Introduction

In asymmetric catalytic reactions, non-linear effects (NLEs) denote the non-linear correlation between the enantiomeric excess (ee) values of the chiral auxiliary or ligand and the ee values of the product. This phenomenon was first found by the Kagan group in 19861, and underwent meticulously studied thereafter2,3,4,5,6,7,8. That led to the development of two mathematical models, the MLn model for poly-ligand and the reservoir model for mono-ligand, to rationalize and quantify NLEs, establishing a foundation for subsequent research. Later, Noyori9,10,11,12,13, Asakura14,15, and Blackmond16,17,18,19 et al. also made significant contributions to NLEs research. Presently, the NLEs serves as a widespread tool for obtaining information on a transition-metal catalyzed enantioselective reaction20,21,22. However, the classic NLEs analysis model based on the relationship between the ee values of ligand (eeligand) and ee values of the product (eeproduct) has certain limitations for exploring reaction mechanisms. Due to the diversity in ligand-metal coordination modes, the eeligand is not equivalent to that of the ee values of metal complex (eemetal), and therefore the information obtained solely from the linear relationship between the eeligand and the eeproduct in complex systems is often indirect. When exploring these intricate catalytic systems, it is often necessary to integrate NLEs with various other techniques, corroborating with each other to elucidate the mechanism23,24,25,26,27. In theory, in most cases, whether the system exhibits a linear relationship between eeligand and eeproduct or a nonlinear relationship, there exists an inherent linear relationship between the ee values of the active catalyst (eeact) and eeproduct (with the exception of few systems such as those with multiple active species, autocatalytic systems, and systems affected by background reactions)28,29,30,31. The origin of NLEs is that the eeact and the eeligand are not equivalent. This discrepancy may stem from the different stability and/or reactivity of homochiral and heterochiral species. With this in consideration, is it feasible to directly investigate the relationship between the eemetal and the eeproduct, and to develop a precise method based on the specific linear relationship between the eeact and the eeproduct? This method could potentially be established as a common strategy for active species determination.

Copper catalytic systems are known for their complexity due to the formation of various copper species. It is a challenging but meaningful task to understand their mechanisms for developing cost-effective, highly active, and stereoselective catalysts32,33,34,35,36,37,38,39,40,41,42. Current methods for studying copper catalysis include kinetic experiments, theoretical calculations, spectroscopic analyses, and X-ray diffraction27,43,44,45,46,47,48,49,50. Among these, mass spectrometry provides structural insights into trace transient or low-concentration intermediates, but its qualitative data alone may not accurately identify active copper species30,51,52,53,54. Quantitative mass spectrometry (QMS), as an emerging analytical technique, combines the high sensitivity and selectivity of mass spectrometry with the precision of quantitative analysis, which has garnered significant attention in the field of enantiomeric excess determination55,56,57. This method may offer a promising perspective for precisely locating catalytically active copper species in complex systems with numerous copper species. By integrating QMS with the study of NLEs, there is a chance to develop a more precise method to identify and understand the key active species within copper catalytic systems, which would provide a better tool for mechanistic studies and new avenues for the discovery of more superior chiral catalysts.

In a recent development, we unveiled a tridentate oxazoline copper-catalyzed radical asymmetric carboesterification of dienes, yielding an array of chiral allyl ester compounds with exceptional enantio- and regioselectivities58. Reflecting on the findings reported in that article, our analysis via electrospray ionization mass spectrometry (ESI-MS) and kinetic studies revealed that the dimerized copper single crystal, LRLRCu2(OTf)2, obtained in a mixture of CuOTf•0.5PhMe and LR, acted as a precatalyst, swiftly disassociated in solution to generate the catalytically reactive monomeric copper species LRLRCu or LRCu.

Herein, we utilize ESI-MS spectroscopy, single crystal analysis, and the density functional theory (DFT) studies to investigate the nonlinear effects of a tridentate oxazoline copper-catalyzed radical asymmetric carboesterification of dienes. The transition metal-catalyzed asymmetric radical reaction involves the steps of radical formation and transformation, which usually involves a change in the valence state of the transition metal. With the change in metal valence, the structure of the metal complexes can also change significantly. In this study, the active catalytic species are confirmed and the origin of the nonlinear effect is revealed by multiple strategies. What’s more, a promising method to determine the active species is proposed.

A substrate-independent (+)-NLE was detected in the radical asymmetric esterification reaction

Initially, we assessed the nonlinear effects of two substrates on esterification under identical conditions. The results revealed a robust positive correlation between the ee values of the ligand (LR) and those of the products 1c and 2c. Despite some differences in the product ee values, both substrates exhibited very similar positive nonlinear relationships (Fig. 1a). To demonstrate that the nature of the active species does not change during the progress of the reaction, we have designed and executed experiments to determine the ee values of the products at different conversions. The results indicate that the ee values of the products remain at a relatively stable high level even at different conversions (Fig. 1b). This steadfastness in enantioselectivity underscores the uniformity of the catalytic process59.

Fig. 1: Reactive species confirmed by multiple strategies.
figure 1

a Non-linear relationship between the eeproduct and the eeligand. b The eeproduct at different conversion of (a). c Impact of catalyst loading (5 ~ 0 mol%) on asymmetric radical carboesterification. d Impact of the ratio of Cu/L on asymmetric radical carboesterification. e ESI-MS data in the presence of various ratio of Cu/L.

Full size image

LLCuI species plays a critical role in the radical asymmetric esterification reaction

Prior research has established that the combination of optically pure ligands with copper can lead to the formation of both mono- and bi-liganded copper complexes. It is crucial to ascertain the roles of these species. To this end, the ee values and yield of the product were evaluated while varying the catalyst concentration. Indeed, a decrease in catalyst loading led to a decrease in yield, but the ee values of the product remained almost unchanged (Fig. 1c). We then investigated the effect of varying the ratio of CuOTf•0.5PhMe to LR on both yield and enantioselectivity. Gradient experiments were performed with Cu/L ratios ranging from 3:1 to 1:3. The data indicated that at a Cu/L ratio of 1:1, we achieved a 75% yield with a 94% ee. When the Cu/L ratio was reduced, there was no discernible alteration in the catalytic efficacy. Remarkably, the reaction efficiency exhibited a marked decrease at a Cu/L ratio of 2:1, with the catalytic activity being entirely abolished at a Cu/L ratio of 3:1 (Fig. 1d). Mass spectrometry was employed to monitor the pure catalyst systems at these ratios, and ESI-MS data suggested the presence of LCuI species across all cases. However, LLCuI species were only detectable at Cu/L ratios of 1:1, 1:2, and 1:3, consistent with the trend of reactivity and enantioselectivity observed in the experiments (Fig. 1e). In short, the yield and enantioselectivity of the reaction are more likely related to the amount of LLCuI in the system. Moreover, the DFT calculation results showed that the redox potential of the LLCuII/LLCuI species (−0.20 V) was lower than that of the LCuII / LCuI species (1.19 V), which further supported the rationality of the LLCuI species as the active catalytic species (see Supplementary Fig. 24 and Supplementary Data 1).

The existence of heterochiral species LRLSCu in the system

We considered that a copper complex containing two different ligands could be the key species for catalytic activity, leading us to speculate that the NLEs of this system may correspond to Kagan’s model1,2,21,22. According to this model, the (+)-NLE is attributed to the lower reactivity of the heterochiral copper complex compared to its homochiral counterpart (Fig. 2a). To verify this hypothesis, we designed and carried out the following experiments. The m/z of the enantiomers is the same, thus it is difficult to distinguish them by conventional mass spectrometry methods. New methods are constantly being developed to differentiate enantiomers60,61,62, of which pseudo-enantiomers have been repeatedly validated to be effective4,63. Initially, we synthesized the deuterated ligand (LS-4D) and mixed it with another ligand (LR) in a 1:1 ratio, forming a pseudo-enantiomeric ligand, which was subsequently complexed with copper metal in solution. Mass spectrometry analysis revealed three distinct copper species: m/z 584.1423 [LRCuI]+, m/z 588.1688 [LS-4DCuI]+ representing monovalent mono-ligand copper species, m/z 1105.3529 [LRLRCuI]+ and m/z 1113.3983 [LS-4DLS-4DCuI]+ representing monovalent homochiral copper species, and m/z 1109.3767 [LRLS-4DCuI]+ representing monovalent heterochiral copper species (Fig. 2b). Collision induced dissociation experiments were performed to further determine the structure of each species (see Supplementary Figs. 14–23).

Fig. 2: Origin of (+)-NLE (1).
figure 2

a Kagan’s model of (+)-NLE. b ESI-MS spectra of the mixture of ligand LR and deuterated ligand LS-4D and CuOTf•0.5PhMe. c Comparison of reactivity between homochiral copper and heterochiral copper. d ESI-MS spectra of the mixture of ligand LR and deuterated ligand LS-4D and CuOTf•0.5PhMe after the addition of LPO. e Catalytic cycling of the heterochiral copper complex LRLSCu.

Full size image

Heterochiral copper complex LRLSCu has no catalytic activity

When racemic ligand and Cu(OTf)2 are used in the reaction, the reactivity is much lower than that of the optically pure ligand and Cu(OTf)2 system (Fig. 2c). ESI-MS analysis of the system with mixture of Cu(OTf)2/LR/LS-4D = 1:1.5:1.5 was almost entirely divalent heterochiral copper complex LRLS-4DCuII, with the absence of divalent homochiral copper complex LRLRCuII or LS-4DLS-4DCuII, indicating that the heterochiral copper complex has no catalytic activity (see Supplementary Fig. 12).

There are two possible explanations for the lack of reactivity of the heterochiral copper complex LRLSCu. (i) The monovalent heterochiral copper complex LRLSCuI cannot be oxidized by peroxide to the divalent heterochiral copper complex LRLSCuII. (ii) The divalent heterochiral copper LRLSCuII obtained by oxidation cannot be reduced by allyl radicals and regenerate monovalent copper. To investigate the potential oxidation of monovalent heterochiral copper to divalent heterocyclic copper by peroxide, we compared the ESI-MS spectra of ligand LR and its deuterated counterpart LS-4D when mixed with CuOTf•0.5PhMe before and after the introduction of Lauroyl peroxide (LPO). Following the addition of LPO, the monovalent copper complexes with two ligands ([LRLRCuI]+, [LS-4DLS-4DCuI]+, and [LRLS-4DCuI]+) were no longer detectable. Instead, divalent copper complexes [LLCuII-OCOC11H23]+ (with m/z values of 1304.5364, 1308.5583, and 1312.5747) and [LRLS-4DCuII-OTf]+ were observed (Fig. 2d). These findings suggested that both monovalent homochiral and heterochiral copper complexes were capable of being oxidized by LPO to form divalent copper complexes, which in turn generate alkyl radicals. Given that monovalent heterochiral copper can be oxidized to form divalent heterochiral copper, it is reasonable to infer that these divalent copper complexes may not be efficiently reduced back to the monovalent copper state by allyl radicals, thus halting the catalytic cycle (Fig. 2e). It is noteworthy that a small amount of [LRCuOCOC11H23]+ and [LS-4DCuOCOC11H23]+ (with m/z values of 783.3196 and 787.3430, respectively) was detected after the addition of LPO. Considering that LCuI species cannot be oxidized under these conditions, we hypothesize that these species may have arisen from the dissociation of a ligand from the LLCuII-OC11H23 species (Fig. 2d).

The divalent heterochiral copper LRLSCuII with a mortise tenon junction structure is more stable and difficult to cleave into active mono-ligand divalent copper species with lower site resistance

To elucidate the significant disparity in reactivity between divalent heterochiral copper and homochiral copper, we endeavored to crystallize both forms. Fortunately, we were able to isolate a heterochiral crystal of LRLSCu(OTf)2 (2) from a mixture containing racemic ligands and Cu(OTf)2. The molecular structure of 2 within the crystals was determined through X-ray diffraction analysis, as depicted in Fig. 3a. The structure of LRLSCu(OTf)2 (2) resembles that of mortise and tenon joints, in which the matching from the π–π stacking interactions impart remarkable stability to the compound. In contrast, homochiral copper single crystals (3) obtained using similar ligands do not exhibit this structure (Fig. 3b). Then, we carried out the catalytic reaction by using 2 or 3 as a catalyst as shown in Fig. 3c. As expected, 2 is less active than 3. Given the findings, we speculate that the coordination sphere surrounding divalent copper complexes containing two ligands, both homochiral and heterochiral, may be overcrowded, making it challenging for sterically hindered allyl radicals to access24. A more probable scenario is that the divalent homochiral copper complex exhibits reduced stability, which leads to its prompt dissociation into reactive divalent mono-ligand copper complexes which then react with the allyl radical. In contrast, the divalent heterochiral copper, with its robust mortise and tenon structure, remains stable and does not dissociate readily into an active mono-ligand form. To verify the hypothesis, fragmentation voltage experiments were conducted (Fig. 3d). The results indicate that the heterochiral copper complex is indeed more stable than the homochiral copper complex (Trap voltage of precursor ions fragmented to 50%: 13.5 eV vs 10.0 eV)64.

Fig. 3: Origin of (+)-NLE (2).
figure 3

a Single-crystal structures of divalent heterochiral copper 2. b Single-crystal structures of divalent homochiral copper 3. c Catalytic activity of complex 2 and complex 3. d Comparison of Fragmentation Voltages between divalent the homochiral copper complex and the heterochiral copper complex.

Full size image

Gradient ratios of mixed ligands were prepared using the ligand LR and its deuterated variant LS-4D, and the distribution of monovalent copper species was analyzed via high-resolution mass spectrometry (The use of pseudoenantiomers via mass spectrometry using isotopologues enables this direct measurement). Since the ligand LR (M = 521.2103) and the deuterated labeled ligand LS-4D (M = 525.2354) are both very close in molecular weight and structure, the abundance of each peak in the ESI-MS is approximately proportional to its concentration (Fig. 4a). The heterochiral copper species LRLS-4DCuI is incapable of completing the catalytic cycle to produce the desired product, and the copper catalyst exhibits a first-order dependency on the reaction rate (previous kinetic experimental research results)58. The relationship between the ee values of the monovalent copper complexes with the two ligands (eeLLCu) and the abundance of the two homochiral copper species detected by ESI-MS can be quantified using equation:

$${{ee}}_{{{{\rm{LLCu}}}}}\,=\,\tfrac{{C}_{{L}_{R}{L}_{R}{{{\rm{Cu}}}}}-{C}_{{L}_{S-4D}{L}_{S-4D}{{{\rm{Cu}}}}}}{{C}_{{L}_{R}{L}_{R}{{{\rm{Cu}}}}}+{C}_{{L}_{S-4D}{L}_{S-4D}{{{\rm{Cu}}}}}}\times 100\%$$
Fig. 4: The relationship between eeligand, eeLLCu, eeLCu, and eeproduct.
figure 4

a The calculation formulas for eeLLCu and eeLCu. b Plots of eeLLCu, and eeLCu with eeligand. c Plots of eeproduct and eeLLCu, with eeligand. d Plots of eeproduct with eeLLCu.

Full size image

For monovalent copper complexes with single ligand coordination, the calculation of ee follows equation:

$${{ee}}_{{{{\rm{LLCu}}}}}\,=\,\tfrac{{C}_{{L}_{R}}-{C}_{{L}_{S-4D}{{{\rm{Cu}}}}}}{{C}_{{L}_{R}{{{\rm{Cu}}}}}+{C}_{{L}_{S-4D}{{{\rm{Cu}}}}}}\times 100\%$$

This analysis assumed the reaction as being catalyzed by two separate systems, LRLRCu and LSLSCu, each with distinct configurations but the same reaction rate, and products with opposite absolute configurations.

As the eeligand increases, a close correlation was observed between the calculated the eeLLCu and the experimentally determined the eeproduct (Fig. 4b, c). Particularly, when plotting the eeproduct against the eeLLCu using the eeLLCu as the abscissa, a remarkably linear relationship is revealed (Fig. 4d). This direct measurement of complex ee provided a plausible explanation for the initially observed nonlinear effect. More importantly, as it suggests that regardless of whether the relationship between the eeligand and the eeproduct is linear or nonlinear, a linear correlation may exist between the eeact and the eeproduct. If this hypothesis holds true, we could potentially utilize this linear relationship to rapidly and accurately identify the catalytically active species in other metal-catalyzed complex reaction systems.

Results

Leveraging the insights gleaned from our findings, we propose a plausible reaction pathway (Fig. 5a). In the presence of a partially racemic ligand coordinating with monovalent copper in solution, three distinct species (A, B, and B’) exist. The monovalent mono-ligand species A remains inert towards peroxides, whereas both the homochiral copper species B and the heterochiral copper species B’ are susceptible to single electron oxidation by alkyl peroxides. This process yields an alkyl radical and divalent dual-ligand copper species (C and C’), which are too sterically hindered to directly engage in reactions with the bulky allyl radical. Conversely, the labile divalent homochiral copper species C can gradually release a ligand, transforming into the divalent mono-ligand copper reactive species D, which then reacts with the allyl radical to form the allyl copper intermediate E. Subsequently, the chiral allyl ester is produced and the mono-ligand copper species A is released, ready to coordinate with another ligand and regenerate the divalent dual-ligand copper species B. For the divalent heterochiral copper species C’, its unique mortise and tenon joint structure confers exceptional stability, preventing the release of a ligand into the reactive mono-ligand copper intermediate D. This stability impedes the completion of the catalytic cycle, which is also responsible for the (+)-NLE (Fig. 5b).

Fig. 5: Plausible mechanism.
figure 5

a Proposed catalytic cycle. b Origin of non-linear effects.

Full size image

To summarize, we have gradually revealed the reaction pathway of radical asymmetric carboesterification of diene by applying a combined approach of ESI-MS, DFT, X-ray investigations as well as synthetic studies based on the study of the nonlinear effect. The study identified a (+)-NLE in asymmetric carboesterification, highlighting the importance of a monovalent dual-ligand copper complex, and further investigations revealed the formation of heterochiral copper complexes with low catalytic activity, which can be attributed to the stable tenon structure preventing their dissociation into active mono-ligand copper complexes and consequently leads to the emergence of NLEs. Furthermore, in studying the eemetal and the eeproduct in solution after pre-coordination, we found a specific linear relationship between the eeact and the eeproduct. Based on these findings, we proposed a promising method for the accurate and efficient determination of active species in the system, namely by directly examining the relationship between the eemetal and the eeproduct, and based on the linear relationship between the eeact and the eeproduct. This method, which combines QMS and NLEs, is expected to extend the strength of traditional methods in analyzing complex systems and is anticipated to become a powerful tool for the study of asymmetric catalysis mechanisms.

Methods

General method for non-linear effects experiments

Two 20-mL scintillation vials equipped with a stir bar were flame dried and then allowed to cool to room temperature and purged with argon. To one vial was added 180 mg (R)-PhBOX and to the second was added 180 mg of (S)-PhBox. Each vial was charged with 10 mL of anhydrous DCE. To a flame-dried, argon-purged 10-mL scintillation vial equipped with a stir bar was added (S)-PhBox stock solution and (R)-PhBOX stock solution in the desired ratio to total 0.4 mL. CuOTf•0.5PhMe (0.01 mmol, 5 mol%) were allowed to stir 10 min before being added to the 10-mL scintillation vials. The mixture was stirred at room temperature for 30 min at which diene (0.2 mmol, 1.0 equiv.) and peroxide 1b (2.4 mmol, 1.2 equiv.) were sequentially added. The reaction mixture was stirred at 35 °C for 72 h. After reaction completion, the solvent was evaporated under reduced pressure. The residue was purified by flash column chromatography on silica gel to afford the chiral allyl ester. The chiral allyl ester was analyzed by HPLC analysis with a chiral OD-H column to evaluate the enantioselectivity.

General method for mass spectrometry experiments

CuOTf•0.5PhMe (0.075 mmol) was introduced into an oven-dried Schlenk flask under the protection of dry nitrogen. Then 2 mL DCE was added into Schlenk flask and dissolved by ultrasound to obtain the copper stock solution. Ligand LR (0.105 mmol) was introduced into an oven-dried Schlenk flask under the protection of dry nitrogen. Then 2 mL DCE was added into Schlenk flask and dissolved by ultrasound to obtain the LR stock solution. Ligand LS-4D (0.105 mmol) was introduced into an oven-dried Schlenk flask under the protection of dry nitrogen. Then 2 mL DCE was added into Schlenk flask and dissolved by ultrasound to obtain the LS-4D stock solution. The Cu stock solution, LR stock solution, and LS-4D stock solution were combined in the desired ratios within an oven-dried Schlenk flask under a dry nitrogen atmosphere, reaching a total volume of 0.4 mL. This mixture was stirred at room temperature under the nitrogen atmosphere for 30 min. Then the mixture was diluted 200 times by MeCN, subsequently transferred into an injection syringe and injected into the high-resolution electrospray mass spectrometry (SYNAPT G2-S HDMS) by injection pump. MS data were collected and analyzed.