QMSA software puts the same information at the fingertips of novices and experts alike.

Paradoxically, for a number of reasons, the relationship between NMR and QMSA has weakened in recent years. Yet, much can be gained by reconnecting them. In practice, due to a certain degree of divergence between the theoretical underpinnings and day-to-day laboratory practice, this reconnection might require realignment of customary NMR terminology to achieve consistency at all levels of structural and quantitative analysis. Moreover, reframing the terms used to describe how a molecular structure is represented in an NMR spectrum yields credence to how fundamental theory can strengthen the interpretation of NMR spectra.

Reconnecting Fundamental Theory with NMR Practice

Incorporating QMSA into daily practice fosters the utilization of the wealth of information encoded in NMR spectra at four major levels:

• 1.Rich Structural Information: NMR spectra provide information about bonding networks, functional groups, through-space interactions, and spatial proximity.
• 2.Dereplication and Elucidation Potential: NMR analysis is often key to reliable differentiation between known and unknown compounds.
• 3.Computational Accessibility: With advanced QM-based NMR processing tools being available for desktop computers and as web-based applications, complete interpretation of spectra and increased degrees of automation in NMR analysis are more accessible than ever.
• 4.Quantitative Capabilities: qNMR spectroscopy enables absolute quantitation with metrological accuracy; when acquired under proper conditions, qNMR signals are proportional to the number of underlying nuclei, and numerous chemically diverse compounds can be quantitatively assessed within one spectrum using a single calibrant.

Advancing NMR Interpretation from Phenotype to Genotype

Taking advantage of QM as the foundational theory of NMR will advance both qualitative and quantitative analysis. Current data interpretation schemes are primarily visual (peak, cross peak), descriptive (multiplicity), and rely on some form of deconvolution (peak picking, fitting, and pattern matching). Also, they are informed by editorially mandated publishing conventions, such as unsophisticated tables. This can be considered a phenotypic (physical appearance) representation of the experimental NMR data. Computational theory-based analysis advances this to a genotypic fundamental properties approach by directly describing NMR spectra by the intrinsic NMR parameters, chemical shifts and coupling constants. Anchored in well-established theory with clear mathematical expressions, genotypic analysis of NMR spectra directly yields both structures and quantities, making NMR genotyping highly definitive and less subjective than phenotypic interpretation. In analogy to the genome/proteome/metabolome triad in molecular biology and NP research, genotypic interpretation can take our understanding of NMR data to a new level.

Another fundamental consideration relates to the volume, management, and utility of interpreted NMR data. While deconvolution involved in phenotypic interpretation is by default arbitrary and fails for strongly overlapping lines, the QM calculations underlying the genotypic approach are guided by NMR theory. Thus, NMR genotyping shifts the logic of NMR data interpretation from visual peaks to QM-based computational pattern analysis. Moreover, QM calculations reduce complex spectra to a very small number of numerical parameters, the spin parameters of the analyzed nuclei. Consequently, even highly complex NMR spectra, such as 1D ¹H NMR spectra of mixtures, can be fully represented by a small number of descriptors. This avoids phenomenological descriptors, especially the widely used term multiplet, simplifies documentation to the use of plain numerical values of frequencies in Hz, and facilitates NMR data aggregation into large data sets, so-called big data, which are remarkably amenable to artificial intelligence (AI) and machine learning (ML) applications.

QMSA⁴ and Density Functional Theory (DFT)⁵ Are Both QM-Based yet Functionally Disparate

While both are associated with NMR spectroscopy, there is a crucial difference between them. DFT is a tool that calculates chemical shifts (δ) and coupling constants (J) from a given structure or a set of conformers.⁶ These values can be used to calculate predicted or simulated NMR spectra which must be distinguished from an acquired experimental spectrum. Thus, DFT is a compound-to-spectrum (C2S) technique, which is used by assignment support engines such as DP-4/DP4AI^7,8 to estimate probabilities for alternative structural configurations without QMSA by generating hypothetical phenotypes based on assumed genotypes. DFT calculates NMR parameters directly from the molecular structure and must make assumptions regarding the conformational space of the molecule. This, in part, explains the frequent divergence between real experimental and DFT-predicted spectra, because the former are contingent on additional variables that affect the average molecular conformation, such as solvent, concentration, pH, and temperature.

Conversely, QMSA leverages QM to perform spectral analysis(9,10) aimed at “decoding” the nuclear genotype of the analyzed molecule. For the most common ¹H NMR spectrum, this process has been called ¹H iterative functionalized Spectral/Spin Analysis (HifSA).¹¹ Interestingly, DFT can generate starting values for QMSA - as can human phenotypic analysis. As QMSA is always anchored to experimental spectra, it extracts all genotypic parameters required to create matching calculated spectra. Therefore, QMSA enables the spectrum-to-compound (S2C) workflow for the complete analysis of experimental spectra, which provides a definitive set of NMR spin parameters (δ, J, atom populations) needed for automatic analysis of NMR data analysis at all magnetic fields. As shown recently,^4,11 QMSA-driven S2C interpretation replaces peak picking in qualitative and integration in quantitative analyses.

Notably a solid S2C foundation enables combining S2C with C2S to enhance the consistency of both qualitative and quantitative NMR analysis. For further discussion, see the section on phenotype vs genotype and C2S vs S2C below.

In short, DFT predicts spin parameters from a given structure, while QMSA (e.g., HifSA) extracts spin parameters from experimental spectra. Thus, QMSA and DFT are both QM-based yet notably distinct methodologies. While QMSA can utilize DFT data, the inverse has not yet been attempted. Also, the spectra generated by DFT and QMSA are distinctly different; it is recommended the term calculated be reserved for spectra that result from QMSA computations, as opposed to designating DFT-derived spectra as simulated or, preferably, predicted, thereby clearly distinguishing between the underlying methodologies.

Structure of this Perspective Article

To put the above principles into practical perspective, in particular for the NMR analysis of NPs and other organic molecules, this article is sectioned as follows:

• First, the current challenges associated with the interpretation of the typically complex yet information-rich and strictly quantitative ¹H NMR spectra are addressed.

• Second, a review of the basic concepts of available computational tools to connect experimental spectra with QM NMR theory. This section also explains the critical differences between C2S vs S2C and the phenotypic vs genotypic workflows in NMR analysis.

• Third, to address the question why some of the fundamental theories almost got lost during the recent development of NMR spectroscopy, and why reestablishing this connection is critical for scientific advancement.

• Fourth, we demonstrate the feasibility of computational QMSA of NMR spectra, and show how it augments visual spectral interpretation and yields more objective and accurate information. Further, this section discusses the reusability of the QM-verified data and its utility for database-driven and other computational applications.

Current Challenges

Current NMR analysis results rarely report full interpretation of the highly informative ¹H NMR spectrum, often leading to both flawed structural deductions and incorrect quantitative estimations. While spectral complexity presents challenges, it also provides opportunities for gaining valuable additional information: (a) Spatial relationship and chemical microenvironment of the atoms in a compound. (b) Description of the environment of a nucleus and the interrelationships of nuclear pairs. (c) The complex patterns depend on the applied magnetic field strength; thus, comparison of spectra collected at various field strengths requires full understanding of interrelationships between the molecular structure and spectral features. (d) While assignment of peak patterns to a given molecular structure may be achieved readily, accurate spectral prediction from a structure remains unestablished. (e) Although NMR energy transitions can be calculated, experimentally confirmed δ and J values are required for reliable structural correlation. (f) The increased dispersion and relative accessibility of information in 2D NMR spectroscopy has led to gradual disregard of the rich information on 1D NMR spectra, which encode essentially all structural and quantitative parameters of molecules. These challenges are further discussed below.

Spectral Complexity

NMR spectra are complex entities as the spatial relationship and chemical microenvironment of the atoms influence the spectra providing a wealth of information about molecular structures. This complexity also poses significant challenges to the analysts and requires a combination of theoretical knowledge, visual recognition, and specialized, well-conditioned analytical logic for interpretation - all representing human factors that bear a certain element of subjectivity.

The ubiquitously performed 1D ¹H NMR experiment embodies a particularly high degree of complexity: ¹H NMR solution spectra of even very small molecules can give rise to rather perplexing spectra that make understanding the underlying molecular structure a daunting exercise.

To illustrate such complexity, Figure 1 provides a subsection of the 400 MHz ¹H NMR spectrum of β-pinene (1). This portion shows only the pattern of a single hydrogen, H-3a, and clearly illustrates the challenges of structure elucidation based on 1D ¹H NMR data alone, even by an experienced NMR spectroscopist. Fortunately, QMSA offers a deeper understanding as NMR spectra are assessed in their entirety. The spectrum shown in Figure 1 matches the spectrum acquired in ref.¹² In this 1997 paper, the authors established the HifSA profile of 1, which was the first published example of a full analysis of a ¹H NMR spectrum with this level of complexity.

Figure 1.

Example of a hypercomplex multiplet. Subsection of the ¹H NMR spectrum of β-pinene (1) showing the peak pattern of one single(!) hydrogen, H-3a (anti to the exocyclic methylene). The spectrum was acquired on a 400 MHz NMR spectrometer (JEOL ECZ-400) and processed with a Lorentzian–Gaussian window function.

Understanding Multiplets via QM Theory

While the principles of QM theory have long explained how NMR works, the amount of information condensed in a ¹H NMR spectrum tends to overwhelm analysts. Humans are not capable of applying fundamental theoretical principles without the use of a computer, and operate with a simplified understanding of the theory.¹³ Accordingly, the term multiplet is ubiquitous in the scientific literature¹⁴ which unfortunately disregards all underlying coupling and chemical shift information. The often complex observed multiplet and its splittings arise from the chemical and magnetic environment of the resonating ¹H nuclei, both within the analyte molecule and with the surrounding solvent/solutes to form a fingerprint for a partial chemical structure. The plethora of structural information encoded within multiplets makes analysis more challenging, but QMSA allows the extraction of this information in the form of NMR parameters via theoretical calculations, which cannot be performed for, e.g., mass spectrometry.

Spectra Acquired at Different Conditions

The observed NMR peak patterns depend on the B₀ magnetic field strength, and the same compound yields different spectra in different fields: as the spectrum is sensitive to the difference in the resonance frequencies of the coupled nuclei (Δν) relative to their coupling (J). The so-called higher-order effects appear when |Δν/J| becomes sufficiently small, typically for values <10. This affects all nuclei within the spin system–not only the ones in close vicinity. The resulting unexpected multiplicities escape the typical d/t/q/dd/etc designations, and multiplet peak distances deviate substantially from the actual coupling constant(s) or do not resemble them at all. This discourages the simple visual phenotypic comparison of NMR spectra and complicates the analysis of identical and closely related molecules. QMSA is immune to these effects as the NMR parameters remain unchanged even when the visual phenotype of the spectrum changes.

Solvent dependence, as well as other sample variables such as concentration, temperature, and pH, often subtly change the resonance frequencies, further complicating the analysis. This explains why identical J coupling networks of molecules produce NMR spectra of different overall shapes when evaluated under different conditions - despite originating from identical molecular frameworks. The effect of different parameters is discussed in the section How QMSA Methodology Got Lost in Mainstream Data Analysis.

Assembling 1D and 2D NMR into a Homogenous Picture

As a result of such complexity, while the assignment of peak patterns to a known molecular structure is relatively straightforward, accurate spectral prediction from a molecular structure remains elusive. While NMR spectra can be calculated, the extraction of true experimental chemical shifts and coupling constants requires strong theoretical and visual skills. Unfortunately, this interpretive ability has always been in demand and seemingly replaced by larger, more expensive instruments. The large variety of homo- and heteronuclear 2D NMR experiments offers a very practical toolbox for solving complex molecular structures. Users acquire a typical set of multipulse experiments that provide all the information they may need: (i) an edited ¹H–¹³C HSQC spectrum to access carbon multiplicities and ¹H directly coupled to ¹³C, (ii) a COSY spectrum to establish ¹H–¹H through-bond connectivity, and (iii) and HMBC spectra for multibond ¹H–¹³C connectivity. This set of experiments is sometimes complemented by additional pulse sequences, such as NOESY to gain information on 3D structures, or INADEQUATE to map ¹³C–¹³C connectivities throughout the molecule. As a consequence, practitioners at large have lost the habit of extracting the rich information available from 1D ¹H NMR spectra. This under-interpretation may lead to incorrect conclusions in terms of structure elucidation, or errors in quantitative assessments, if the number of nuclei assigned to a specific spectral pattern is attributed incorrectly. Also 1D NMR spectra, especially ¹H, are much cheaper to acquire and, thus more amenable to routine use. These challenges call for a renaissance of QMSA, for interpreting experimental spectra, as discussed in the subsequent sections.

The QMSA Approach Offers Existing Solutions and Tools

One benefit of NMR is that the observed spectrum can be fully explained and understood by QMSA. While QMSA is commonly perceived to be difficult and only for specialists, today it is more accessible than ever for everybody. Given the current state of art, practitioners are enabled to properly apply NMR theory to the qualitative and quantitative interpretation of NMR spectra and augment phenotypic analysis with genotypic QMSA. This section addresses (a) the brief history and theoretical foundations of QMSA; (b) the essential steps involved in the iterative QMSA process and its advantages; (c) the concepts of phenotypic and genotypic approaches to NMR Spectral Analysis.

History and Basics of QMSA

The theoretical foundation of NMR was developed in the first half of the 20^th century, well before the first NMR spectrum was acquired. The technology evolved from the initial measurement of nuclear magnetic moments in the 1930s to the first independent descriptions of NMR phenomena in the 1940s¹⁵ and the commercial availability of NMR spectrometers in the early 1950s.^16,17 One outstanding property of NMR is that it benefits from its historical foundation in fundamental physics, drawing from both classical physics and QM theories to support its applications, which allows for computational approaches that extend beyond the traditional evaluation of spectroscopic data focused on peak frequencies and intensities. Instead, the NMR QM theory leverages intrinsic NMR parameters, such as δ, J and atom populations, which can be linked to the chemical structures.

The QMSA Process

Many approaches exist that permit extraction of NMR parameters from experimental spectra, such as (i) line/peak frequencies, intensities; (ii) deconvolution of lines or peaks; (iii) multidimensional correlations by peak-picking algorithms; (iv) chemical shifts and coupling constants by simplistic first order rules (n+1); and (v) full NMR spectral analysis using QMSA. By matching the experimental and calculated spectra, QMSA extracts information beyond the first-order multiplet annotations. Table 1 summarized the main characteristics of the five approaches.

Table 1. Assessment of Various Approaches in the Practice of NMR Spectral Interpretation.

Attribute	Advantages	Disadvantages
Line/peak frequencies and their intensities	Easy to compute	Overlap, no line shape, no relation to molecular structure, field dependent
Deconvoluted lines	Line shape information, distinguish overlapping lines	No relation to molecular structure, field dependent, unable to resolve full overlap
Multidimensional correlations	Additional dispersion and information reduces ambiguity in assignments, field independent	Requires considerable instrument resources, usually does not yield coupling constants, which are essential for relative configuration
Chemical shifts and coupling constants by simplistic first-order interpretation	Simple rules (n+1), easy to understand	Field dependent. Less accurate and usually incomplete - multiplet annotations instead of coupling constants, requires correlation information for unambiguous assignments
Chemical shifts and coupling constants by QMSAintrinsic parameters	Self-consistency of spin information, highly accurate, fully explains higher-order effects, resolves complete overlap, field independent	Computationally demanding, requires correlation information in complicated cases

The development of QMSA tools spans over 60 years^17,18 and includes NUMARIT^19,20 in the 1970s; DAVINS,²¹ DAISY²² and PERCH²³ in the 1980s and 1990s.²⁴ Historically, the entry barrier to performing QMSA has been rather high. QMSA is regarded as a complicated computationally intensive approach. It uses an iteratively optimizing computed spectrum to match the experimental spectrum and yields accurate values for all NMR parameters, such as chemical shifts, J-coupling constants, line shape, and intensities.

Meanwhile, it is important to recognize that the key challenges such as computing power demands in complicated molecules have been largely overcome. In fact, contemporary tools installed on a personal computer enable analysis of complex spin-networks, such as those of steroids, terpenoids and oligopeptides. The combination of NMR and QMSA also offers insights into structural details and quantitative information.⁹

Phenotypic vs Genotypic NMR Spectral Analysis

While NMR spectroscopy in the 1950s and 60s utilized QMSA regularly, the contemporary data acquisition and interpretation workflows tend to use a phenotypic interpretation of NMR spectra either with computers or manually. The development of 2D-correlation experiments further nurtured this phenotypic approach as a full interpretation of the 1D ¹H NMR spectrum seemed to be superfluous and much of the information contained in this most accessible NMR spectrum is insufficiently analyzed. The deficient, yet highly abundant, multiplet (m) designation in the scientific literature leaves the intrinsic NMR parameters, accurate chemical shifts and relevant J values, undefined (see upper half of Figure 2).

Figure 2.

Example of the common ABCD ¹H spin system such as in aspirin (acetylsalicylic acid) exemplifies how specific NMR terminology connects visual observations (phenotype) with fundamental QM theory (genotype). The observed spectrum and its NMR parameters (blue) are compared to the calculated spectra (red).

In contrast, QMSA starts from establishing starting values for the NMR parameters from the given structure using a priori knowledge or prediction like DFT, which eventually connects the chemical structure to parameters thus establishing a genotype. QMSA maintains this connection while iteratively optimizing NMR parameters until the spectrum calculated from the parameters matches the experimental one in every detail. This includes complex peak patterns that escape first-order multiplet annotations (see Peaks and Overlapping Lines in Figure 2). Thus, this whole process can also be referred to as an S2C approach which provides definitive NMR parameters for confirmation or dismissal of a given molecular structure, with full understanding of the nuclear genotype of the molecule,¹¹ including highly coupled and/or convoluted peak patterns which would be described as multiplets in phenotypical analysis. While C2S (i.e., DFT) can help support deductive reasoning, it is important to note that the validation of C2S approaches requires experimental data, which has to be provided by S2C (i.e., QMSA). Also S2C requires reasonable starting values, especially for novel molecules, and thus the two techniques form a virtuous circle.

Typically, contemporary QMSA implementations have the ability to combine both C2S and S2C approaches, represent iterative workflows, and involve the following five essential steps:

Step 1. Establish a QMSA Starting Template by Predicting an NMR Spectrum from Chemical Structure (C2S)

The starting template can originate from phenotypic/human spectral interpretation, or can utilize various means of predicting NMR spin parameters from a putative chemical structure (e.g., via DFT calculations) when experimental data or prior knowledge is unavailable. Such parameters will inevitably differ from true values in the experimental spectra and will instead yield a predicted or simulated spectrum However, high accuracy is not a requirement for QMSA as the predicted spectrum only serves as a point-of-entry for the iterative matching of the experimental data in steps 2–4.

Step 2. Obtain an Experimental Spectrum (S2C)

Ensure the highest quality NMR data by using standards with the highest available purity and a qualified instrument. The increased spectral dispersion of high magnetic fields facilitates deduction of accurate NMR parameters. Many factors impact the quality of acquired NMR spectrum, such as magnetic field homogeneity (shimming), sample preparation (e.g., solvents, sample humidity and pH), as well as the instrument methods and settings.

Step 3. Perform Signal Assignments Based on Accurate Structural Information and QMSA (C2S plus S2C)

Once the structural information is connected to peak patterns in an experimental spectrum, QMSA can extract by iteration, the true NMR parameters to fully match the experimental data.

Step 4. Conduct Spectral Comparison and Similarity (C2S plus S2C)

Next, a detailed comparison can be performed to assess the similarity between the two spectra. Several metrics can be used to evaluate chemical shifts, peak patterns, intensities, and line shapes to determine how closely they match.

Step 5. Quantitatively Calibrate the Calculated QMSA Result (C2S plus S2C)

QMSA is highly adaptable, allowing for seamless transfer of QMSA profiles between high-field and benchtop NMR equipment, as QMSA computes all peak frequencies in the spectra from the δ and J values and matches all peak intensities. The chemical shift calibration follows the equation: resonance frequency (Hz) = chemical shift (δ, ppm) × frequency of the reference (MHz)/10⁶. The calculated spectra will align with experimental data across different magnetic field strengths. By comparing spectra from different field strengths, QMSA can be further refined to correct minor inaccuracies through fractional adjustments of the computed NMR parameters. The process iteratively fine-tunes δ and J until the computed NMR spectrum perfectly matches the experimental spectrum at every field strength.

The QMSA Genotyping Advantage

Using genotypic, QMSA-derived NMR parameters (δ, J) rather than phenotypically observed peak frequencies and intensities has major advantages (Figure 3). For instance, the NMR parameters provide direct information about chemical structure: while δ reflects the chemical environment of the corresponding nuclei and is rather empirical, J values encode three-dimensional geometry and distance information on the coupled nuclei. NMR parameters are intrinsic physicochemical properties of molecules that are highly reproducible and field-independent (see above). Thereby, quantitative analysis can center on δ (chemical shift, Hz or ppm) and J (coupling constant, Hz) values rather than integration of more or less accurately assigned phenotypic multiplets. Prior knowledge can facilitate and help replicate an NMR analysis on any instrument as long as the sample conditions are comparable. This allows benchtop instruments to benefit from knowledge achieved on higher field instruments. In comparison to the phenotypic peak frequencies and intensities, the intrinsic genotypic NMR parameters explain experimental data with a much smaller number of variables, which by default define a self-consistent spin network. This reduces the ambiguity of NMR assignments and enhances the accuracy of identification and quantification even when signals overlap completely. QMSA-based calculated vs experimental spectra provides a means of deriving numeric measures of consistency and/or interpretation confidence, thereby enhancing transparency and reproducibility. QMSA has been demonstrated for numerous compound classes with spectra of varying complexity, including, e.g., cholines, monoterpene glycosides,²⁵ tridecameric cyclopeptides,^25,26 and proanthocyanidin oligomers²⁷ (see ref (4) and references cited therein for an overview).

Figure 3.

Comparison between the common phenotypic NMR spectral interpretation using n+1 and 2ⁿ rules versus the theory-driven genotypic QMSA approach. The aromatic ¹H patterns of guaiacol (2; 500 MHz) exhibit severe overlap and higher-order effects. Both mislead traditional 1D/2D-based peak and δ assignments and result in ambiguous, wrong, or no coupling constants. The QMSA-driven genotypic approach provides a complete and accurate interpretation and encodes everything in just 13 variables: four chemical shifts, six J-couplings, one intensity, and two line shape descriptors (line width, Gaussian contribution). In contrast, phenotyping picks up to 33 peaks (depending on spectral resolution, field strength, acquisition, and processing/picking algorithms), each with position, intensity, and two line shape parameters, for a total of 132 variables. Phenotyping still cannot decode the molecular spin parameters, even at 1.2 GHz, as NMR spectra of 2 retain their higher order.

All NMR parameters from the molecular structure available in the experimental data can be matched, and each QMSA data set is an independent entity, amenable to operations such as addition and subtraction. NMR parameters that produce a calculated spectrum that does not fully resemble the experimental data are either faulty or inconsistent. This stringent relationship enables automation as even small deviations from prior knowledge data can be detected and offers a safe means of checking NMR parameters obtained by correlation spectroscopy (2D NMR). Once QMSA profiles are established, practitioners including nonspecialists can properly apply NMR theory, even in automation, to interpret qualitative and quantitative NMR spectra. This transforms NMR analysis from empirical, user-driven phenotypic interpretation into automated or semiautomated genotypic methodology.

How QMSA Methodology Got Lost in Mainstream Data Analysis

Multifactorial Reasoning

QMSA used to be an integral part of NMR data interpretation. Advancement of instruments (ultrahigh fields, multidimensional NMR, spin/pulse choreography, cryoprobes) and lack of adequate computational capability led to a gradual abandonment of QMSA as seemingly less relevant. Improved feasibility of analyzing larger molecules, mixtures, and dilute samples have indirectly constrained NMR to phenotypical interpretation. This fostered simplified interpretation and an increasingly incomplete understanding, especially of 1D NMR spectra, and trends toward incomplete data reporting, inconsistent assignments, and sometimes incorrect structures.

In parallel, five factors have contributed to QMSA methodology gradually losing its place in mainstream NMR data analysis: (i) Propagation of anachronisms, lore, and myths that evolved over the ∼70-year history of applied NMR spectroscopy. (ii) Challenges in balancing spectral complexity with required analytical simplicity. (iii) Prevalence and power of 2D/nD experiments which, although offering unique capabilities and convenience, are costly and fail to explain the data fully. (iv) Technological and educational developments in STEM resulting in over-reliance on nonmathematical scientific methods. (v) Prevalence of the single peak paradigm in analytical science, fostering reductionism that deprioritizes information-mining of complex phenomena.

Computational Power Is Key, High Field Strength Is Helpful, and Tools Are Available

As instrument capabilities rose almost linearly, computational speed increased exponentially (Figure 4), QMSA methods have developed alongside both technological underpinnings. While NMR hardware benefited from the advent of cell phones and hand-held computing devices spurring digitization and miniaturization, QMSA has benefited primarily from the development of highly powerful and affordable computers.

Figure 4.

Technology and capacity growth in NMR analysis. Summary of the advances in NMR magnetic field strength (blue), computational advances (red) related to the speed of QMSA, and the complexity of molecules for which HifSA profiles have been established (green) show the close relationship between the last two. The sharp rise in computational power means that QMSA is presently feasible for practically all molecules in pharmaceutical and NP space.

While QMSA is now accessible on a variety of platforms, it is often overlooked in favor of phenotypic or nD NMR analysis even though the same information is available from a readily and inexpensively acquired 1D ¹H NMR spectrum. As various nD NMR spectra and software tools help organize essential structural information, QMSA yields a vast amount of detail in a compact package, supports a more comprehensive understanding, and helps unravel the universality of ¹H NMR spectra.

While innovation has made NMR instruments and pulse programs much more powerful, computational NMR innovations have languished - despite QMSA being the quintessential tool for NMR analysis (see above). Today, QMSA is not only fully supported by standard personal computers, but also accessible to those unfamiliar with the principles of QM: available translational software fills this interdisciplinary gap and eliminates the need for unrealistic specialization. As benchtop instrumentation is making NMR measurement ever more widely accessible, such software tools become even more useful: as the magnet field strength goes down, QM-based computational analysis becomes increasingly important - if not indispensable. Finally, it should be stressed that NMR is no longer primarily used for fairly pure samples. QMSA not only facilitates interpretation of data from impure samples, but makes work with complex (NP) mixtures feasible.

QMSA Bridges Theory–Practice Gaps and Opens New Opportunities

Employing fundamental theory via QMSA enables unambiguous and complete interpretation of even very complex NMR spectra and reduces bias and variability inherent in phenotypic interpretation. The intrinsic self-consistency of QMSA also improves accuracy and specificity by alleviating issues caused by peak pattern overlap. This section will exemplify how QMSA is not only powerful to solve complex cases, but ought to be generally adopted for NMR spectral interpretation.

Improving Human Interpretation of NMR Spectra

Historically, NMR experimental output has evolved into the foundational expectation of representing spectra in tabulated formats, such as those set forth in ACS guidelines. Thus, it is prevailing practice to reduce the NMR properties of molecules to numerical values of chemical shifts and coupling constants after extracting them phenotypically from the spectra. These, mostly observational, means are commonly augmented by peak picking algorithms or multiplet analysis software, pairwise descriptors derived from 2D NMR data, and static chemical drawings; the latter often result in approximative values, sometimes mere ranges, for chemical shifts and largely incomplete sets of coupling constants.

Being human-centric processes, they are subject to bias and, often enough, depend on simplifying assumptions made during the software development. The assignment of the multiplicity of peak patterns and determination of resonance frequencies are predominantly made by the interpreters, rather than derived from mathematical calculations grounded in data and theory. Employing QMSA as described above, largely eliminates human bias: the ability to reduce the description of interpreted NMR data to spin parameters and well-established equations makes NMR data interpretation scientifically more straightforward. Moreover, it helps avoid ambiguous textual descriptions and tabulations that oversimplify complex features of NMR spectra.

Enhancing the Objectivity, Accuracy, and Completeness of NMR Information

Non-first-order scalar coupling effects and signal overlap are key aspects where human bias must be reduced to improve analytical accuracy. The pervasive use of multiplet annotations indicates that pure first-order coupling is an exception rather than the rule even with the advent of ultra high-field instrumentation. A relatively small (commonly, ≤ 10 ppm) ¹H chemical shift window makes peak overlap near-ubiquitous. Highly convoluted peak patterns make the extraction of the coupling information based on first-order rules impossible. This has significant implications: first, the deduced chemical shifts and coupling constants are inaccurate; second, the multiplet designation disregards all valuable coupling information. Consequently, tabulated data cannot be reconstituted into the original spectra and leads to an irreversible loss of NMR information. This prevents reuse of valuable experimental information.

Although computational power has been a bottleneck for decades, this no longer applies (see above): today, 1D ¹H and other NMR spectra of even complex molecules can be fully calculated with sufficient speed to permit iterative extraction of all underlying spin parameters. Calculations are no longer a limiting factor as large systems can be split into subsystems of manageable size that collectively reproduce the full spectra with minimal error. In fact, the quality of the experimental spectra, namely their fine structure and line shape detail, is more often the limiting factor. In practice, however, iterative fitting of large, second-order systems requires more accurate NMR parameters for starting values.

While QMSA is technically possible for all molecules in the greater space of natural products and biomedical structures, and an impressive range of structural complexity can already be covered at this point of technological development, a detailed discussion of limitations of QMSA methodology is provided in S3, Supporting Information.

Employing fundamental theoretical principles, thus, has the advantage of making the interpretation of NMR data more objective, accurate, and complete. This opens new opportunities for more automation in the interpretation process. As this advantage is independent of the abundance of higher-order effects and signal overlap, the QMSA-based approach is not only preferable for complex molecules and spectra, but should be universally adopted for NMR interpretation. This is further supported by the extraordinarily high reproducibility and field-independence of chemical shifts and coupling constants.

Collectively, QMSA enhances NMR analysis at various stages of data interpretation and documentation: (i) QMSA supports Good Scientific Practices by yielding high-accuracy data and (ii) facilitates reporting due to the numeric nature of its outcomes. (iii) By providing definitive interpretations as the essential prerequisite, QSMA helps advance automation and enables distinction of fitting vs nonfitting structures with QM-based accuracy. (iv) QMSA provides metrics such as local RMS values that are essential yet currently missing in NMR analysis and enable numeric consistency checks. Accordingly, QMSA can play key roles in both structure verification/dereplication and ab initio structure elucidation, which have different requirements and conceptual frameworks. For example, evaluation of candidate structures by HifSA can help eliminate incorrect structures and replace them with correct structures by taking into account the otherwise neglected wealth of information in 1D ¹H NMR spectra.

Reproducibility, Quality, and Trends

Provided that sample preparation and instrument measurement parameters are comparable, NMR experiments are highly reproducible. The standard deviation of the chemical shifts derived from the ¹H NMR spectra of two independently prepared samples of the sesquiterpenoid lactone, α-santonin (3; Figure 5), may serve as an example: acquired independently on two different instruments, the deviation was less than 5 ppb (0.005 ppm), equivalent to 2.5 Hz at 500 MHz, despite the 2-fold difference in sample concentrations (∼50 mM in DMSO-d₆ vs 100 mM in CDCl₃). Chemical shifts are widely recognized to vary with solvent, pH, temperature, and sample concentration; from a few ppb to 1 ppm or more, especially for nuclei close to proton donors/acceptors at different pH. Consequently, failure to report sample parameters makes chemical shifts irreproducible.

Figure 5.

Importance of adequate terminology in NMR analysis. The spectrum of the axial H-9a in (−)-α-santonin (3; 500 MHz, CDCl₃) exemplifies how clear definitions of the terms transitions, resonances, signals, lines, and peaks matter for the interpretation of the observed pattern. Refer to the main text for further explanations. In this example, the number of peaks is due to the very large number and very close proximity of the underlying 155 transitions. This myriad of transitions can be considered as producing 155 lines that are indistinguishable with current instrumentation. Note the differences in the exact positions of the individual peaks of the apparent dt/ddd pattern vs those of the lines in the first-order coupling trees that represent the J-couplings with the geminal H-9b (13.66 Hz), the vicinal H-8a (4.63 Hz) and H-8b (13.16 Hz), and long-range with the angular Me-14 (0.76 Hz). This apparent mismatch demonstrates the subtle but important difference between the first-order assumption of a visual interpretation (phenotypic) and the actual spin parameters determined by QM-based (genotypic) full spin analysis. This case exemplifies why non-QM-based fitting methods (peak deconvolution) and automated methods of multiplicity analysis are bound to yield fundamentally inaccurate results, with the degree of inaccuracy depending on the particular spin system.

In contrast, coupling constants are highly stable: J values tend to be nearly unaffected by the experimental conditions unless associated with a major change in the conformational averaging space. For example, the standard deviations of all coupling constants derived from the two independent ¹H NMR data sets of 3 were <0.01 Hz (0.02 ppb at 500 MHz) in CDCl₃, and <0.3 Hz in DMSO-d₆. These variations were smaller than the natural line width in the corresponding spectra. Deriving NMR parameters from experimental data with adequate precision requires HifSA processing, which accounts for the complete, continuous line shape of all resonances individually.

The very favorable accuracy and precision of chemical shifts and, in particular, J-coupling constants derived from samples measured under similar conditions explain why their accurate and precise determination via QMSA/HifSA enables generation of highly selective ¹H NMR profiles that may serve as unique identifiers of most organic structures (unless they are severely ¹H-deficient). Indeed, even when compared across different solvents, the coupling constants of a given molecule are indeed rather constant even though the corresponding peak patterns often vary substantially due to overlap or changes in the chemical shifts and field strength. While conformational changes in more flexible systems can have substantial effects, J values generally are indeed constant, as their name coupling constants implies (albeit for a different historic reason). For all practical purposes, this makes J values important focal points in the interpretation of ¹H NMR spectra. Conversely, the observed chemical shifts of identical or analogous hydrogens in ¹H NMR spectra often show variability, adequately reflecting the notion of shift. However, both (the constancy of Js and the shifting of δs) remain self-consistent entities that can be described completely by NMR theory. In other words, even when the chemical shifts change due to slightly different sample conditions, the resulting spectrum is still fully defined by the correlation of the underlying spin parameters.

Fostering the Reusability of NMR Information

The spin parameters gained from employing NMR theory in spectral analysis are fully suitable for database-driven applications and other big data approaches (AI/ML). Moreover, the ability to calculate NMR spectra accurately from the spin parameters intrinsic to the molecule and, thereby, explain experimental observations in full detail offers new approaches for more reliable automated structure elucidation workflows. First, this provides means for deriving the actual spin parameters directly from the experimental data. Second, assessing the congruence between known spin parameters of molecules and those derived from experimental spectra of the same or congeneric compound can be used to calculate unbiased scores that reflect structural identity vs relatedness and are measures for reliability. This yields new potential metrics for AI/ML-driven tools aimed at structural ID in metabolomics and pharmaceutical analysis.

Advancing the Specificity of NMR Terminology

The above considerations collectively rationalize the importance of precise terminology as a prerequisite for the integrity of the entire process of data acquisition and interpretation. Because the practice of visual interpretation employs language, terminology becomes an essential element of integrity, as exemplified for 1 in Figure 5. To this end, a recent initiative led by a qNMR Expert Panel at the United States Pharmacopeia (USP) has laid the foundation for an updated NMR terminology framework,^28,29 employed in the General Chapters <761> Nuclear Magnetic Resonance Spectroscopy(30) and <1761> Applications of Nuclear Magnetic Resonance Spectroscopy(31) currently in revision, and summarized briefly below:

A transition is the nuclear absorption of energy re-emission of a photon of a given discrete radio frequency, ν, by an isotope going from one energy level to another, as described by QM. Transitions occur spontaneously and continuously once the sample is placed in a magnetic field, account for the distribution of nuclei among energy levels, and are driven by molecular motion at a frequency that equals the energy level separation of the nuclear levels, ν. Transitions are not directly observable and are intrinsic to the genotypic characteristics of the NMR process.

A resonance is the physical absorption of radio frequency, ν₀ (Larmor frequency, in hertz [Hz]), which reflects the natural nuclear precession frequency for that isotope in a given magnetic field. Expressed in a field-independent term, its chemical shift in dimensionless units of parts-per-million (ppm) relates the frequency difference of the observed nucleus to a reference nucleus as δ (ppm) = 10⁶ (Δν/ν_R). A resonance is also not directly observable and may be characterized as another genotypic characteristic.

A signal is the electronic response detected in the coil of an NMR spectrometer due to a transition, which is caused by the absorption of ν₀. Signals are directly observable by an NMR spectrometer and, therefore, can be considered phenotypic characteristics.

A line is a theoretical component: all lines combined explain the intensity distribution in the frequency-domain spectrum, and their position measured in Hz can be determined by QM calculation. Lines are the positions of the individual transitions, and their positions in spectra are measured in Hz. Lines from the same transition have identical lineshapes. The number of lines from a given nucleus will form peaks that have a simple pattern in first-order cases or a more complicated pattern in second and higher-order cases. Lines are the genotype and differ conceptually from peaks, which are the phenotypical local maxima in the intensity distribution. Peaks often result from multiple lines and require arbitrary peak-picking algorithms for determination.

A peak is the continuous segment of a spectrum, with a defined maximum and flanked by local minima. Peaks represent one or multiple lines, the latter not necessarily from the same origin. While the location and intensity of peak maxima can be determined, their overall assessment is problematic, especially when peak shape is ignored as is the case in the typically performed peak picking process. In some cases, a peak can consist of more than a single line, each with an individual line shape. Originally, spectra were obtained by sweeping the magnetic field while holding the radiofrequency (RF) constant. This resulted in the terms high-field and low-field to indicate where a peak appeared in the spectrum. Modern spectrometers obtain spectra by applying a pulse of RF to a sample to generate a Free Induction Decay (FID), which is a spectrum of intensity of the signal as a function of time. There is no variation in the field or the RF. However, Fourier transformation of the time domain signal results in a spectrum consisting of intensity as a function of frequency. Therefore, the terms high field and low field are anachronistic and misleading, and they should be replaced by high frequency and low frequency, which fortuitously correspond to the values of the chemical shifts in ppm.

A (peak) pattern is the segment of a frequency-domain NMR spectrum that results from multiple overlapping or closely adjacent peaks. As such, a (peak) pattern may or may not have an identifiable multiplicity except when not overlapped by other peaks and when following true first-order coupling conditions; the pattern can then be designated as singlet, doublet, triplet, etc.

Resolution refers to the degree of distinguishability of peaks or lines, and reflects the relationship between peak or line width, shape, and relative location on the x-axis of a frequency-domain spectrum. The actual, or achievable, spectral resolution of an NMR spectrum is the result of many factors: the proper operation of the spectrometer and careful sample preparation, adequate field and pulse homogeneity, nuclear relaxation conditions, as well as properties of the sample such as solvent, pH, viscosity, and homogeneity. In contrast, digital resolution refers to the number of digital data points in the spectrum, and is usually determined by acquisition parameters.

Dispersion refers to the degree of separation between peaks and patterns on the frequency-domain scale of the spectrum. Dispersion is a direct linear function of the static magnetic field strength. Spectra with increased dispersion have fewer overlapping (peak) patterns and less higher-order effects, making them less complex. While greater dispersion is associated with greater separation of peak patterns and wider distribution of resonance frequencies, it should not be confused with resolution.

Best Practices for Data Acquisition and Analysis

Window Functions and Resolution

Many modern NMR spectrometers, including entry-level cryomagnetic instrumentation (300+MHz), exhibit significantly improved sensitivity, especially when equipped with cryoprobes. Considering the relationship between resolution and signal-to-noise ratio (SNR), it is important to emphasize that high-SNR 1D ¹H NMR spectra are more readily susceptible to resolution enhancement processing, e.g., via Lorentzian–Gaussian multiplication. This opens an opportunity for extracting more (precise) structural and quantitative information from the same FID: the use of resolution-enhancing pre-FT window functions (which may have an impact on the quantitative nature of the spectra) or non-FT methods such as CRAFT offers great potential for generating a better understanding of ¹H NMR spectra. The resolving power (see definitions above) of the modern NMR spectrometers is generally superb. Depending on the specifics of the molecule such as rigidity/flexibility, relaxation, exchange, and other dynamic properties, and also proper operation, spectrometers can resolve peaks and lines that are as little as 0.2 Hz apart. In this context, regular instrument performance checks with the classical CHCl₃ line shape sample (1% CHCl₃ in acetone-d₆) are a worthwhile - or even necessary - exercise.

Trading a Few Seconds and Some Bytes for Better Resolution

Another aspect of NMR data acquisition that deserves attention is the use of sufficient acquisition times (AQ) and/or FID data point sizes, to afford optimal digital point resolution of the spectrum. Especially when employing ultrahigh magnetic field strengths, which are associated with higher frequencies and spectral widths expressed in Hz, the number of acquired data points should be increased proportionally to reflect the highest resolution. As the maximum resolution of an FT NMR spectrum is 1/AQ and also expressed in Hz, the proper magnitude of AQ constitutes a critical parameter for collecting good-quality data. This said, excessive AQ leading to sampling beyond the point where the FID has truly decayed to zero, will only lead to collecting noise and, thereby, decrease the SNR.

If sampling the data to the end of the FID still results in an insufficient number of data points for adequate peak definition (points per peak), subsequent postacquisition zero-filling of the time-domain (TD) data is critical for proper digital definition of the spectrum. This is essential for the interpretation of 1D ¹H NMR spectra, which depends on the proper extraction of accurate locations of peak and line frequencies as well as frequency differences. For practical considerations, it should be noted that setting AQ is the most direct way to determine the digital resolution of the acquired raw NMR data. Unlike TD, AQ does not have to be a multiple of 2 to be amenable to FT. Thus, in FT-NMR spectroscopy, proper settings of the basic acquisition and processing parameters, AQ and TD respectively, is of paramount importance. While the experimental “costs” of such choices are zero, they are immensely helpful for data interpretation and recognition of the modular characteristics of the terminology relevant to ¹H NMR spectra.

Summary and Outlook

The Power and Value of Classical NMR Analysis

Classical 1D ¹H NMR spectra contain a wealth of information that leads to unequivocal structure elucidation, verification, and reliable quantitation when properly utilized. This information richness has lately been overlooked, partly due to higher field strengths and multidimensional NMR. The ubiquity of overlapping peaks and peak patterns severely limits the amount of information phenotypic analysis can gain, whereas molecular genotyping by QMSA provides full access. The emergence of powerful desktop processors and easy-to-use software facilitate the application of QMSA techniques by non-QM experts and evolve continuously toward automation. As a modern form of classical NMR analysis, QMSA (re)introduces major value to ¹H NMR spectra: (i) the magnetic field independence of δ/J makes the spectra transferable and increases the versatility of NMR spectroscopy. (ii) Spin parameters are unequivocal molecular properties for structure verification and elucidation and (iii) increase the accuracy and reproducibility of structural reporting; (iv) the QMSA approach compares favorably to phenotypic line-fitting techniques and reduces output data size by order(s) of magnitude; (v) QM-based analysis increases the specificity of qNMR protocols.

Evolution of Descriptive Language and NMR Utility

A modular and systematic terminology is foundational for understanding and interpreting NMR spectra. Over the decades, a certain degree of inconsistency in terminology has emerged. As long-term NMR practitioners, we sense and show above that terms widely used since the inception of NMR spectroscopy such as transition, resonance, signal, line, peak, pattern, as well as resolution, dispersion, and multiplicity require more consistent and universally agreed-upon definitions. Clarifying essential NMR terminology will not only ensure integrity, but also spur methodological advancements in both qualitative and quantitative NMR.

Clean unambiguous terminology is essential for understanding QM-based concepts and consistent scientific communication of QMSA outcomes, including for growing qNMR applications. Much of this fundamental argumentation has been introduced in the USP General Chapter <1761> in revision and the companion Stimuli article.²⁸ The terms defined in this article are at the heart of the NMR thesaurus and are intended to help unlock the potential inherent to the modular physical principles encoded in NMR spectra, and to increase specificity in data interpretation and quantitative accuracy of qNMR as a primary analytical tool. Broad adoption of an evolutionary updated terminology will benefit natural products, chemicals and other biomedical research fields that utilize NMR analysis extensively.

To this end, this Perspective contributes a piece to the greater puzzle of qualitative and quantitative NMR spectroscopy and its increasing prominence in chemistry and the applied health sciences. The authors posit that the concerted broad implementation of consolidated NMR terminology, recently evolving raw NMR data (FID) sharing, available QMSA software tools, and standardized digital reporting of interpreted data into NMR practice and literature are key to advancing NMR and the sciences that apply it as a tool.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jnatprod.4c01013.

• QMSA Limitations; the HifSA profile of (−)-α-santonin (3) (PDF)

The authors declare no competing financial interest.