Ryusei Oketani

Marine Hoquante

Clément Brandel

Pascal Cardinael

Gérard Coquerel

Resolution of an atropoisomeric naphthamide by second-order asymmetric transformation: A highly productive technique

Keywords: deracemization, second-order asymmetric transformation (SOAT), productivity, atropisomerism

Temperature-cycle-induced deracemization (TCID) has been widely studied in the field of chiral separation, ranging from fundamental research to applications. In this study, the secondorder asymmetric transformation (SOAT) of 2-methoxy-1-naphthamide in an azeotropic mixture of ethyl acetate and cyclohexane is compared with TCID, in terms of process productivity. The results indicate that the volumetric productivity using SOAT was over 100times higher than that using TCID, such that a scale-up by a factor of 10 was easily implemented.

Introduction

Chiral separation is an important field of research because of the impact of chirality on the development of high-value materials (e.g., pharmaceuticals, agrochemicals, and optics).

Crystallization is often the preferred chiral separation technique at industrial scales because it has a smaller carbon footprint and is cheaper than other methods like chromatography. [START_REF] Suwannasang | A Novel Design Approach to Scale Up the Temperature Cycle Enhanced Deracemization Process: Coupled Mixed-Suspension Vessels[END_REF][START_REF] Noorduin | Scaling Up Attrition-Enhanced Deracemization by Use of an Industrial Bead Mill in a Route to Clopidogrel (Plavix)[END_REF][START_REF] Van Der Meijden | Attrition-Enhanced Deracemization in the Synthesis of Clopidogrel -A Practical Application of a New Discovery[END_REF] Preferential crystallization (PC) is a chiral resolution technique that can be applied to a conglomerate-forming system. [START_REF] Coquerel | Preferential Crystallization[END_REF] It is noteworthy that no racemization occurs during PC (i.e. enantiomers cannot interconvert), leading to the gradual enrichment of the enantiomeric excess of the solution in the counter enantiomer. This puts a limit in the yield of every single operation. The theoretical maximum yield after recycling several times the mother liquors is 50%. By contrast, deracemization by crystallization is a promising chiral separation technique although it needs also a conglomerate-forming system, because it is performed under racemize conditions which steadily produce the desired enantiomer, leading to a theoretical yield of 100%. [START_REF] Rachwalski | Recent Advances in Enzymatic and Chemical Deracemisation of Racemic Compounds[END_REF] In addition to this major advantage, deracemization by crystallization is quite facile. For example, temperature-cycle-induced deracemization (TCID) is a process that converts a racemic mixture of the substrate to a nearly pure enantiomer in the solid phase without any external chiral source through temperature cycling. [START_REF] Suwannasang | A Novel Design Approach to Scale Up the Temperature Cycle Enhanced Deracemization Process: Coupled Mixed-Suspension Vessels[END_REF][START_REF] Oketani | Practical Role of Racemization Rates in Deracemization Kinetics and Process Productivities[END_REF][START_REF] Belletti | Role of Additives during Deracemization Using Temperature Cycling[END_REF][START_REF] Breveglieri | Deracemization of NMPA via Temperature Cycles[END_REF][START_REF] Uchin | Model of Temperature Cycle-Induced Deracemization via Differences in Crystal Growth Rate Dispersion[END_REF][START_REF] Li | Deracemization of a Racemic Compound via Its Conglomerate-Forming Salt Using Temperature Cycling[END_REF][START_REF] Suwannasang | Use of Programmed Damped Temperature Cycles for the Deracemization of a Racemic Suspension of a Conglomerate Forming System[END_REF] Scheme 1. Schematic representations of PC, TCID, and SOAT process.

Recently, we reported the TCID of atropoisomer 1 (Figure 1) and its racemization rate (k1), [START_REF] Oketani | Practical Role of Racemization Rates in Deracemization Kinetics and Process Productivities[END_REF] where we showed that the process productivity appears to be proportional to the racemization rate (k1), multiplied by the solubility. The productivity of a separation process is defined as the amount of enantiomer produced per unit time and unit volume of crystallizer or suspension. [START_REF] Breveglieri | Deracemization of NMPA via Temperature Cycles[END_REF][START_REF] Rougeot | Application of Continuous Preferential Crystallization to Efficiently Access Enantiopure Chemicals[END_REF] Productivity =

m crop × 𝑒𝑒𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 -m seeds time • volume (Eq. 1)
where mcrop and eefinal are the mass and the enantiomeric excess of the collected crystals, respectively, and mseeds is the mass of the seed crystals. Although a few examples exhibit good productivity (for example, the PC of baclofen [START_REF] Coquerel | Method for the resolution of baclofen salts[END_REF] attained an average productivity of 69 g h -1 L - 1 taking into account the equilibration time before crystallization), the typical productivity of PC ranges from 10 to 20 g h -1 L -1 . [START_REF] Eicke | Efficient Resolution of Enantiomers by Coupling Preferential Crystallization and Dissolution. Part 2: A Parametric Simulation Study to Identify Suitable Process Conditions[END_REF][START_REF] Galan | Continuous Preferential Crystallization of Chiral Molecules in Single and Coupled Mixed-Suspension Mixed-Product-Removal Crystallizers[END_REF] In comparison, the productivity of TCID is as low as 0.1-5.0 g h -1 L -1 . [START_REF] Oketani | Practical Role of Racemization Rates in Deracemization Kinetics and Process Productivities[END_REF][START_REF] Breveglieri | Deracemization of NMPA via Temperature Cycles[END_REF] Thus, although TCID can double the theoretical yield, the productivity of the process is almost one order of magnitude lower than that of PC.

The low productivity of TCID is obviously due to the associated long process times. Indeed, the usual minimum process duration for TCID is about 10 h. [START_REF] Belletti | Role of Additives during Deracemization Using Temperature Cycling[END_REF][START_REF] Breveglieri | Deracemization of NMPA via Temperature Cycles[END_REF][START_REF] Engwerda | Deracemization of a Racemic Compound by Using Tailor-Made Additives[END_REF][START_REF] Rougeot | Ultrasound-Enhanced Deracemization: Toward the Existence of Agonist Effects in the Interpretation of Spontaneous Symmetry Breaking[END_REF] In contrast, PC runs typically involve rapid cooling; thus, the process times are much shorter. It is therefore important to shorten process times to significantly improve the process productivities and achieve a process with high productivity.

The scaling up of PC often lead to problems in sub-operations, even when chiral crystallization is effective. In particular, the filtration step could affect the feasibility, and occasionally this kind of problem causes PC to fail. For example, laboratory-scale filtration can usually be completed in a reasonable amount of time, but large-scale production requires much longer.

The PC process normally incorporates a quick filtration after the end of the entrainment because a longer crystallization period could trigger the nucleation of the counter-enantiomer and reduce the optical purity of the crop. Therefore, the time required for filtration with a scaled-up process could constitute a critical problem. By contrast, deracemization processes generally do not incur such a problem, since enantiomers are steadily interconverted in the solution. Moreover, the supersaturation of both enantiomers is always held close to 1, thus the probability of the nucleation of the counter-enantiomer decreases. This feature eliminates the limitation incurred in the scaling up of the process and helps to apply the process in the industrial field.

Second-order asymmetric transformation (SOAT) is defined as a crystallization-induced asymmetric transformation during which the racemic mixture is converted into either a pure enantiomer or a mixture in which one enantiomer is present in excess. [START_REF]Asymmetric Transformation[END_REF] In other words, SOAT can be regarded as being a PC process under racemization conditions, as shown in Scheme 1.

As a hybrid of PC and deracemization, SOAT offers great promise as a process affording high yield and high productivity. To the best of our knowledge, there have been relatively few reports on the SOAT process and no studies have investigated the productivity of the process. 19- 46 In the present study, we examined the application of the SOAT process to naphthamide 1 (Figure 1), a conglomerate-forming system that exhibits solid-state atropisomerism (i.e., it spontaneously racemizes in solution) at two different scales. In addition, we show that SOAT of this compound is more productive than that of regular TCID even if the two processes are comparable in term of interplay between homogeneous and heterogeneous equilibria.

Experimental methods

Compound 1 was synthesized as described in our previous work. [START_REF] Oketani | Practical Role of Racemization Rates in Deracemization Kinetics and Process Productivities[END_REF] The solubility of 1 in a 45/55 (wt/wt) mixture of cyclohexane and ethyl acetate (Certified AR for Analysis, Fisher Chemical, France), was measured by a gravimetric method from 10-60 °C. The temperature was controlled by a thermostat (F25-HL Cryostat, JULABO GmbH, Germany). Racemization kinetic constants (k1) of 1 from 10-45 °C were also measured over time using a polarimeter (P-2000, Jasco France, France) at 365 nm with a Hg-lamp. [START_REF] Oketani | Practical Role of Racemization Rates in Deracemization Kinetics and Process Productivities[END_REF][START_REF] Ebbers | Controlled Racemization of Optically Active Organic Compounds: Prospects for Asymmetric Transformation[END_REF] The TCID of 1 was performed by applying the following procedure. The SOAT process of 1 was carried out by applying the following procedure. A variable mass of powdered enantiopure seed crystals (prepared by grinding a single crystal) was added France) for the 1-g scale experiment or a double-jacketed 150-mL three-neck flask for the 10g scale experiment. The temperature was controlled by a thermostat (F25-HL Cryostat, JULABO GmbH, Germany). The mixture was then stirred at 500 rpm by a cross magnetic stirrer throughout the experiment. After a 3-minute isotherm, the suspension was cooled to 30 °C over a period of about 85 min by using two types of cooling profiles, shown in Figure With cooling profile A, temperature decreases linearly versus time (Figure 3) and the CT/C30 ratio, CT and C30 being gravimetric solubility respectively at T and 30 °C, changes drastically at the beginning of the process. Due to the solubility change, the supersaturation of the solution is expected to increase drastically, and primary nucleation of the counter enantiomer can occur.

In contrast, as can be seen in cooling profile B, solubility linearly decreases with time in order to achieve a constant rate of crystal growth when the cooling rate was sufficiently slow to reach the solubility equilibrium at a specific temperature. In general, the rate of crystal growth in the fast cooling process depends on the diffusion and/or surface integration behavior of the molecule; therefore, this rate cannot be considered to be constant.

Results and Discussion

Figure 4 shows the solubility and k1 values of 1 as a function of temperature in an azeotropic mixture of ethyl acetate and cyclohexane (45/55 wt/wt). As can be seen from Figure 4, the solubility variation is small from 10-30 °C but increases abruptly from 30 °C onward. This behavior suggests the existence of a metastable miscibility gap, at higher or lower temperatures, also called submerged liquid demixing or the metastable oiling-out phenomenon. [START_REF] Brandel | Crystal Growth, Structure, and Polymorphic Behavior of an Ionic Liquid: Phthalate Derivative of N -Butyl, N -Methylimidazolium Hexafluorophosphate[END_REF] Therefore, seeded crystallization is well suited for this compound in order to avoid liquid demixing which may cause high supersaturation in one of the two liquids and thus uncontrolled crystallization.

Racemization kinetic constants k1 obtained by polarimetry measurements [START_REF] Ebbers | Controlled Racemization of Optically Active Organic Compounds: Prospects for Asymmetric Transformation[END_REF] have been used to plot an Arrhenius's graph, and the Gibbs free energy of activation (ΔG ‡) was found to be 17.1 kcal‧mol -1 . In general, a torsion rotation energy barrier lower than 20-25 kcal‧mol -1 can show the interconversion within a few hours around room temperature. [START_REF] Laplante | Assessing Atropisomer Axial Chirality in Drug Discovery and Development[END_REF] Thus, this value indicates that racemization in the solution is sufficiently fast to facilitate the development of a deracemization process during a reasonable period of time. Details of the solubility data and k1 are given in the Supporting Information. In the present study, the productivity was calculated using Eq. 1 in which the volume of the solution (calculated using a solvent density of 0.856 g mL -1 and the measured mass at 20 °C) was used instead of the suspension volume. To compare process robustness of TCID and SOAT, the yield was calculated using Eq. 2:

Yield[%]= m crop × ee final -m seeds m -m solute, final ×100 (Eq. 2)
where m and msolute, final represent the total mass of 1 and the mass of the solute in the saturated solution at the final temperature, respectively.

In general, crystallization yield does not consider the mass of the final solute which remains in solution since it can be varied by changing the operating conditions. Thorough optimization of the operating conditions would, therefore, be necessary for comparison of such factors for different processes is beyond the scope of this study. The yield should be 100% when the mass of collected crystals is the same as the theoretically affordable mass (i.e. taking into account the mass of the solute that remains solvated at the final temperature. Thus, the yield can be considered as a factor for determining process robustness. 2 summarizes the suspension density, the deracemization time (which is the time required to reach 95%ee from 0%ee), and the process productivity. As shown in Figure 5, a larger suspension density resulted in a longer deracemization time. Although the process productivity for the 144-mg•mL -1 suspension density was 10% lower than in the other cases, there was no significant difference in this range of suspension density. Thus, the process productivity of TCID can be regarded as being an independent factor affecting the suspension density, ranging from 10-150 mg•mL -1 . A higher suspension density than these conditions may give rise to an issue with the homogeneity of the system, while the suspension density would not be an independent factor from the process productivity. Hereafter, the average value, 0.67 g•h -1 •L -1 , is used as the process productivity of TCID for comparison. The solubility measurements were used to develop the SOAT process of 1 (see the experimental section for more details). The experimental results are summarized in Table 3. The mass of the crystals collected after Runs 1-3 (performed using linear cooling) was almost equal to the maximum value, (i.e., the crystallized mass accounts for the solubility difference between the initial and final temperature). However, the average enantiomeric excess was only 12%. Because of this low enantiomeric excess, the yield was also low.

Although the productivities of Runs 1-3 were higher than those obtained for TCID for the same solvent (0.67 g h -1 L -1 ), additional enantio-purification would be needed to achieve enantiopurity, which is undesirable.

To understand the reason for this low enantiomeric excess, we performed a 10-g scale SOAT experiment (Run 11 in Tables 1 and2) and monitored the enantiomeric excess of the crystal during the process. As shown in Figure 6a, the crystal enantiomeric excess starts to drop at the beginning of the experiment. Because the CT/C30 ratio decreases rather abruptly in this temperature domain (Figure 3), this is likely to cause uncontrolled primary nucleation of the counter-enantiomer upon cooling. This is further supported by Figure 6b, which depicts the supersaturation profile of the solution and shows that the supersaturation remained quite high (~1.2) during the process. The increase in the supersaturation at the end of the experiment is likely due to the crystallization rate slowing down at lower temperatures and which cannot adapt to the corresponding temperature change. crystals was also identical to that of the seed crystals. Accordingly, the monitoring of the crystal enantiomeric excess (Figure 7a) showed that the initial enantiomeric excess of the seeds was almost constant throughout the process. The cooling profile applied to these experiments implies a slow cooling rate at the beginning of the process, which reduces the primary nucleation of the counter enantiomer (Figure 7b). The cooling profile maintains the supersaturation at close to 1.0 during the whole process (the crystal growth of the seeds is sufficiently fast to compensate for the moderated supersaturation increase). The average productivity of TCID for 1 was 0.67 g h -1 L -1 , while that of SOAT at the same scale (i.e., runs 4-7) was an average of 135 g h -1 L -1 . This productivity difference is a result of the process time: although this depends on the scale of the crystallizer, TCID is generally performed in a time frame of several hours to some days, whereas SOAT can be performed in a few hours because it requires only a single cooling process. Moreover, for the 10-g scale experiment (Run 8-10), without sophisticated optimization (i.e., the mass of the compound and solvent increased proportionally), the time required for the process remained the same, with a decrease in productivity of only 10% compared to the 1-g scale. Therefore, scaling-up for industrial applications is expected to be relatively easy.

Figure 8a shows a SEM image of crop crystal after cooling profile A. The crystals exhibited a size distribution 10-100 μm, while small particles adhered to those crystals. Those small particles could have been produced by the primary nucleation during the process, implying that primary nucleation frequently occurred during cooling profile A. Since the chirality of the primary nucleation could not be controlled, the nucleation included both enantiomers.

Therefore, the enantiomeric excess dropped during cooling profile A. By contrast, the relatively large crystals (100-1000 μm) are found in the crop after cooling profile B, as shown in Figure 8b. These crystals can be regarded as grown seeded crystals. As scars of abrasions was visible on the large crystals, abrasion phenomena might also occur during the process. Since abrasion produces small crystals which have the same chirality as the original crystals, the resulting crystals do not cause a decrease in the enantiomeric excess. Smaller crystals could be generated by the abrasion process of the large crystals or by secondary nucleation.

Conclusion

We performed SOAT on atropoisomeric naphthamide 1, which exhibits spontaneous racemization in solution in the absence of any racemization reagent, with two different temperature profiles at 1-g and 10-g scales. Monitoring of the supersaturation of the solution and enantiomeric excess of the solid phase upon cooling highlighted that the so-called "solubility-controlled cooling" is better suited to producing high enantiomeric excesses of crystals. Moreover, we showed that the productivity of SOAT is considerably higher than that of TCID. The present study was the first to compare the productivities of SOAT and TCID for the same compound, naphthamide 1. In addition, we found that scaling up by a factor of 10 was also feasible. Although SOAT requires enantiomerically pure seed crystals, it could feasibly be part of an efficient process in the future. For example, TCID could be used to prepare enantiopure crystals, which could then be used as seed crystals in a SOAT process.

Alternatively, a continuous SOAT process could be envisaged as a more productive technique than TCID.

47

 47

Figure 1 .

 1 Figure 1. Chemical structure of naphthamide 1.

Compound 1

 1 was completely dissolved by heating in 10 mL of an azeotropic mixture of ethyl acetate and cyclohexane (55/45, wt/wt) in a 30-mL screw vial that contained a cross-type Teflon-coated stirring bar. Subsequently, the solution was cooled to 10-20 °C to induce spontaneous crystallization. Then, the suspension was held at 20 °C for 30 min to allow it to reach equilibrium. The heterogeneous mixture was stirred under the temperature-cycling conditions shown in Figure2for a maximum of 10 days. To confirm the scalability of the process, we performed TCID of 1 in 4 different scales of suspension density ρ, namely, 14.4, 36.0, 72.0, and 144 mg mL -1 . Since the temperature cycle between 20 and 30 °C gives a 7.2-mg mL -1 dissolution-crystallization cycle, 50, 20, 10, and 5% of the crystals were deliberately dissolved during the heating step. For the off-line monitoring of the deracemization experiments involving 1, a small amount (~30 μL) of the suspension was drawn off and filtered through an 8φ filter paper in a Kiriyama Rohto VB-8 funnel. The collected crystals were dried under a vacuum, weighed, and then dissolved in MeOH (1.200 mL, HPLC grade) at 4 °C. The enantiomeric excess was determined by comparing the optical rotations at 365 nm and 4 °C with the previously determined specific optical rotations. ([α] 365[START_REF] Coquerel | Preferential Crystallization[END_REF] = 662.3°).[START_REF] Oketani | Practical Role of Racemization Rates in Deracemization Kinetics and Process Productivities[END_REF]

Figure 2 .

 2 Figure 2. Temperature profile applied in the TCID experiments.

  to a saturated solution of 1 in a 45/55 (wt/wt) mixture of cyclohexane and ethyl acetate at 60 °C (mass fraction concentration S = 22.2 wt%) in a 40-mL vial (ϕ27.5 × 95 mm, VWR France,

Figure 3 .

 3 Figure 3. Two types of a cooling profile applied to SOAT of 1. (A) Linear cooling. (B)

Figure 4 .

 4 Figure 4. Racemization rate constants (▲) and solubility curve of 1 (○) in the azeotropic

Figure 5

 5 Figure 5 displays the enantiomeric excesses (ees) of the collected crystals of 1 as functions of

Figure 5 .

 5 Figure 5. The enantiomeric excess of the collected crystals of 1 as a function of time during

Figure 6 .

 6 Figure 6. (a) Enantiomeric excess (ee) values of the collected crystals of compound 1. (b)

Figure 7 .

 7 Figure 7. (a) Enantiomeric excess (ee) values of the collected crystals of 1. Each line

Figure 8 .

 8 Figure 8. (a) SEM images of collected crystals after (a) the cooling profile A, and (b) the

Table 1 .

 1 Experimental

	Run	Cooling profile	1/g	solvent / g S / wt%	Seed / mg T initial / °C T final / °C	Duration / min
	1	A	1.425	5.00	22.2	27.0	60	30	82
	2	A	1.426	5.00	22.2	32.4	60	30	82
	3	A	1.422	5.00	22.2	33.0	60	30	82
	4	B	1.428	5.01	22.2	10.9	60	30	85
	5	B	1.424	5.00	22.2	21.5	60	30	82
	6	B	1.427	5.01	22.2	30.8	60	30	83

3, hereafter referred to as cooling profiles A and B. The experimental conditions are summarized in Table

1

. The temperature of the solutions was monitored every 30 s with a data logger (LogStick LS450-T(K), Osaka Micro Computer Inc., Osaka, Japan) equipped with a thermocouple. The supersaturation of the solutions was monitored during cooling by sampling aliquots of the solution for gravimetric analyses. The crystals were collected by filtration and dried under a vacuum. The enantiomeric excess was determined by comparing the optical rotation measurements at 365 nm and 4 °C with the previously determined specific optical rotation. conditions for SOAT of 1 in 45/55 (wt/wt) mixture of cyclohexane and ethyl acetate.

Table 2 .

 2 Summary of suspension density, deracemization time, and process productivity.

	Suspension density ρ / mg•mL -1	Deracemization time / h	ee final [%]	Productivity / g•h -1 •L -1	Yield[%]
	14.4	20	96	0.68	>95
	36.0	48	98	0.71	>95
	72.0	102	97	0.67	>95
	144	220	97	0.62	>95

Table 3 .

 3 Summary of the experimental results of SOAT crystallization.

	Run	Cooling profile	m crop / g	ee final [%]	Productivity / g h -1 L -1	Yield [%]
	1	A	1.208	4	3	2
	2	A	1.211	26	35	23
	3	A	1.220	5	3.5	<1
	4	B	1.205	87	125	86
	5	B	1.219	93	139	92
	6	B	1.206	97	141	94
	7	B	1.188	89	133	87
	8	B	8.317	77	104	75
	9	B	8.360	83	118	80
	10	B	8.432	85	124	85
	11	A	8.646	51	75	51

The authors thank the Horizon 2020 Research and Innovation Programme and Marie Sklodowska Curie Grant for funding this research.

Funding Sources

This research received funding as part of a CORE project (October 2016-September 2020) from the Horizon 2020 Research and Innovation Programme of the European Union under Marie Sklodowska-Curie Grant Agreement No. 722456 CORE ITN.

ASSOCIATED CONTENT

Supporting Information. Solubility data and racemization kinetic constants of 1 (PDF).

AUTHOR INFORMATION Corresponding Author

* E-mail: gerard.coquerel@univ-rouen.fr ORCID Ryusei Oketani: 0000-0001-7860-2456 Clément Brandel: 0000-0002-7747-0823 Gérard Coquerel: 0000-0001-8977-8676

Author Contributions

The manuscript was written through the contributions of all authors. All authors have given approval to the final version of the manuscript.

Notes

The authors declare no competing financial interests.

ACKNOWLEDGMENT


Ryusei Oketani

Francesco Marin

Dr Paul Tinnemans

Dr Marine Hoquante

Prof. Dr Anne Laurent

Clément Brandel

Pascal Cardinaël

Dr Hugo Meekes

Prof. Dr Elias Vlieg

Yves Geerts

Prof. Dr Pascal Cardinael

Gérard Coquerel
email: gerard.coquerel@univ-rouen.fr

Prof. Dr C Blandel

Geerts

Deracemization in a complex quaternary system with a second-order asymmetric transformation using phase diagram studies

Introduction

Chirality or asymmetry is a fundamental property and has critical importance in many avenues of nature, particularly in biology and pharmaceutics. Indeed, the human body consists of a large variety of chiral amino acids and sugar molecules, and the availability of chiral separation techniques is paramount to enable studies relating to the biological function and activity of chiral molecules. Access to the desired polymorph and enantiomer of the particular compound is a critical issue in the field of pharmaceutical chemistry owing to the difference of bioavailability and bioactivity among polymorphs and enantiomers. Among the 42 drugs of chemical entities approved by the Food and Drug Administration (FDA) in 2018, 25 molecules contain a chiral center [START_REF]FDA's Center for Drug Evaluation and Research's (CDER's) Advancing health through innovation 2018 New drug therapy approvals[END_REF][START_REF] De La Torre | [END_REF] , and over 80% of the active pharmaceutical ingredients (APIs) exhibit polymorphism or solvate formation [3,4] and may show differences in physical properties, which makes chiral separation and polymorph control vital aspects of drug development. Classical chiral resolution techniques such as chemical transformation mediated diastereomeric resolutions are robust and reliable approaches to prepare enantiomerically pure materials and are preferentially used in industrial chemistry. However, in such approaches, the undesired enantiomer, which constitutes half of the product is wasted or needs to be recycled.

To reduce such waste and improve productivity, chiral separation by deracemization, an approach which combines racemization with crystallization, has been the subject of intense studies. Viedma ripening (VR) [5][6][7][8][9] and temperature cycle induced deracemization (TCID) [10][11][12][13][14][15] are key approaches to deracemization. and are being actively studied. We recently reported that second-order asymmetric transformation (SOAT) [16] , a combination of preferential crystallization (PC) and racemization, could achieve relatively high process productivity compared to TCID due to short process time. In this report, we use a SOAT based approach for an efficient chiral resolution. Phase diagrams are important tools for understanding and controlling the crystallization. Indeed, the construction of a phase diagram is essential for rationally: (i) determining appropriate crystallization conditions of molecules exhibiting multiple solid phases, (ii) assessing the thermodynamic stability of solid phases, (iii) controlling the supersaturation. [START_REF] Coquerel | Polymorph. Pharm. Ind[END_REF][START_REF] Brandel | [END_REF][19] Recently, our group demonstrated that PC could be applied on a metastable conglomerate of diprophylline, which crystallizes in multiple crystal forms depending on the conditions. [20] However, the utility of such an approach using phase diagram investigations for deracemization has not been reported yet. While deracemization is a well-developed chiral resolution technique, it still suffers from limitations. For example, it is applicable only to conglomerate forming systems, i.e. 5-10 % of the racemic crystals. [START_REF] Jacques | Enantiomers, Racemates, and Resolutions[END_REF] Since racemization of the substrate is a requirement for the deracemization process, the gap of two thermodynamic equilibrium states of the process must be tuned to design reaction conditions for an efficient deracemization. For advanced industrial applications, the availability of model studies is crucial in order to facilitate process modeling. The present work aims at serving as a model study for the use of a phase diagram based approach for deracemization of molecules that exhibit a complex solid phase landscape.

In the present study, we characterized two new solid phases of atropisomeric naphthamide 1, shown in Figure 1, using SC-XRD, DSC, and XRPD measurements and constructed the quaternary phase diagram of 1 in a mixture of methanol (MeOH) and water (H2O) using XRPD and solubility measurements. Further, we studied the impact of temperature on the racemic isoplethal section. Based on the conditions obtained from the phase diagram study, we successfully performed the chiral resolution of 1 by SOAT in a MeOH/H2O solution and achieved up to 97% ee and a productivity of 6.5 g h

-1 L -1 O N 1 Figure 1. Chemical structure of atropisomeric naphthamide 1.

Results and Discussion

Preparation and characterization of C, Rac, and Me

In 2005, Sakamoto et al. reported the crystal structure of the first form of 1 and designated it as C, [START_REF] Sakamoto | [END_REF] which can be prepared from solutions of 1 in many conventional solvents, except in MeOH, by slow evaporation. The space group of C is P212121, and the crystals form a conglomerate. Racemic compound, Rac, could be obtained in the first crop by cooling crystallization from a mixture of chloroform and heptane (1/1, v/v). Indeed, after the collection of Rac by filtration, only C crystallized from the filtrate. Rac can also be prepared by suspending any crystal form in a mixture of MeOH/H2O (70/30, v/v) at 15 °C. As the melting point of Rac is lower by 12 °C than that of the racemic mixture of C, it could be considered as a less stable phase than C at high temperature in the binary system. Further, comparison between the enthalpy of fusion (ΔHfus) also supports the order of stability. A <1-1> racemic MeOH solvate (hereafter Me) could also be prepared. The deposited crystals appeared highly transparent in the solution, and after filtration, the surface of the crystals desolvated and turned to C. The desolvation temperature of Me was determined by TGA-DSC-MS measurement. The incorporated MeOH molecules were released at 50.4 °C, and Me turned to C and/or Rac depending on the heating rate. XRPD measurements confirmed that each phase could be prepared as a structurally pure phase (Figure 2). 3a and b, respectively. The overlaid molecular structures of Rac and Me (Figure 3c) indicate that the conformations in both solid phases are almost identical. By contrast, the major difference between Rac and C was found in the piperidyl residues, as shown in Figure 3d. In both solid phases, the piperidyl groups exist in the chair conformation. However, the conformation of the piperidine ring are opposite, with the two piperidyl rings related as flipped chairs. In Rac, the centrosymmetric pairs are stacked along the a-axis.

Other columns with the same stacking direction are arranged in an ac plan, and the columns with opposite stacking direction are arranged in the next ac planes shifted by + and -1/2 b-axis (Figure 4a). In Me, the packing structure is basically the same as in Rac (Figure 4b). However, the differences between the Rac and Me are as follows: (i) the MeOH molecules are accommodated in the pocket next to the molecules of 1, and (ii) the direction of the stacked columns in the adjacent ab plane is similar but the centrosymmetric pairs are swapped.

2.3 Quaternary phase diagram of R, S-1, MeOH, and water Since the quaternary equilibria of MeOH, H2O, and the enantiomers of 1 resulted in a complicated system due to the spontaneous racemization in solution, we briefly introduce the ternary systems relevant for the solid phases of 1. Figure 5 summarizes the ternary phase diagrams of the enantiomers of a chiral molecule with a solvent, both for the presence and absence of racemization in the solution. [START_REF] Coquerel | Polymorph. Pharm. Ind[END_REF][23][24][25] Any composition in the undersaturated or saturated solutions will evolve towards the racemic composition because of the racemization in the liquid phase. Many results have reported an irreversible evolution to a single chirality in the solid state for racemizable conglomerate forming systems. [8,[26][27][28][29] As long as the system remains an undersaturated solution, the enantiomeric excess of the system remains zero. However, once the conglomerate starts to crystallize, the system in equilibrium will consist of a racemic solution and a single chiral solid. In case of a racemic compound, only the racemic compound and a racemic solution are accessible for the system in equilibrium.

(c) (d) (e) (f) ⑤ ⑥ MeOH H 2 O R-1 S-1 (±)-1 H 2 O MeOH ② ④ ① ③ I (±)-1•MeOH (= Me) I' ⑤ (±)-1 (=Rac) (a) H J H 2 O MeOH ② ④ ① ③ I'' J H (b) T > 34 °C T < 34 °C (±)-1•MeOH (= Me) (±)-1 (=Rac)
Figure 8. Quaternary system with two different solvents (MeOH, and H2O), and a couple of enantiomers (R and S) with and without racemization in the liquid phase with two types of racemic isoplethal section shown in Figure 6. The systems with racemization correspond to the (±)-1/MeOH/H2O. In Case 1, the curves in the racemic isoplethal section (H -I, I -I', I' -J) correspond to the solubility curves of Me, Rac, and C, respectively. When deracemization occurs, conglomerate domain of stability degenerates to a 2D surface involving one of the enantiomers and the racemic compound (±), as coloured in green. In addition, the domain in the ternary system (MeOH/R/S) is also involved in the equilibrium. In Case 2, the solubility lines in the racemic isoplethal section (H -I'' and I'' -J) correspond to the solubility curves of Me and C, respectively. In contrast to Case 1, the conglomerate domain of stability does not include racemic compound (±). Only domains limited by full lines are accessible.

Figure 8 summarizes isothermal and isobaric quaternary systems with and without racemization. The domains highlighted in green or purple represent the areas of chiral discrimination, i.e., these domains involve conglomerate forms. Another similar case was described in detail in a review. [30] Under the usual condition without racemization in Case 1, the upper surface of conglomerate stability domain is delineated by the S -R -I' plane, it contains the racemic compound (±). In Case 2 without deracemization, the two symmetrical quadriphasic domains related to racemic plane are delineated by the line from the common point I'' and the stoichiometric point of (±)•MeOH.

Beyond point I'', toward richer concentration in water, there is a single monovarient curve down to the doubly saturated solubility point J in pure H2O, that represents the edge of the conglomerate domain of the stability. Conversely, in case of deracemization conglomerate, the crystals of a single enantiomer and racemic solution are in equilibrium at the end of the deracemization as described above. Thus, both cases 1 and 2 are degenerated and should be drawn by the system as shown in the right column of Figure 8. For enthusiastic readers, the animated perspectives are available in Supporting Information. To understand the concrete heterogeneous equilibrium at different temperatures, we studied the isoplethal sections of (±)- Overall, the thorough phase diagram study afforded guidelines for the chiral separation of 1 by crystallization. As the conglomerateforming system is necessary, the chiral separation could be ideally implemented above 34 °C. Considering the solubility of 1, the chiral separation of 1 was carried out in MeOH/H2O (70/30, v/v) above 28 °C, and at this solvent composition, C is stable, and its solubility is moderate at this operating temperature.

Without racemization With racemization and deracemization when possible

Case 1 T < 34 °C Case 2 T > 34 °C MeOH I" H J H 2 O S (±) R R S J I'

Conglomerate domain of stability

MeOH

I" H J

Deracemization by SOAT

To confirm racemization of 1 in solution, and to implement deracemization by SOAT, the kinetic constants k1 for the racemization process were measured by polarimetry at a temperature range from 15 to 45 °C. The values were used to construct an Arrhenius plot. [16] The Gibbs free energy of activation (ΔG ‡ ) was determined to be 96 kJ•mol -1 (See Supporting Information). The racemization rate was slower in polar solvents compared to non-polar solvents, and particularly in protic solvents such as MeOH and a mixture of MeOH/H2O (70/30, v/v). This behavior is similar to a pyrrolidine, and the observations can be attributed to hydrogen bonding between the carbonyl oxygen atom of 1 and the solvent, which reduces the rate of racemization. Generally, a slow racemization of the molecule during the deracemization process is not preferred as the enantiomeric composition in the solution during the crystallization would gradually shift in the direction of the undesired enantiomer, which could eventually cause nucleation of the counter-enantiomer due to the relatively high supersaturation, as shown in Figure 10. In this context, the deracemization of 1 in a mixture of MeOH/H2O (70/30, v/v) would not be preferable. Further screening test might give a solution to such a problematic case. However, considering the feasibility of SOAT, a too high or poor solubility was trade-off problem by considering MeOH mixtures. Thus, we used the mixture of MeOH and H2O with optimization of the crystallization duration, because the behavior of 1 had been well studied as abovementioned.

The results of the SOAT of 1 are summarized in Table 3. As expected from the racemization behavior of 1, the short crystallization duration of 10 h resulted in a low ee of the isolated crystals. The crystallization duration of 20 h furnished high ee with a maximum of 97% ee. To confirm the reproducibility of the experiment, we performed SOAT with the same duration and used seed crystals of the opposite enantiomer, which afforded a good ee after 20 h with an average value of 90% ee. The average volumetric productivity, [32] which indicates the quantity of the desired product that can be obtained per time unit and volume was 6.5 g h -1 L -1 for the process. Compared to our previous study, [16] which demonstrated a comparison of productivity between SOAT and TCID, the productivity in the present work is low owing to the long crystallization duration caused by the poor racemization rate.

Conclusions

The crystal structures of a racemic compound (Rac) and a racemic compound methanol solvate (Me) of axially chiral naphthamide 1 have been determined. The quaternary phase diagram of enantiomers of 1 in MeOH and H2O has been constructed. Particularly, the impact of temperature on the racemic isoplethal section of 1 in solution was thoroughly studied over a temperature range from 15 to 34 °C. At 15 °C, Rac is a stable phase in high H2O concentration, while Me was stable at a low H2O concentration. The domain for the stable C gradually expands from a high H2O concentration region with increasing temperature. Eventually, the domain for Rac disappears at 34 °C, and only C and Me are stable up to 50 °C. Based on the phase diagram study, it is demonstrated that the chiral separation of the enantiomers of 1 by SOAT in MeOH/H2O (70/30, v/v), resulted in crystals with high enantiomeric excess (up to 97% ee). These results further prove the efficiency of the phase diagram approach for enabling chiral separation by crystallization even when there is a stable racemic compound forming system which is typically challenging. The lessons from the present study will serve as a model for developing deracemization applications for industrial processes.

Experimental Section

Synthesis of 1 and preparation of C, Rac, and Me

Naphthamide 1 was synthesized using our previously reported procedure, [10] with a slight modification. The conversion of 2-hydroxy-1naphthoic acid (Sigma-Aldrich) to 2-methoxy-1-naphthoic acid was carried out in 2 steps, and the condensation of the prepared 2-methoxy naphthoic acid with piperidine afforded 1. The methods for the preparation of the conglomerate (C), racemic compound (Rac), and MeOH solvate racemic compound (Me) are summarized in Table 4.

Chiral HPLC analysis

The accurate chiral composition of 1 in solid samples (powder or single crystals) was determined by using high-performance liquid chromatography (HPLC) with an (S, S) Whelk-O1 column (Regis Technologies, Inc., φ4.6 × 250 mm × 5 μm) employing a mixture of heptane and isopropyl alcohol (1/1, v/v) as the mobile phase, at a flow rate of 1.5 mL/min. The wavelength employed for UV detection was 230 nm.

To suppress racemization during analysis, the column temperature was controlled at 0 °C using a thermostat with a double glass jacket. Under these conditions, retention times of 3.8 and 5.5 min were observed for (R)-1 and (S)-1, respectively. Analyses were performed using a SpectraSYSTEM (P1000XR, AS3000, UV2000, and SN4000, and Fisher Thermo Scientific). The enantiomeric excess (ee) values were obtained by integrating and comparing the peak areas of (R)-1 and (S)-1 using ChromQuest software.

Differential Scanning Calorimetry (DSC)

DSC experiments were performed using a Netzsch DSC 204 F1 apparatus equipped with an intracooler. Each DSC run was completed in aluminum pans with pierced lids at a heating rate of 5.0 K/min. The atmosphere of the analytes during the analysis was regulated by a nitrogen flux (40 mL/min), and Netzsch-TA Proteus software was used for data processing. Onset temperatures used as the melting point or desolvation point were calculated from the intersection between the baseline and the slope of the first (respectively last) portion of the endotherm. Reflections were measured on a Bruker D8 Quest diffractometer with a sealed tube, and a Triumph monochromator (λ = 0.71073 Å) and the intensity integration was carried out using the software Saint. Absorption correction was performed with SADABS. The structures were solved with direct methods using SHELXT. [33] Least-squares refinement was performed with SHELXL-2014 [34] against all reflections. Non-hydrogen atoms were refined freely with anisotropic displacement parameters. The positions of the hydrogen atoms were calculated or located by differences in Fourier maps. All hydrogen atoms were refined with a riding model.

Copies of the data can be obtained free of charge on application to CCDC, 12 Union Road, Cambridge CB2 1EW, U.K. (deposit@ccdc.cam.ac.uk). CCDC 1936797, 1936798, and 1937666 .

Solubility Measurements for the construction of the phase diagram

The solubility of 1 in MeOH and in the mixture of MeOH and H2O was measured in triplicate using a gravimetric method or by the determination of clear point using Crystal16 (Technobis B.V.). The identity of the solid phase(s) in equilibrium with a saturated solution was monitored by XRPD analysis. To be sure of the stable character of a solid phase in certain composition of the solution, the sample for the solubility measurement was prepared by cross-seeding technique, i.e., the mixture of different forms of crystals was added in the clear saturated solution at the given temperature, and a long elapsed time before sampling the solution and analysis by XRPD of the solid phases.

Second order asymmetric transformation (SOAT)

SOAT of 1 was carried out according to the following procedure. To a double jacketed 100 mL crystallizer (Reactor-Ready Lab reactor, Radleys) equipped with a thermocouple and a mechanical stirrer, compound 1 and MeOH/H2O (70/30, v/v) were added, and the mixture was heated to 50 °C with stirring (500 rpm) to dissolve 1 completely. The jacket temperature was controlled using a thermostat (Unichiller, HUBER). The solution was cooled to 34 °C at a rate of 1 K•min -1 , and the temperature was maintained for 20 min. The seed crystals (>99% ee of R or S isomer) were added to the solution at a stirring rate of 200 rpm, and the solution was cooled to 28 °C with a controlled cooling profile. Typically, the optimization of cooling curves for different operating conditions is complex. However, Mullin et al. reported the simplified relationship depicted by Eq. 1, which is adequate for general applications. [START_REF] Mullin | Crystallization[END_REF]  t =  0 -( 0 - f) (t/) 3 (Eq. 1)

Where  0,  f, and  t are the temperatures at the beginning, end, and any time t during the crystallization, respectively, and is the overall duration of the crystallization. Details of the operating conditions are summarized in Table 5.

Figure 3 .

 3 Figure 3. ORTEP representations of the (R)-enantiomer (a) in Rac, and (b) in Me of 1 at 150 K. Thermal ellipsoids are displayed at 50% probability. Overlaid molecular structures in (c) Rac (blue) and Me (magenta), and (d) Rac (blue) and C (orange).

  Reported by Sakamoto et al. Ref code: NATQEF.

Figure 4 .

 4 Figure 4. Crystal packing of (a) Rac and (b) Me along the a-axis. Hydrogen atoms are omitted for clarity. R-and S-isomers are colored in red and blue, respectively.

Figure 6

 6 depicts the schematic isothermal and isobaric quaternary system of MeOH, H2O, and the enantiomers of 1. Every face of the tetrahedron represents a ternary isotherm. Compound 1 forms a stable MeOH solvate racemic compound in methanol and a stable conglomerate in water. Since compound 1 exhibits spontaneous racemization in any solution, the two conglomerate isotherms are degenerated. Regarding the racemic isoplethal section outlined in magenta lines, (±)-1/MeOH/H2O, two cases were observed depending on the temperature as shown in Figure7. Depending on the solvent composition, the following solid phases; C, Rac, and Me could be stable in the racemic isoplethal section, with Me being the stable phase at a high MeOH concentration, Rac being the stable phase at a moderate MeOH concentration, and C being the stable phases at low MeOH concentration. It is also surprising that regardless of the relative stability of C with Rac in the binary system, Rac is more stable phase than C at a moderate MeOH concentration at lower temperature. Indeed, C crystals were converted to Rac in such suspension, and cross-seeding experiments gave similar results. Point H indicates the solubility of Me in MeOH. Point I is the common point in the solubility curves of Me and Rac, in case these two phases would have had a monotropic character point I' would have not existed in equilibrium. At point I', the intersection of the solubility curves of Rac and C, three solid phases co-exist before racemization occurs. Thus, measuring the point where the composition of the two phases does not change is a straightforward approach to confirm the existence of I'. We used XRPD measurements after crossseeding and continuous stirring for one week to confirm the presence of point I'.

Figure 5 .

 5 Figure 5. Ternary system of solvated racemic compound, conglomerate, and racemic compound and corresponding degenerated system due to the racemization in solution. Only domains limited by full lines are accessible. Deracemization is supposed to occur only when a stable conglomerate is in contact with a solution. The stable phases for the ternary system are : (a) ① undersaturated solution; ② ⟨S⟩+ saturated solution; ③ ⟨R⟩+ saturated solution; ④ ⟨(±)•MeOH⟩ + saturated solution; ⑤ ⟨(±)•MeOH⟩+⟨S⟩+ saturated solution; ⑥ ⟨(±)•MeOH⟩ + ⟨R⟩+ saturated solution; and ⑦ ⟨(±)•MeOH⟩+⟨S⟩+⟨R⟩, (b) ① undersaturated solution; ② ⟨S⟩+ saturated solution; ③ ⟨R⟩+ saturated solution; and ④ ⟨S⟩ + ⟨R⟩ + racemic saturated solution, (c) ① undersaturated solution; ② ⟨S⟩ + saturated solution; ③ ⟨R⟩ + saturated solution; ④ ⟨(±)⟩ + saturated solution; ⑤ ⟨S⟩ + ⟨(±)⟩ + doubly saturated solution; and ⑥ ⟨R⟩ + ⟨(±)⟩ + doubly saturated solution. The stable phases for the degenerated ternary equilibrium are: (d) ① undersaturated solution; ② ⟨(±)•MeOH⟩+ racemic saturated solution H; ③ ⟨(±)•MeOH⟩+⟨S⟩+⟨R⟩, (e) ① undersaturated solution; ② ⟨S⟩ or ⟨R⟩ + racemic saturated solution J, (f) ① undersaturated solution; ② ⟨(±)⟩ + racemic saturated solution K.

Figure 6 .

 6 Figure 6. Quaternary isotherm system with a couple of enantiomers of 1, MeOH, and H2O. The triangular face (MeOH/S-1/R-1) represents the ternary isotherm indicating a stable solvated racemic compound with racemization. The base of the tetrahedron corresponds to the ternary isotherm (H2O/S-1/R-1) showing the stable conglomerate with racemization. Magenta triangular plane is the racemic isoplethal section, (±)-1/MeOH/H2O.

Figure 7 .

 7 Figure 7. The ternary equilibrium at the racemic isoplethal section of (±)-1/MeOH/H2O (a) below 34 °C ① unsaturated solution; ② ⟨(±)-1•MeOH⟩ + saturated solution; ③ ⟨(±)-1⟩ + ⟨(±)-1•MeOH⟩ doubly saturated solution I; and ④ ⟨(±)-1⟩ + saturated solution; ⑤ ⟨(+)-1⟩ + ⟨(-)-1⟩ + saturated solution, and (b) above 34 °C ①unsaturated solution; ② ⟨(±)-1•MeOH⟩ + saturated solution; ③ ⟨(+)-1⟩ + ⟨(-)-1⟩ + ⟨(±)-1•MeOH⟩ triply saturated solution I''; and ④ ⟨(+)-1⟩ + ⟨(-)-1⟩+ saturated solution. Every solution has a racemic composition.

Figure 9 .

 9 Figure 9. (a) The isoplethal sections of the quaternary phase diagrams of (R)-and (S)-enantiomers of 1, H2O, and MeOH at 15 °C (○), 20 °C (▲), 23 °C (◇), 28 °C (×), and 34 °C (■). (b) Schematic diagram of the isoplethal section along the temperature axis.

Figure 10 .

 10 Figure 10. Schematic representation of the chiral separation by crystallization with (a) fast racemization and (b) slow racemization.

  -ray Diffraction (SC-XRD)

Table 1 .

 1 Thermochemical properties of the four solid phases of 1. C: {(+) and (-)}, Rac, and Me. Crystal structures of Rac and Me Crystallographic data for C, Rac, and Me of 1 are summarized inTable 2 for comparison. The data for C has been included from Sakamoto's report, ref code NATQEF. Rac and Me correspond to racemic compound. ORTEP representations of Rac and Me are shown in Figure

		C	Rac	Me
	Thermodynamic stability	Stable	Slowly transforms to C at high temperature	The surface can be desolvated under ambient condition
	Melting point / °C	111.2	99.4	50.4
	ΔHfus / kJ•mol -1	24.8	20.8	desolvation

Table 2 .

 2 Crystallographic data of C, Rac, and Me.

	5 Intensity / a.u.	10	15 2-theta /	20 Racemic compound (Sim.) 25 30 Conglomarate (Obs.) Conglomerate (Sim.) MeOH solvate (Obs.) °Racemic compound (Obs.) MeOH solvate (Sim.)

No. of formula units per cell, Z

Table 3 .

 3 Experimental results of SOAT of 1 in MeOH/H2O (70/30, v/v).

	Duration / h	mcrop / g	eefinal [%]	Pr / g h -1 L -1
	10	16.5	(S) 11	0.9
	15	14.7	(S) 68	6.0
	20	16.1	(S) 97	7.3
	20	15.4	(R) 92	6.6
	20	14.9	(R) 81	5.5

Table 4 .

 4 Preparation methods for the three solid phases of 1.

	Solid phase	Preparation method
	C	Slow evaporation from conventional solvents [a]
		Cooling crystallization from CHCl3/Heptane (1/1,
	Rac	v/v) mixture or slow evaporation from a MeOH/H2O
		(8/2, v/v) mixture
	Me	Cooling crystallization or slow evaporation from a solution in MeOH

[a]Ethanol, Isopropyl alcohol, tert-Butyl alcohol, Acetonitrile, Isobutyronitrile, Methyl tert-butyl ether, Tetrahydrofuran, Acetone, and Methyl iso-butyl ketone

Table 5 .

 5 Operating conditions for SOAT of 1

	Mass of 1 (g)	28.2
	Mass of solvent (g)	85.4
	Concentration (wt%)	24.8
	Mass of seeds (g)	1.00
	Stirring speed (rpm)	200
	Duration (h)	10, 15, 20

Acknowledgements

The authors are grateful to Prof. Dr. Lucia Maini in University of Bologna for single crystal X-ray diffraction measurement of Rac at 293 K. This research received funding as part of a CORE project (October 2016-September 2020) from the Horizon 2020 Research and Innovation Programme of the European Union under Marie Sklodowska-Curie grant agreement No. 722456 CORE ITN. F.M. and Y.G. would like to thank Erasmus+ Programme of the European Union for the opportunity to carry out this project. Keywords: Deracemization • Second-order asymmetric transformation (SOAT) • Phase diagram • Atropisomerism