Data-Driven Prediction of Circular Dichroism-Based Calibration Curves for the Rapid Screening of Chiral Primary Amine Enantiomeric Excess Values

Abstract

Here, we describe the prediction of the circular dichroism (CD) response of a three-component chiroptical sensor for enantiomeric excess (ee) determination of chiral amines using a multivariate fit to electronic and steric parameters. These computationally derived parameters can be computed for nearly any amine and correlate well with the CD response of the 12 amines comprising the training set. The resulting model was used to accurately predict the CD response of a test set of chiral amines. Theoretical calibration curves were then created and used to determine the ee of solutions of unknown ee. Using this method, the error in ee determination differed by less than 10% compared to experimentally generated calibration curves.

Graphical Abstract

INTRODUCTION

High-throughput experimentation (HTE) has become an integral part of reaction discovery and optimization.^1-3 Asymmetric synthesis is an area in which HTE demonstrates prowess as it is used to screen thousands of reaction conditions exploring ligand, additive, solvent, and catalyst chemical space to afford rapid reaction optimization.⁴ Methods for conducting reactions on such scale are mature, and yet, analysis of reaction outcome, such as yield determination, still relies heavily on serial chromatographic separation. Moreover, asymmetric synthesis requires chromatographic resolution of enantiomers to assess enantioselectivity, further slowing HTE analysis.⁵ Chiroptical methods address this bottleneck by enabling ee determination on time scales amenable to HTE.⁶ Chiroptical assays have been developed for numerous functional groups, and the techniques have proven useful in many reaction screening contexts.^7-14

With either chromatographic or chiroptical techniques, asymmetric reaction analysis starts with the development and validation of a method that allows for reliable ee determination of the anticipated product. If one chooses chiral high-performance liquid chromatography (HPLC) for this purpose, one needs to obtain the reaction product in racemic form to search for a chiral stationary phase (CSP) and conditions that achieve sufficient enantioresolution. With that in hand, a chemist is able to determine ee values for that particular compound. If one uses chiroptical sensing, an enantiopure or enantioenriched reference is needed to construct a calibration curve with a suitable probe that interacts with the analyte to generate a quantifiable circular dichroism (CD) signal. In the end, both techniques require reference material before they can be developed and used, albeit a racemic sample is typically more easily available than an enantiopure one. The workload increases further when the application scope of an asymmetric reaction protocol is under investigation–a very common scenario in synthetic methodology development laboratories. For each new reaction product, a reference sample must be prepared in a racemic or enantioenriched form to acquire a suitable HPLC or CD method, respectively. This is time-consuming and decelerates the discovery pace. Chiral HPLC method development can be particularly arduous because it often is a trial-and-error approach, at least when polysaccharide, cyclodextrin, or protein CSPs are tested, and there is no guarantee that satisfactory enantioseparation can eventually be achieved. In some cases, days to weeks are spent to no avail in search for a method that allows ee determination. We envisioned that one could remove this bottleneck with a rationally calculated, universally applicable calibration curve that correctly predicts CD intensities across a whole compound class, e.g., for all conceivable chiral amines. If possible, this would enable ee determination of any asymmetric reaction product without the need for a reference and individual method development.

Linear free energy relationships (LFERs) use physicochemical parameters that describe and predict chemical reactions and properties.¹⁵ Recently, the use of multiparameter LFERs has found wide success in modeling reaction outcomes in asymmetric catalysis by guiding reaction discovery and optimization via screening.¹⁶ However, examples in which spectroscopic properties associated with analytical methods for screening are modeled and predicted are less common.¹⁷

For ee assays that rely on CD, the signal is largely governed by differences in the steric size of the groups on the analyte’s point stereocenter.¹⁸ Our group has used this steric dependence to predict the calibration curves of a tripodal zinc(II) complex for the ee determination of chiral secondary alcohols, as well as a tripodal quinoline-Cu(II) sensor for chiral carboxylic acids.⁸ In the case of the alcohol sensor, the three-component assembly 1 adopts a preferred configurational twist (P or M) upon binding a chiral analyte resulting in exciton coupling (Figure 1A). In this previous work, we demonstrated that the diastereomeric ratio (dr) of P and M isomers correlates to the CD signal intensity. This relationship can be used to generate theoretical calibration curves, thus bypassing the need for calibration experiments.^18,19 Using only Charton steric parameters, the calibration curves enabled ee determination of unknown samples. However, the use of Charton parameters limits this approach as they are experimentally determined and have been measured for only select functional groups, thus narrowing the range of chiral analytes accommodated by the model. Additionally, predictive models based solely on steric parameters would become unreliable for analyte CD responses that are also dependent on electronic effects. A more universal approach would be to use computationally generated parameters so that calibration curves for any chiral analyte could be known a priori.

Figure 1.

(A) Three-component chiroptical sensor adopting P and M axial configurations, allowing for ee determination of alcohols without prior calibration experiments. (B) Bull-James assembly for ee determination of chiral amines via ¹H NMR spectroscopy. (C) Wolf assembly for ee determination of a variety of analytes via CD spectroscopy. (D) Three-component chiroptical sensor for the ee determination of amines used in this study.

Sterimol parameters are prime candidates for a computational approach, as they divide the steric description into dimensional components: width, length, etc.,^20,21 and have been widely impactful in asymmetric catalysis modeling.²² More recently, several groups have demonstrated the utility of distance resolved parameters, which describe the size of functional groups within a certain spatial region.²³ This dimensional specificity enables chemists to distinguish the most relevant steric parameters that describe the steric effects (e.g., proximal versus distal steric interactions). Further, if necessary, adding electronic parameters, such as Hammett σ values, IR-stretching frequencies, or computed HOMO/LUMO energies, would further deconvolute the CD response of the sensors, thereby revealing any noncovalent interactions (NCIs) responsible for the sensor function.

The predictive modeling of CD based ee assays has been reported. In a collaboration with our group, Sigman and co-workers parametrized chemical derivatives of the α- and β-chiral alcohol sensor 1 to guide the design to accommodate γ-chiral alcohols.²³ The goal was to optimize the sensor for this new analyte class, which required steric and electronic parametrization of sensor derivatives. Critically, while not explored, such an approach should also lead to the prediction of ee calibration curves that reveal the relationship between analyte parameters and CD intensity.

To explore this prediction, we examined assemblies involving orthoimino boronic acids. Such boronic acids are frequently used in sensing applications.^24-26 For example, the Bull-James assembly using 2-formylbenzeneboronic acid (2, Figure 1B) involves both boronic acid/diol and amine/aldehyde condensations to create ¹H NMR chiral shift reagents (such as 3) for both chiral amines and chiral diols.^27,28 The complex equilibria of these systems are well-studied by our group, making such assemblies attractive platforms for sensing applications.²⁹ Building upon this work, Wolf and co-workers introduced stereodynamic diol (4) that increased the sensitivity and enabled ee determination via CD for a wide variety of analytes (Figure 1C). The high sensitivity of tropos biaryl sensors has been established,^10,30 making Wolf’s assembly a suitable system to expand upon.

In the study reported herein, we combined steric and electronic modeling, as used in reaction discovery and optimization,³¹ to develop a predictive model of calibration curves for a three-component orthoimino boronic-acid-based sensor (Figure 1D). This removes the necessity of chiral resolution to generate calibration curves for chiroptical sensing used in asymmetric reaction discovery and optimization.

RESULTS AND DISCUSSION

Initial Sensor and Limitations.

Before model construction, we first confirmed that the Wolf assembly behaved much like other orthoimino boronic acid assemblies. To no surprise, the sensor speciated into numerous boronic acid-diol complexes, which were observable by ¹¹B NMR spectroscopy (Figure S1 in the Supporting Information (SI)), but most importantly, we confirmed the dominance of species 6, which features an N─B dative bond in aprotic solvents. Any disparity between the computationally modeled assembly and the structure in solution could result in parameters that do not accurately describe the Wolf assembly and thus hinder model development.

Following the initial ¹¹B NMR study, we sought to derive a relationship between the CD response of the Wolf assembly and several Sterimol parameters that describe the analyte. The stereodynamic binaphthol 4 is CD-silent until the addition of a chiral amine and boronic acid 5, after which it adopts either a P or M helical configuration. The energetic preference for one configuration (i.e., dr) is what ultimately gives rise to a couplet in the CD spectrum at 232 nm.

To replicate our previous CD modeling approach (Figure 1A) in the context of the Wolf assembly, we first attempted to quantify the CD-active diastereomers that result from the twist of the binaphthol chromophore.^10,32 However, even at −80 °C, these diastereomers were not observable by ¹H NMR spectroscopy, suggesting the ΔG^‡ of P and M isomerization was too small to allow for resolution of these stereoisomers (Figure S2 in the SI). This observation is in agreement with dynamic NMR and computational investigations of 4 and analogous systems, such as 1,3-cycloheptadienes, which possess interconversion barriers of approximately 4 kcal mol⁻¹ and require much lower temperatures than typical NMR probes can tolerate.^33,34 To overcome this technical challenge, we redesigned sensor 6 to increase the barrier of rotation enough to observe the P and M diastereomers at a higher temperature.

Wolf Assembly Modification and Characterization.

Before synthesizing an analogue of 4, we scoured literature values for similar biaryls with rotation barriers slightly higher than that of 4. We ultimately arrived at binaphthol 14, which we calculated to possess a higher barrier to rotation (20.0 kcal mol⁻¹) than the initial binaphthol (Table 1 in the SI for calculation details). The modified binaphthol ligand is easily synthesized by bromination of the 1-naphthol and 2-naphthol subunits with NBS and protection with methyl iodide. Miyaura borylation provided the boronic ester coupling partner, 12, which was subjected to Suzuki cross-coupling conditions with 9. Demethylation with boron tribromide afforded the modified binaphthol 14 (Scheme 1).

Scheme 1.

Synthesis of Asymmetric Binaphthol Ligand

Replacing binaphthol 4 with 14 in the three-component assembly results in an additional stereocenter at boron due to the removal of the C₂ symmetry axis of the binaphthol ligand. Four diastereomers of assembly 7 therefore exist upon introduction of a chiral amine (Figure 2A). This arises due to the existence of three stereocenters: the point stereocenter of the chiral amine (R or S), the point stereocenter of the boron atom (R or S), and the axial stereocenter of the binaphthol ligand (M or P). This produces 2³ = 8 stereoisomers (four diastereomers and their enantiomers) which results in 4 resonances in the ¹H NMR spectra (Figure 2B). Interconversion of two of these diastereomers occurs via ring puckering that converts the M and P configuration of the axial stereocenter, while a second set of diastereomers interconvert by dissociation of the N─B dative bond and rotation along the boron-benzene ring single bond. We confirmed the dynamic nature of this process by VT-NMR using S-1-cyclohexylethylamine and observed that the four signals of the diastereomers coalesce at approximately 95 °C (Figure 2C). The observation that two diastereomers do not coalesce before another two implies that the interconversion of all four diastereomers is coupled to the same rate determining step, which is most likely the breakage of the N─B dative bond, followed by a more rapid M/P axial stereocenter interconversion.

Figure 2.

(A) Four diastereomers of sensor 7 formed with amine S-1-cyclohexylethylamine. The stereochemical descriptors are in order: binaphthol axial stereocenter (M/P), amine point stereocenter (S in this example), and boron stereocenter (R/S). (B) ¹H NMR spectrum featuring the four diastereomers of 7. (C) VT-NMR experiment showing coalescence of the methoxy resonances of the four diastereomers at 95 °C (DMSO-d₆, 600 MHz).

In general, the aromatic region of the spectra of 7 with different chiral amines was too crowded for meaningful interpretation. However, the methoxy group of boronic acid 5 served as a spectroscopic handle by which the diastereomers can be quantified. For most of the amines used in this study, four signals were observed in the δ4.2–δ3.8 region corresponding to the methoxy groups of the interconverting diastereomers. The ¹H NMR spectra of our initial training set (Figure 3B) were collected and integrated from δ4.2–δ3.8 to provide the dr for our initial model. Although each resonance represents a single CD-active diastereomer, assigning each resonance to a particular diastereomer was difficult. The signals exhibit no spin–spin splitting or nuclear Overhauser effects (NOEs) to inform our diastereomer assignments. Nevertheless, we were able to calculate the dr using the following reasoning.

Figure 3.

(A) Sensor 7 and diagram of Sterimol parameters for an isopropyl group. (B) Initial training set. (C) Relationship between CD and dr. (D) Relationship between ΔB1 and log(dr).

We recognized that two resonances were associated with the boron epimers and two were associated with the binaphthol axial epimers. It stands to reason that the sum of the integrations of two of resonances divided by the sum of the remaining two results in a dr value of either the boron or the axial stereogenic element. We found that the first and the third largest resonance by area represented the predominate axial twist because it correlated strongly to the CD signal (for a detailed discussion on dr measurements see the SI). However, this experimental approach has substantial drawbacks as residual boronic acid 5 and its corresponding boronate ester were also present if the assembly had not fully formed or if 5 was in slight excess. Additionally, any analytes bearing an additional methoxy group crowded the δ4.2–δ3.8 region, making interpretation difficult. Despite these difficulties, we were able to measure this form of a dr for 15a–15f.

These dr measurements were correlated to the CD signal associated with the binaphthol reporter chromophore at 232 nm using our previously established relationship between the two values (CD = m × [1/(1 + log(dr))], Figure 3C).¹⁹ While several amines (15b, 15c, 15f, and 15d) produced a reasonably straight line, two of the lower dr amines (15a and 15e) considerably deviated from the correlation. Nevertheless, we continued to explore how steric size differences of the two substituents of the amine stereocenter affected this relationship by generating three Sterimol values for each of the amine-incorporated assemblies, which represent the length (L), minimum width (B1), and maximum width (B5) of each of the substituents of the chiral amine (Figure 4B).

Figure 4.

(A) Conformer–rotamer ensemble generation workflow using CREST. (B) Select features generated for each analyte.

Sterimol parameters are highly sensitive to conformation. For instance, the length of a butyl group varies greatly depending on the number of methylene units in anti or gauche conformations.²⁰ Additionally, the local environment of a substituent influences its accessible conformations, such as that of the boronic-acid assembly, and thereby the steric parameters. Thus, we opted to model the entire assembly as opposed to just the isolated substituents of interest. The resulting Sterimol values are then Boltzmann averaged as they would be for an experimentally determined steric parameter (e.g., Charton or A-values).

To gain a realistic conformer ensemble, each assembly was subjected to a Conformer–Rotamer Ensemble Search Tool (CREST) conformer search (Figure 4A).³⁵ The conformer–rotamer ensembles (CREs) were further optimized at the B3LYP/6-31G(d,p) level and then filtered for similarity based on root-mean squared deviation (RMSD) of atomic positions. After duplicate structures were removed, the remaining structures of the CRE were subjected to a single-point energy calculation at the M06-2X/Def2TZVP level. Only conformers within 5 kcal/mol were considered for the calculation of descriptors. The Sterimol parameters were collected using a modified Python script based on Paton’s wSterimol program.²⁰

Using a stepwise multivariate linear regression, we identified the difference between the B1 values (ΔB1) of the two substituents on the amine stereocenter to be the only significant predictor. However, the LFER between log(dr) and ΔB1 was poor (Figure 3D). Almost all of the amines in the initial training set had ΔB1 values close to 0, resulting in a large distribution of points along the y-axis. This was a strong indication that additional parameters must be included for a more nuanced picture of the relevant steric, and possibly electronic, effects necessary to predict CD intensity. Despite the limitations of this steric-only approach, we were able to gain insights into the degree to which steric interactions influence CD intensity.

Initially, we found that 15d and 15e were not well-tolerated as they possessed larger ΔB1 values (~0.7 Å), yet their measured dr values were similar to the dr values of 15a. The large ΔB1 was attributed to distal steric bulk of 15d and 15e, which bear an isopropyl and tert-butyl group, respectively, at the para- position of the benzene ring. We concluded that, at some distance along the L Sterimol axis of the substituents, steric effects became inconsequential toward the CD response of sensor 7. To address this, we moved to distance-resolved Sterimol parameters, which are calculated on substructures of the parent molecule truncated a predefined distance. We found Sterimol parameters calculated within 3.8 Å to give the best fit with dr (see the SI for details on distance-resolved Sterimol parameters).

We sought to improve our model by calculating a variety of electronic parameters. Taking lessons from the multivariate analysis of catalytic reactions, we began by calculating HOMO/LUMO energies, natural bond orbital populations (NBOs), vibrational frequencies, polarizability, and dipole moments (Figure 4B). Select structural features such as bond lengths and the dihedral angle between the 1-naphthol and 2-naphthol subunits were also calculated.

The increased number of predictive parameters would prove challenging with such a small initial training set. The primary bottleneck for increasing the training set size was determining dr values, as many amines possessed coincidental resonances in the ¹H NMR spectrum, which prevented us from measuring an accurate dr. Therefore, although we have historically correlated substituent effects to dr to gain insight into how structural parameters influence the thermodynamics (i.e., LFERS), followed by then correlating the dr values to CD intensities (e.g., Figure 3),^8,18,19 we opted to directly predict CD instead of using dr as an intermediate predictor. While we lose the ability to calculate thermodynamic differences between diastereomers, we are still able to gain insight into which structural parameters most influence the CD intensities and in turn postulate about steric and electronic interactions within the three-component assembly.

Using the scikit-learn package of Python, we attempted several multivariate linear regression (MLR) techniques to relate our descriptors to CD. Both ridge regression and stepwise MLR showed promise, however, the relationship between the selected features and CD response was ambiguous. Due to the large number of descriptors and limited size of the training set, we arrived at LASSO regression, a popular MLR technique for problems with few observables and many descriptors.³⁶ LASSO implements a cost function during the regression process that penalizes models for including additional parameters. During the training process, irrelevant variable coefficients ultimately reduce to zero and are removed, allowing for a more stable and interpretable model.³⁷

During model development, LASSO regression found three variables to be significant: binaphthol dihedral angle (θ), ΔB5, and NBO population of the imine nitrogen atom (NBO_N) (eq given in Figure 5B). Visual inspection of the regression line shows excellent correlation with the predictor variables, while the slight scatter results in an R² = 0.87. Of the three variables, the dihedral angle is unsurprisingly positively correlated with CD, as this angle between coupling chromophores partially governs CD intensity via exciton coupling, which makes its inclusion into the regression equation imperitive.^32,38 The twist of the reporter chromophore arises from a combination of steric effects imposed by the substituents of the amine, as well as attractive NCIs, each of which vary between analytes. It is possible that this angle parameter also serves as a “catch-all” for minute steric and electronic effects not accounted for by other descriptors.

Figure 5.

(A) Training set for second generation model. An asterisk indicates both enantiomers were analyzed. (B) Multivariate regression equation for predicting CD (mdeg/abs) and graphical explanation of selected parameters. (C) Test set for second generation model.

In contrast to θ, the other two variables inclusion is not immediately obvious, showing the power of using a blind multiparameter fit. The NBO_N values were negatively correlated with CD (eq given in Figure 5B). NBO analysis gives insight into the distribution of charge in a molecule.³⁹ In sensor 7, the NBO_N value reflects the electron density of the imine nitrogen atom and thus the degree of N─B dative bond formation. Amines with electron donating p-substituted benzene rings (e.g., 15d, 15e, 15i, and others) had the largest NBO_N values and the lowest CD signals of the training set. This suggests that electron rich substituents hinder point-to-axial chirality transfer to the reporter binaphthol ligand. Additionally, each amine featuring electron withdrawing substituents, such as 15g, 15h, and 15k, exhibited diminished NBO_N values. Our computational investigation revealed that the electron deficient moieties of each substituent often resided directly above the naphthyl groups for the lowest lying conformers of the CRE. We suspect that this donor–acceptor interaction brings the point stereocenter of the analyte closer to the reporter chromophore, thus enhancing point-to-axial chirality transfer.

While our initial model (Figure 3) was falsely predicated on steric effects being the only factor of the CD response of 7, the multiparameter fit finds that steric interactions are still influential in the sensor’s function. However, to our surprise, ΔB5 (differences between the B5 values of the two substituents on the amine stereocenter) was negatively, not positively, correlated with CD despite our previous findings with sensor 1. This negatively correlated steric parameter, ΔB5, was calculated in the same manner as ΔB1 our initial model. Because the training set is mostly composed of amines with methyl groups at the stereocenter, which have the same B5 value, this term is effectively a measure of the steric size of the amines along the N─C* axis (where C* is the point stereocenter of the amine). The largest ΔB5 values are found for 15g and 15h, which feature an o-trifluoromethylbenzene ring and a tert-butylacyl group, respectively. These substituents add steric bulk near the reporter chromophore and reduce CD intensity. We further explored this assertion by calculating Sterimol parameters for along the N─C* axis. When B5 is measured along this bond, a strong negative correlation between CD intensity and B5 was observed for all but two amines we tested (see the SI for details). Amines 15d and 15e also had a substantial contribution from this term due to the large p-substituted benzene ring substituents.

Although the relationship between the ΔB5 parameter and CD can be rationalized by a repulsive steric argument, certain attractive NCIs appear to be enhancing point-to-axial chirality transfer between the point and axial stereocenters which may counteract this effect. With bulky amines (e.g., 15b and 15l), the C─H bond at the amine stereocenter was found in the CRE to reside directly above aryl─aryl bond of the binaphthol ligand. This is best rationalized as the minimum energy conformer adopting a geometry that places the medium sized substituent (methyl) and the large substituent (cyclohexyl or tert-butyl) away from the binaphthol chromophore. However, amines bearing aromatic rings (15a, 15c, 15d, 15e, and others) adopted conformations that placed their rings much closer or directly over the binaphthol ligand, apparently maximizing attractive NCIs. This positioning maximizes donor–acceptor interactions between the binaphthol and amine substituents, which enhances point-to-axial chirality transfer. Such interactions are clearly visible in the computed NCI plots (Figure 6), which are used to visualize van der Waals interactions, hydrogen bonds, and other NCIs.⁴⁰ The computed NCI plots revealed the presence of large dispersion interactions between aromatic amine substituents and the binaphthol chromophore, while much smaller NCI surfaces were observed for bulkier aliphatic amines. This finding is in agreement with the fact that electron withdrawing groups greatly enhance the CD signal of sensor 7.

Figure 6.

(A) NCI plot of 7g showing π–π stacking geometry and a large NCI surface. (B) NCI plot of 7l exhibiting diminished NCI surface as the tert-butyl group is placed away from the naphthalene ring.

The combination of NBO_N, which likely embodies the NCIs (Figure 6), and ΔB5 in the regression equation demonstrates the importance of point-to-axial chirality transfer in the sensor’s function. The CD intensity of 7 is maximized when NBO_N is small, indicating a strong N─B dative bond and the point stereocenter is “pulled” closer to the reporter chromophore by NCIs. Conversely, once substituents at the point stereocenter are too large, steric interference “pushes” the point stereocenter away and hinders point-to-axial chirality transfer.

To validate our model with a test set, we made predictions for three additional amines with qualitatively similar features to those of the training set (Figure 5). The largest NBO_N of the test set was found with 15m, which unsurprisingly gives CD responses similar to other electron rich aromatic amines (e.g., 15e, and 15d). This combined with an intermediate ΔB5 value of 2.3 explained why 15m gave one of the lowest CD values of the amines we explored. Conversely, 15n and 15o had similarly low NBO_N values and thus larger CD signals. However, the ΔB5 of 15o substantially attenuated the predicted CD signal owing to the high steric congestion between the benzhydryl group and the reporter chromophore.

Single-Blind ee Determination Study.

To demonstrate the utility of these predictions, theoretical calibration curves were generated by our model (eq given in Figure 5B). This was done by calculating the expected CD values of mixtures of enantiomers knowing that the enantiomers will have equal and opposite CD values, with mixtures thereof proportionally contributing to the CD (where racemic mixtures have CD = 0). These calculated calibration curves were overlaid with experimentally generated calibration curves (Figure 7) for two amines of the test set (15n and 15o) because the larger CD intensities of these amines gives a larger dynamic range. One researcher (ZA) prepared two solutions each of 15n and 15o. Each sample’s ee was only known by researcher Z.A. Another researcher (J.R.H.) analyzed these solutions with sensor 7 and used both the predicted and experimental calibration curves to calculate ee values.

Figure 7.

(A) Predicted and experimental calibration curves for 15n and results from single-blind ee determination study. (B) Predicted and experimental calibration curves for 15o and results from single-blind ee determination study.

When applied to 15n, the experimental and theoretical calibration curves match and provide similar errors when used to determine the ee of unknown samples. The difference in errors between the experimental and theoretical calibration curves is approximately 6% for the three randomized samples. As the table accentuates, our experience is that the error associated with chiroptical ee assays increases with the ee of the sample.⁴¹

The multivariate equation (Figure 5B) predicted a slightly lower CD intensity at 100% ee for 15o, which is reflected in the diminished slope of the theoretical calibration curve. As a result, the ee values of the unknown samples were overestimated using the theoretical calibration curve. At higher ee values, the disparity between the predicted and experimental calibration curves is exaggerated, which in turn makes the ee measurements less accurate in these ranges. Irrespective of the increased disparity, the differences in errors found for the ee values between the experimental and theoretical curves was around 10% (i.e., 11.4%). Moreover, the role of a theoretical calibration curve is to serve as a coarse analytical tool when optimizing asymmetric transformations. After all, in a screening experiment, the goal is to measure relative ee values (i.e., increasing or decreasing) and the greatest enantiomeric excess values could be confirmed separately by chiral HPLC. Most importantly, the multiparameter fit introduced here serves as a useful tool for predicting whether or not chiroptical ee determination would be a worthwhile endeavor for a desired analyte based upon its structural features. For instance, a high-throughput reaction optimization campaign would be less effective if the predicted CD signal, based upon θ ΔB5, and NBO_N, is too low to accurately differentiate ee values during screening.

CONCLUSION

The determination of ee using chiroptical assays has demonstrated great utility in recent years. Its speed relative to chromatography is superior, however, this rate increase is only possible once calibration curves have been generated. In this study, we demonstrated the prediction of calibration curves for ee assays using a data-driven approach that analyzes a three-component assembly based on point-to-axial chirality transfer. After parametrizing a set of α-chiral primary amines in both electronic and steric domains, LASSO regression predicted the CD signal at 100% ee, allowing for the generation of calibration curves. Solutions of unknown ee were subject to the three-component assembly for ee determination. The average difference between the predicted and experimental calibration curves was 8.7%.

We believe that our findings will have far-reaching implications and, if adapted, will streamline future asymmetric reaction discovery projects by eliminating the need for reference materials and traditional analytical method development including trial-and-error efforts that can become very time-consuming and after all may prove unsuccessful. The understanding of the physicochemical underpinnings that determine the CD signal intensities obtained with a broadly applicable sensing assay and the prediction of a universal calibration curve thus remove current bottlenecks and roadblocks.

This data-driven approach also gives insight into factors that influence point-to-axial chirality transfer. Within the context of assembly 7, while steric interactions between the groups on the stereocenter of the amine with the binaphthol were important, attractive NCIs and the extent of N─B dative bond formation were invaluable in predicting sensor function. Thus, chirality transfer for ee assays can be significantly more complex than a simple steric analysis may predict.

Important to the future development of chiroptical assays for ee determination, we have shown that one can circumvent calibration experiments via a multiparameter fit that encompasses a series of steric and electronic factors. Just as the synthetic methodology community is increasing using such analyses to understand and optimize catalyst performance, the same approach can be applied to analytical chemistry pursuits within the organic chemistry community.