Dr Lenka Pallova

Dr Etienne Gauthier

Dr Laura Abella

Dr Marion Jean

Nicolas Vanthuyne

Dr Vincent Dorcet

Dr Laure Vendier

Jochen Autschbach
email: jochena@buffalo.edu

Dr Jeanne Crassous
email: jeanne.crassous@univ-rennes1.fr

Dr Stéphanie Bastin
email: stephanie.bastin@lcc-toulouse.fr

Dr Vincent César
email: vincent.cesar@lcc-toulouse.fr

Prof. J Autschbach

Synthesis and Properties of Partially Saturated Fluorenyl-Derived [n]helicenes Featuring an Overcrowded Alkene

Keywords: helicene, fluorene, chiroptics, Chiral resolution, quantum-chemical calculations 10.1002/chem.202100150

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Introduction

Helicenes are a special class of inherently chiral molecules that combine a helical topology and an extended -conjugated structure. [1] Owing to this unique screw-shaped -delocalization, helicenes display enhanced chiroptical properties (Optical Rotation (OR), Electronic Circular Dichroism (ECD), Circularly Polarized Luminescence (CPL) …) compared to other common chiral molecules. [1,2] Thus, they have gained great significance over the past decade as key constitutional units in materials for optoelectronics, [3,4] supramolecular chemistry, [5] chiroptical switches [6] or in the design of chiral ligands for asymmetric catalysis to name a few. [1f,7] At the heart of these blossoming applications lies the possibility to tune the chiroptical properties of helicenic compounds by modifying their structure. Starting from the basic carbo[n]helicenes, formally composed of ortho-fused benzene rings, several strategies were indeed found suitable to increase the diversity of helicenic scaffolds by: i) introducing maingroup elements (B, Si, N, P …) leading to the design of heterohelicenes; [8] ii) varying the size and nature of the rings within the helix; iii) designing helicenoid or helicene-like systems formed of non-fully aromatic ortho-fused rings; [9] iv) inclusion of a positive or negative charge within the helical scaffold, [10] or v) incorporating helicenic ligands into organometallic complexes. [11] In this context, the development of efficient, flexible and convenient methods for the synthesis of helicenic compounds appears of utmost importance, as the field cannot grow without the advent of more practical, scalable and cost-efficient synthetic pathways.

In a joint research program, we were interested in using the [5] and [7]-helicene-like fluorenes 1 and 2 as building blocks to generate novel helicene-NHC-based ligands for organometallic chemistry (Figure 1). [12,13] While the dibenzo [c,g]fluorene 1 (dbf) has been known for more than half a century, [14] the [7]helicenelike fluorene 2 was described in 2016 by Nozaki. [15,16] Both compounds are obtained by reduction of the corresponding ketone analogues using hydrazine at elevated temperature. Moreover, the syntheses of the keto-compounds involve either a decarboxylative condensation of binaphthyl 2,2'-dicarboxylic acid under very harsh conditions (300°C) or a transition-metal catalyzed, multistep synthesis. We thus devised to develop a common, direct and efficient synthetic protocol towards the fluoreno[n]helicenes 1 and 2 from easily available starting materials and without going through the ketone intermediates. Our strategy relies on the key intermediates 3 and 4, which would generate compounds 1 and 2 respectively in a final dehydrogenative aromatization. Compounds 3 and 4 are thus partially-hydrogenated (or saturated) fluoreno[n]helicenes, and their most striking feature is the presence of a tetra-substituted, overcrowded C=C bond. As such, they can be considered as the cyclic analogues of the chiral helical alkene (3R,3'R)-(P,P)-trans-5, [17] which is the archetype of the well-known Feringa's molecular motors. [18] Figure 1. Structures of helicene-like fluorenes 1 and 2, of their partiallyhydrogenated analogues 3 and 4 and of the related acyclic, overcrowded alkene 5. Notation: Compounds 1 and 3 are composed of the five ortho-fused rings in black, while compounds 2 and 4 (in blue) possess the five rings in black and the two additional terminal phenyl rings in blue.

We report herein the efficient, multi-gram scale synthesis of compounds 3 and 4, along with the isomer separation, structural characterization of their different stereoisomers. The solution behavior and chiroptical properties of the latter have been examined and analyzed with the help of quantum-chemical calculations, as well as their conversion into the aromatic Flu[n]helicenes.

Results and Discussion

Synthesis and characterization of the partially saturated fluoreno[n]helicenes 3 and 4 and of the aromatic fluoreno[n]helicenes 1 and 2 (n= 5, 7).

By analogy to the synthesis of the acyclic chiral helical alkene (3R,3'R)-(P,P)-trans-5, the key final cyclization step leading to 3 and 4 was devised through a McMurry coupling reaction between the two carbonyl moieties of the corresponding symmetrical 1,5diketones 8 and 9 respectively. By optimizing the direct, baseassisted condensation of formaldehyde with 2 equivalents of tetralone 6 or tetrahydrophenanthren-4-one 7, [19,20] the synthesis of the 1,5-diketones 8 and 9 was found to proceed efficiently in good yields and on a multi-gram scale (up to 18 g) (Scheme 1). Compounds 8 and 9 are each composed of an equimolar mixture of the racemic (R,R)/(S,S) couple and of the (R,S) meso compound. Then, submitting the 1,5-diketone 8 to the McMurry conditions cleanly furnished the corresponding partially saturated helicenelike compound 3 in an excellent 96% isolated yield after column chromatography (Scheme 1). While its formulation was firmly inferred from HRMS and elemental analysis, the 1 H NMR spectrum of 3 after chromatography indicated the presence of 2 diastereoisomers at room temperature in a ratio 2.3/1, which was further confirmed by HPLC (vide infra). Gratifyingly, the [7]helicene-like alkene 4 was also obtained under the same conditions from 9, albeit in a lower yield of 35%, which can be ascribed to the high steric congestion around the generated, internal C=C double bond. Analogously to compound 3, the analysis of the 1 H NMR spectrum of 4 recorded at room temperature led to the conclusion that 4 might be composed of a diastereoisomeric mixture (ratio of 1.77/1), whose one diastereoisomer exhibits a fluxional process in view of the broad signals observed for one set of the signals (vide infra). [20] Noteworthy, both reactions could be carried out on a multi-gram scale, which is highly beneficial to the synthetic utility of the strategy.

Scheme 1. Optimized synthetic route to the fluoreno[n]helicenes 1 and 2.

The last aromatization step was performed directly on the diastereoisomeric mixtures of the partially saturated 3 and 4 without further separation of the latter and consists in an oxidative dehydrogenation using tritylium tetrafluoroborate as hydride scavenger. The aromatic helicenic fluorenes 1 and 2 were smoothly isolated in 77% and 76% yields respectively. While the dibenzo [c,g]fluorene 1 is not configurationally stable and is thus achiral, the [7]-helicene-like fluorene 2 was obtained as a racemic mixture and the M and P enantiomers of 2 were obtained with ee's of more than 99.5% and 98.5% respectively by preparative HPLC separation on a chiral stationary phase, following the conditions reported by Nozaki. [15a] Isomer separation of the stereoisomers of 3 and 4, their structural characterization and their solution behavior The H6-Flu[n]helicenes 3 and 4 possess two stereogenic carbon atoms at the bridgeheads between the cyclopentenyl and the neighbouring cyclohexenyl rings, anda priori -a helical chirality, which led to consider the possible generation of the three pairs of enantiomers depicted in Scheme 2. The two pairs of C2symmetric enantiomers (R,R,P)/(S,S,M) and (R,R,M)/(S,S,P) share the same central chirality and only differ by their helicity, The HPLC analysis of the crude stereoisomeric mixture of 3 on a chiral stationary phase showed three peaks and the chiral resolution of 3 by HPLC on a preparative scale enabled the isolation of the corresponding three diastereoisomers of 3. While the second eluted compound is achiral, the first and third eluted compounds correspond to a pair of enantiomers, as confirmed by their mirror-image spectra of electronic circular dichroism (ECD) (see Figure 6a), and were isolated in remarkable >99.5% optical purities. Noteworthy, the ratio between the isolated diastereoisomers of 2.4/1 is consistent with the ratio measured by 1 H NMR on the mixture of 3 before the chiral resolution (2.3/1). The 1 H NMR spectrum of the achiral diastereoisomer features a diastereotopic pattern for the apical CH2 protons of the cyclopentenyl ring, with one resonating at  = 2.35 ppm (dt, J = 11.8, 6.1 Hz) and the other one at  = 1.22 ppm (pseudo-q, J = 11.1 Hz). It is also consistent with a Cs-symmetry of the molecule. Indeed, considering that (R,S,P) / (S,R,M)-3 is a chiral C1symmetric molecule, of overall apparent CS symmetry in NMR due to unstable helical configuration, the achiral diastereoisomer could be firmly assigned to the enantiomers (R,S,P) / (S,R,M)-3, which are in fast equilibrium at room temperature. Moreover, decreasing the temperature up to -80°C did not allow to freeze this interconversion process and the achiral compound was then best described as the meso compound (R,S)-3. As expected, the 1 H NMR spectrum of the isolated pair of enantiomers confirmed their C2-symmetry, with a triplet at  = 1.87 ppm (J = 7.1 Hz) corresponding to the two equivalent, apical CH2 protons. At that point, the helical configuration could not be determined yet and we decided to perform DFT calculations using Gaussian 16, [START_REF] Frisch | Gaussian 16, Revision B.01[END_REF] the B3LYP functional, [START_REF] Becke | [END_REF] the def2-SV(P) basis set for atoms, [23] and the polarizable continuum model (PCM) for dichloromethane. [24] The DFT-optimized structures for the different stereoisomers and the calculations of their relative energies revealed that the enantiomers (R,R,P)-3 and (S,S,M)-3 are just 0.4 kcal.mol -1 higher in energy than the achiral meso compound (R,S)-3 (Table 1). However, the energy level of 7.8 kcal.mol -1 (relative to (R,S)-3) of the diastereomeric compounds (R,R,M)-3 and (S,S,P)-3 is too high to allow the existence to these compounds, and confirms that only the pair of enantiomers (R,R,P)-3 and (S,S,M)-3 and the achiral, "meso" compound (R,S)-3 are observed experimentally. This analysis also revealed that, despite having only 5 ortho-fused cycles, (R,R,P)-3 and (S,S,M)-3, are configurationally stable and that the helical chirality is dictated by the central chirality of the two carbon atoms. Moreover, a conformational search on the diastereoisomers yielded two conformers for each compound, which differ in the ring puckering of the cyclohexenyl rings adjacent to the central cyclopentenyl ring (see SI for details).

Table 1. Computed relative energies of stereoisomers of 3 and 4. [a] Compound Erel (kcal.mol -1 ) [b] (R,R,P)-3 / (S,S,M)-3 0.4 (conformer 1) 16.2 (conformer 3) [a] The different conformers are depicted in the supporting information. [b] The energies are given relative to the more stable stereoisomer and conformer.

Similar chiral stationary phase HPLC analysis and resolution were performed on compound 4 and showed that the diastereoisomeric mixture of 4 is also composed of a pair of enantiomers as first and third eluted compounds and of an ECD-non-responsive compound as the second eluted compound. Concerning the pair of enantiomers, their NMR spectra are consistent with a C2symmetry and present in particular a typical triplet signal at  = 2.17 ppm (J = 6.9 Hz) corresponding to the apical CH2 protons of the cyclopentenyl ring. Moreover, a first proof of the helical structure was found in the significantly high field-shifted resonance at  = 6.52 ppm (ddd) of two aryl protons compared to the other aromatic protons, as they experience the aromatic ring current anisotropy generated by the close proximity of the naphthalene moiety in the opposite part of the molecule. To unequivocally prove the molecular geometry and the complete configuration of this pair of enantiomers, single crystals of the first eluted enantiomer suitable for an X-Ray diffraction analysis were grown (Figure 2). [25] The crystal was found to be orthorhombic with the space group P212121 and it corresponds to (R,R,P)-4 stereoisomer. As it is apparent from Figure 2, the naphthalene moiety and the proton at the stereogenic carbon atom of the same one-half of the molecule are orientated on the same side of the plane defined by C14, C1, C29 and C16. The central double bond 10.1002/chem.202100150

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.

C1-C29 [1.352( 9) Å] is only slightly elongated compared to the literature values of 1.323 Å for cyclopentene derivatives, [26] and is highly similar to the other over-crowded C=C bonds reported in related Feringa's molecular motors [1.345-1.350 Å]. [17b,27] The sp 2 ), [28] andmore importantly -higher than the value of 42.17° measured for the aromatized Flu [7]helicene 2. [15a] Figure 2. Molecular structure of (R,R,P)-4 determined by XRD analysis (ellipsoids drawn at 30% probability level). Selected bond length: C1-C29 1.352( 9) Å.

The ECD-non responsive second eluted compound exhibits a symmetrical 1 H NMR spectrum (recorded at 300 MHz) at 25°C but the presence of some broad signals suggested a fluxional process.

A variable-temperature NMR experiment was thus carried out.

Upon lowering the temperature to -80°C, all signals became duplicated (Figure S1.13), indicating that the dynamic process was frozen at that temperature and that the molecule is C1symmetric, as all protons are unequivalent. This led us to assign this compound as the pair of enantiomers (R,S,P)-4 and (S,R,M)-4, in which the helical chirality is not configurationally stable at room temperature with a rapid interconversion of the two helixes at that temperature (Scheme 3).

Scheme 3. Interconversion equilibrium between the (R,S,P)-4 and (S,R,M)-4 enantiomers.

The VT NMR behavior of the (R,S,P)-4 and (S,R,M)-4 couple is illustrated in Figure 3 on the more shielded aromatic protons Ha and Hb. In the 1 H NMR spectrum recorded at 25°C on a 600 MHz spectrometer, only one broad signal at  = 6.39 ppm is observed for the two indicating a fast exchange process at that temperature. At 0°C, this resonance coalesces, and two signals at  = 6.16 ppm and 6.58 ppm are detected at -80°C. The estimated G ≠ of the exchange process associated with this coalescence is ca. 52 kJ.mol -1 .

Figure 3.

Variable temperature 1 H NMR spectra of (R,S,P)/(S,R,M)-4 in the region 6.75-6.05 ppm (CD2Cl2, 600 MHz)

The formulation of this compound as the racemic mixture between (R,S,P)-4 and (S,R,M)-4 was then firmly confirmed by an XRD analysis of single crystals grown at room temperature. It consists of the racemate and crystallizes in the centrosymmetric space group P21/c. The two enantiomers found in the unit cell are depicted in Figure 4. Unfortunately, the poor quality of the crystal prevented any discussion on the metrics and only proved molecular architecture. DFT calculations (see Computational Details) confirmed the experimental results and showed that the (R,R,M)-4 / (S,S,P)-4 pair is 13.2 kcal.mol -1 higher in energy than (R,R,P)-4 / (S,S,M)-4, which explains why only the latter pair of enantiomers was isolated. It is worth noting that this is the same trend as in the case of the 5-ring-containing compound 3, where the energy difference is 7.8 kcal.mol -1 . The energy difference is higher in 4 due to the presence of the two additional terminal aryl rings. In a conformational search, two iso-energetic conformers for (R,R,P)-4 / (S,S,M)-4 were identified, which only differ in the ring puckering of the cyclohexenyl rings. The average energy (R,S,P)-4 / (S,R,M)-4 was calculated at 2.4 kcal.mol -1 above the most stable (R,R,P)-4 / (S,S,M)-4 stereoisomers and three conformers were 10.1002/chem.202100150

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. identified (Figure S2.2 and S2.3). While the most stable conformer of (R,S,P)-4 / (S,R,M)-4 corresponds to the structure determined by crystallographic analysis, a second possible conformer is only 1.3 kcal.mol -1 higher in energy. The high energy of a third conformer at 13.8 kcal.mol -1 excludes its presence in the experiments.

VCD spectroscopy

To get more insights into conformational and stereochemical features, these helical crowded alkenes were studied by infrared and vibrational circular dichroism (VCD) spectroscopy. [29] Indeed, helical organic molecules are known to display clear strong VCD signals originating from stretching and bending modes that are generally coupled [START_REF] Abbate | [END_REF] and that are diagnostic of their absolute stereochemistry obtained by comparison with theory. For enantiomers (R,R,P)-3 and (S,S,M)-3, the type of vibrations observed from low to high wavenumber are found as follows: bending at 1287 cm -1 (peak 1), combination of bending and stretching at 1393 cm -1 (peak 2), stretching at 1510 cm -1 (peak 3) and bending at 1524 and 1660 cm -1 (peaks 4 and 5, respectively) (see Figures 5c andS2. 7 and S2.8). For enantiomers (R,R,P)-4 and (S,S,M)-4, the assignment corresponds to bending at 1252 cm -1 (peak 1), C-C stretching at 1341 cm -1 (peak 2), combination of bending and stretching at 1392 cm -1 (peak 3) and bending at 1431 and 1500 cm -1 (peaks 4 and 5, respectively) (see Figures 5f and S2

UV-Vis and ECD spectroscopy

Helical molecules display characteristic experimental absorption and electronic circular dichroism (ECD) spectra that can also be used to describe their inherent stereochemistry. [1] UV-vis and ECD spectra of compounds 2, 3 and 4 were therefore measured (in CH2Cl2 at concentrations around 5x10 -5 M) and compared to the calculated ones. The UV-vis spectra are reported in Figures S2.14 and 2.17 while the ECDs are depicted in Figure 6a and c for 3 and 4, respectively, and in Figure S2.13 for 2. For instance, the ECD spectrum of (+)-3 displays a strong positive band at 185 nm ( = +77 M -1 cm -1 ), a strong negative band at 200 nm (-69) followed by a band of moderate intensity at 227 nm (-26) and two strong positive ones at 241 (+39) and 245 (+45) nm, and finally a broad negative band of weak intensity at 290 nm (-7). Calculated spectra determined from time-dependent DFT (TD-DFT) linear response calculations, were performed with the PBE0 [31] functional, the def2-SV(P) basis and solvent effects for dichloromethane. Regarding the general performance of TD-DFT for chiroptical spectra, see, for example, references [32a] and [32b]. The calculated UV/Vis spectra for the two conformers found for enantiomers (R,R,P)-3 and (S,S,M)-3 are shown in Figure S2.14. The experimental and the Boltzmann-averaged computational spectra are in good agreement. Three distinct spectral bands can be identified, which are assigned from low to high energy as resulting predominantly from the following occupied-to-unoccupied orbital transitions: HOMO to LUMO, HOMO-1 to LUMO, and HOMO-1 to LUMO+2 (see selected molecular orbitals in Figures 6e andS2.15). The molecular orbitals (MOs) of (R,R,P)-3 associated with the most intense excitations (Table S2.2) are provided in Figure S2.15. For (R,R,P)-3, the HOMO and the LUMO are localized on the conjugated system and the two fragments are involved, while the HOMO-1 is mainly localized on one of the -conjugated sixmembered rings. We note that the HOMO-1 and HOMO-2 levels are quasi-degenerate, with a very small energy difference of 0.067 eV, essentially corresponding to in-phase and out-of-phase (+/-) linear combinations of orbitals on either one of the moieties. S2. 3). Like in the (R,R,P)-3 system, the highest occupied and lowest unoccupied MOs are localized over the -conjugated system. We note that the LUMO+2 and LUMO+3 with a small energetic splitting are mainly localized on one moiety, with some contributions from the other moiety, in an in-phase/out-of-phase sign relationship. The ECD spectra of (R,R,P)-4 and (S,S,M)-4 are in line with the absorption spectra, but also showing additional features such as a weak negative band from the HOMO-1 to LUMO+1 transition (exc. #4 at 292 nm)

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. and an intense positive band for HOMO-4 and HOMO-2 to LUMO transitions (exc. #7 at 264 nm). Like in the UV/Vis spectra, the strongest band in the ECD spectra also appear at 230 nm, caused by excitations #14 and #15 with rotatory strengths of -385 and -305 esu 2 cm 2 , respectively. Similarly to 3, comparison between experiment and theory enabled to confirm the (R,R,P)-(+) and (S,S,M)-(-) absolute configurations for 4.

Stereoselectivity of the oxidative aromatization of 4 to the fluoreno[7]helicene 2

In the first part of this work, the fluoreno [7]helicene 2 was obtained as a racemic mixture from the mixture of stereoisomers of 4.

Having in hand the enantiopure (R,R,P)-4 and its enantiomer (S,S,M)-4, we were prompted to study the stereoselectivity of the oxidative aromatization reaction under the standard reaction conditions, namely reaction with tritylium tetrafluoroborate in DCE at 80°C for 3 hours. Starting from the enantiopure (R,R,P)-4 (99.5% ee) led to the isolation of (P)-2 in 81% yield but with a diminished ee of 46% (Scheme 4). A similar drop of enantiopurity was observed with the opposite enantiomer (S,S,M)-4 (99.5% ee), as it furnished (M)-2 in 71% and in 42% ee. These results led to the conclusion that, while the reaction is stereospecific, it is not 100% stereoselective as an erosion of the enantiopurity was observed.

Scheme 4. Synthesis of enantioenriched Flu [7]helicene 2 form enantiopure partially-hydrogenated helicenes 4.

An obvious reason for this loss of enantiopurity would be a configurational instability of product 2 under the reaction conditions. As no data was available on this process, we decided to experimentally quantify the racemization for compound 2. Thus, the kinetic of enantiomerization of (P)-2 in chlorobenzene at 132°C gave access to the experimental inversion barrier value of 142.3 kJ.mol -1 . While being a little bit smaller than the enantiomerization barrier for [6]-carbohelicene (151 kJ.mol -1 ), [33] this barrier showed that fluoreno [7]helicene 2 is configurationally stable at 80°C [t1/2 > 2 years]. The loss of enantiopurity might be thus ascribed to a configurational instability of some intermediate generated during the reaction. A reasonable possibility would be the formation of a 1,3-cyclopentadiene as the central 5membered ring by abstraction of a hydride at one of the stereogenic allylic positions by tritylium cation followed by loss of a proton on the apical methylene group. A suprafacial [1,5]hydrogen shift would then readily occur on this intermediate leading to a scrambling of the remaining stereogenic center within the topical ring and to a loss of the chiral information. [34]

Conclusion

In this paper we have reported the synthesis of the new, partially hydrogenated fluoreno[5]-and [7]helicenes H6-Flu[n]helicenes by a straightforward McMurry coupling as key cyclization step. The interplay between the central and helical chirality types has been established within these cyclic compounds. For each compound, the successful isomer separation and isolation of the two configurationally-stable enantiomers (R,R,P) and (S,S,M), supplemented by quantum-chemical calculations, indicate that the helicity is induced by the configuration of the two pre-formed stereogenic carbon atoms. Moreover, due to the presence of two rather-flexible cyclohexenyl rings, the helical configuration in the (R,S,P)/(S,R,M) couple is not stable at room temperature leading to the perception of this couple as the achiral, meso (R,S) compounds at that temperature. As typical helical compounds, the chiral (R,R,P) and (S,S,M) H6-Flu[n]helicenes display clear, strong responses in VCD and ECD spectroscopy. Finally, the H6-Flu[n]helicenes constitute valuable intermediates to access on gram-quantities the corresponding aromatic fluoreno[n]helicenes through an oxidative dehydrogenation. The synthesis of helical NHC ligands by the combination of the latter fluoreno[n]helicenes with carbenic units is currently under study in our laboratories and will be reported in due course.

Scheme 2 .

 2 Scheme 2. General depiction of the possible stereoisomers for compounds 3 and 4 and the respective relationships between them.

2. 2 (

 2 conformer 2) (R,R,M)-3 / (S,S,P)-3 7.8 (R,S,P)-3 / (S,R,M)-

  hydridization of C1 and C29 carbon atoms is evidenced by the sum of the bond angles around them very close to 360° [C1 = 360° and C29 = 359.2°]. The central, over-crowded C1=C29 bond is only slightly twisted [dihedral angles: C14-C1-C29-C28 = 168.65°, C2-C1-C29-C16 = 179.45°, C14-C1-C29-C16 = 0.06°, C2-C1-C29-C28 = -11.98°], which is quite similar to the case of the acyclic analogue (3R,3'R)-(P,P)-trans-5. Eventually, the helicity (dihedral angle between the terminal rings) of (R,R,P)-4 is 56.33°, which is quite similar to the values recorded for [6]carbohelicene (58.5°

Figure 4 .

 4 Figure 4. Molecular structure of the racemate (R,S,P)-4 and (S,R,M)-4 determined by XRD analysis (ellipsoids drawn at 30% level of probability).

  .9 and S2.10). Finally, comparison between experimental and theoretical VCD enabled to assign the absolute configurations of 3 and 4 (i.e. (R,R,P)-(+) and (S,S,M)-(-), see the SI part for the specific rotation values). Analogously to 3 and 4, (M) and (P) enantiomers of helicenic fluorene 2 display similar experimental IR and mirror-image VCD spectra (see Figures S2.4 and 2.6). Seven dominant peaks are numbered in the VCD spectra of fluorene 2 (Figures S2.4 and S2.5). Calculation shows bending vibrations in all the numbered peaks with the only exception of peak 3 at 1342 cm -1 , which is a combination of bending and stretching vibrations. Here again, the good agreement between calculation and experiment enabled to assign the (P)-(+) and (M)-(-) absolute configurations of 2.

  The broadened calculated ECD spectra are in very good agreement with the experiments(Figures 6b and 6d and S2.16). The calculated ECD peaks are systematically blue shifted by 0.1-0.3 eV, which is not unusual due to the combination of approximations made in the TD-DFT calculations. In general, the transitions with large oscillator strength f also have large rotatory strength R, and the assignments of the ECD bands are of course in line with the absorption peaks at wavelengths where both types of spectra have peaks. Additionally, two  → * electronic transitions appear active in the ECD spectra, from excitation #7 (HOMO-3 to LUMO) and excitation #23 (HOMO-3 to LUMO+3). The latter excitation shows the largest R value (415), leading to the strongest band of the ECD spectrum. Finally, comparison between experiment and theory enabled to confirm the (R,R,P)-(+) and (S,S,M)-(-) absolute configurations for 3. Two dominant spectral regions with distinct intensities can be identified for the absorption spectra of (R,R,P)-4 and (S,S,M)-4, which are assigned from low to high energy as resulting predominantly from transitions among the following pairs of occupied and unoccupied MOs: HOMO to LUMO for the lowintensity low-energy region and HOMO-1 to LUMO+2 and LUMO+3 for the high-intensity high-energy region (see Figures S2.17

  and S2.18, and Table

Figure 5 .

 5 Figure 5. a) Experimental IR and b) VCD spectra of enantiopure (R,R,P)-3 and (S,S,M)-3. c) Calculated VCD spectra for (R,R,P)-3 and (S,S,M)-3. The numbers indicate the corresponding peak associated to the vibrational normal modes visualized in Figure S2.8. d) Experimental IR and e) VCD spectra of enantiopure (R,R,P)-4 and (S,S,M)-4. f) Calculated VCD spectra for (R,R,P)-4 and (S,S,M)-4. The calculated VCD spectra correspond to the Boltzmann average of the two conformers of (R,R,P)-3 and (R,R,P)-4. The numbers indicate the corresponding peak associated to the vibrational normal modes visualized in Figure S2.10.

Figure 6 .

 6 Figure 6. Experimental ECD spectra of a) (R,R,P)-3 / (S,S,M)-3 and c) (R,R,P)-4 / (S,S,M)-4. Calculated ECD spectra of b) (R,R,P)-3 / (S,S,M)-3 and d) (R,R,P)-4 / (S,S,M)-4. e) Selected isosurfaces (±0.03 au) of MOs for 3 and 4.For helicenic fluorene 2, the calculated UV/Vis spectrum reveals the appearance of four absorption regions with distinct intensities(Figure S2.11). The assignment of the absorption bands from low to high energy is as follows; HOMO to LUMO, HOMO to LUMO+2, HOMO-2 to LUMO+3 and HOMO-2 to LUMO+4. The HOMO and LUMO of (P)-2 are mostly localized on the -conjugated system of the hexagonal rings close to the pentagon (FigureS2.12). The calculated broadened ECD spectrum of (P)-2 reproduces the experimental spectrum very well(Figure S2.13). Excitation #4 at 317 nm has a particularly large rotatory strength (R = 648) and corresponds to a combination of two helicene  → * transitions from HOMO-2 to LUMO and HOMO to LUMO+1. Comparison between experiment and theory enabled to confirm the (P)-(+) and (M)-(-) absolute configurations for 2.

  The experimental IR and VCD spectra of enantiopure compounds 2, 3 and 4 were measured in CD2Cl2 at concentrations around 0.15 M, in the 1000-2000 cm -1 region. As depicted on Figures5a,b andd,e both enantiomers of 3 and 4 display similar IR and mirrorimage VCD signatures, with several clear active bands that have been analyzed by theory. Compared to (R,R,P)/(S,S,M)-3, the VCD spectra of (R,R,P)/(S,S,M)-4 appear richer and less defined due to the presence of many peaks of moderate intensity.

The calculated VCD spectra for enantiomers (R,R,P) and (S,S,M) of 3 and 4 are displayed in Figures

5c and 5f

. They are Boltzmannaveraged for the two conformers found for (R,R,P) and (S,S,M) of both compounds. Calculations well reproduce the experiments. Notably, for both 3 and 4, five dominant peaks are numbered in the VCD spectra, corresponding to the vibrational normal modes shown in Figures S2.

8 and S2.10, respectively.

Acknowledgements

We thank the Centre National de la Recherche Scientifique (CNRS) and the University of Rennes. This work was supported by the Agence Nationale de la Recherche (ANR-16-CE07-0019 "Hel-NHC" grant). L.A. and J.A. acknowledge the Center for Computational Research (CCR) at the University at Buffalo for providing computational resources. [35] The computational part of this research has been supported by Grant CHE-1855470 from the National Science Foundation.

Entry for the Table of Contents

Blocking a molecular motor: The partially saturated H6-fluoreno[n]helicenes (see figure), cyclic analogs of the well-known Feringa's molecular motors, are produced via a similar McMurry cyclization approach. While being composed of three diastereoisomers, they serve as valuable intermediates for the efficient, multi-gram scale access to the aromatic fluoreno[n]helicenes.

Institute and/or researcher Twitter usernames: @vinc_cesar, @Bastin31, @JeanneCrassous, @EGA_chem 10.1002/chem.202100150


Wenhua Zhao

P H Taylor

H A Wolgamot

B Molin

R Eatock Taylor

Group dynamics and wave resonances in a narrow gap: modes and reduced group velocity

Keywords: Gap resonance, Wave propagation, Group velocity, Heading effect, Spatial structure, Wave-structure interactions

, albeit for a slightly different box cross-sectional shape.

Introduction

In side-by-side scenarios, one vessel may be moored alongside another, creating a gap that is very narrow relative to the principal dimensions of the two bodies. One practical application might be an offloading operation between a floating liquefied natural gas facility and an LNG carrier [START_REF] Zhao | Current practice and research directions in hydrodynamics for FLNG side-by-side offloading[END_REF]. The fluid inside the narrow gap may experience significant resonant response (gap resonance) when excited at particular wave frequencies.

Early pioneering studies [START_REF] Molin | On the piston and sloshing modes in moonpools[END_REF][START_REF] Molin | Experimental study of the wave propagation and decay in a channel through a rigid ice-sheet[END_REF][START_REF] Sun | First-and second-order analysis of resonant waves between adjacent barges[END_REF]) have demonstrated that gap resonances are standing waves in a gap, where the gap length is close to an integer number of half wavelengths for each standing wave (or gap mode). The gap resonances with different but close mode frequencies interfere in the gap, making the resonance rather complex. Gap resonance is an interesting hydrodynamic phenomenon, also in the sense that the narrow width makes it difficult for wave energy to 'escape' from the gap, leading to large responses at resonance. In such a scenario, viscous damping becomes relatively important as the radiation damping is small.

Various methods have been proposed in the frequency domain to consider the viscous damping contribution to obtain reasonable agreement between potential flow calculations and physical model test results in gap resonance. For instance, [START_REF] Huijsmans | Diffraction and radiation of waves around side-by-side moored vessels[END_REF] suppressed vertical motion in the gap completely by introducing a rigid lid, [START_REF] Newman | Wave effects on multiple bodies[END_REF] split the gap motion into generalized modes, allowing different damping rates for each motion, and [START_REF] Chen | Hydrodynamic analysis for offshore LNG terminals[END_REF] introduced a dissipative damping term in the free surface condition.

In addition to frequency-domain analysis, intensive time-domain simulations can be conducted to account for viscous and nonlinear contributions. For instance, [START_REF] Kristiansen | Application of a vortex tracking method to the piston-like behaviour in a semi-entrained vertical gap[END_REF] ran a fully nonlinear 2D numerical wavetank coupled with an inviscid vortex tracking method, suggesting that flow separation is the main source of discrepancy between linear potential theory and model tests. A model is then developed for the estimation of viscous damping, based on small-amplitude harmonic flows through a slot in a slatted screen [START_REF] Faltinsen | On damping of two-dimensional piston-mode sloshing in a rectangular moonpool under forced heave motions[END_REF]. [START_REF] Feng | Wave resonances in a narrow gap between two barges using fully nonlinear numerical simulation[END_REF] carried out fully nonlinear numerical simulations and reported that nonlinearity may slightly increase the resonant frequency, though with limited effect on the amplitude. Using a multi-phase Navier-Stokes equation model, the flow field in the gap is examined in [START_REF] Feng | Numerical investigation of viscous effects on the gap resonance between side-by-side barges[END_REF] with focus on vorticity.

Numerous studies have been made to improve the agreement between numerical simulations and experimental data, by better understanding and modelling the damping. It seems that the majority of the efforts have been focusing on the resonant elevations at an individual location (e.g. the centre of a gap), while very few have considered the spatio-temporal structure of enhanced surface elevation along the gap. How wave groups propagate along the gap and how these couple into the gap resonant modes have not been studied previously.

In light of the above, we carried out a series of experiments (using the same setup as in [START_REF] Zhao | Gap resonance and higher harmonics driven by focused transient wave groups[END_REF]) to investigate the group dynamics and wave propagation of the resonant responses in a narrow gap. The gap resonance is excited by focused transient wave groups from different headings. A brief description of the experimental set-up follows in §2. The gap resonance phenomenon driven through a linear process is discussed in detail in §3. The evolution of the gap resonance is briefly discussed, and the linear transfer functions, with multiple peaks corresponding to various gap modes, are reported in §3.2. The temporal and spatial structure of the gap resonance is demonstrated more clearly in §4 through nonlinear excitation -a frequency-doubling process. Some new observations on the phase speed and group velocity of components related to the gap resonance modes are given in §5. We show that the group velocity within the gap drops to one twentieth of the phase speed close to the lowest gap mode, significantly different to that for deep-water free waves. Finally, some conclusions are drawn at the end of this study.

Experimental set-up

The experiments were conducted in the Deepwater Wave Basin at Shanghai Jiao Tong University. The basin is 50 m long, 40 m wide and the water depth was set to 10 m. To focus on the gap responses and to simplify the study, we selected two identical rectangular boxes to represent a side-by-side moored two-body system. Each model is 3.333 m long, 0.425 m high, 0.767 m wide and the gap width between them is 0.067 m. The vessel models have round corners at both bilges, each with a radius of 0.083 m running along the full length, as shown in figure 1.

During the model tests, the two boxes are fixed to a gantry which provided enough stiffness to hold them rigidly in place. Each box was immersed to a draft of 0.185 m. As shown in figure 1, there are seven wave gauges (WG) 1 and 7, 2 and 6, 3 and 5 being symmetric in pairs about the gap centre, and WG4 being central in the gap. A more detailed description was reported in a previous study [START_REF] Zhao | Gap resonance and higher harmonics driven by focused transient wave groups[END_REF].

Rather than generating random waves in the tank, requiring long duration runs, we used transient focused wave groups as the incident waves. Prior to the experiments, a series of transient wave groups were generated in the absence of the model, based on a hypothetical Gaussian spectrum (representative of swells) given by

S η (f ) = H 2 s 16 1 δ √ 2π exp[- (f -f p ) 2 2δ 2 ], (2.1)
where H s refers to an assumed significant wave height, f p the peak frequency of the spectrum and δ=0.0775 Hz. Two sets of transient wave groups were generated (see details in Appendix A): one of them has a spectral peak frequency f p = f m=1 =1.02 Hz (where f m=1 is the frequency of the mode with one half-wavelength along the gap in this experiment) and the other f p = 1 2 f m=1 . The two wave group tests drive the gap resonance through different processesthe former (f p = f m=1 ) by a simpler linear process and the latter (f p = 1 2 f m=1 ) through a more complex nonlinear (frequency-doubling) process. The target maximum surface elevation for the incident wave packet for both sets was 50 mm in the lab. The wave paddle signals which generated these wave groups were stored and repeated with the model in place producing the data analysed in the following sections. The calibration of the wave probes and the high accuracy of the measurements have been demonstrated in the appendix of [START_REF] Zhao | Gap resonance and higher harmonics driven by focused transient wave groups[END_REF] for similar tests, and thus we do not repeat this here.

Gap resonance driven via a linear process

This section presents the gap response driven through a linear process, i.e. by the transient wave groups (see Appendix A) with peak frequency of f p = f m=1 for the underlying spectrum. In the absence of the model, these wave groups were generated with the waves focusing at the location of the central gauge WG4 (see figure 1). Without moving WG4, the same wave paddle signals were repeated when the model was installed in the tank. The heading direction of the model was adjusted in the tests, so that the wave groups approach the model from different directions, i.e. achieving beam sea and head sea conditions.

The gap resonances were excited in both beam and head seas using the same undisturbed incident wave surface elevations. Time histories were measured at the location of WG4 (the centre of the gap) in the absence of the model (undisturbed incident waves, marked as η) and at the seven gauge locations with the model in place (response, marked as ϕ). A decomposition of the temporal structure of the transient gap resonant behaviour at an individual location has been reported in our previous study [START_REF] Zhao | Gap resonance and higher harmonics driven by focused transient wave groups[END_REF]. Here, we focus on the spatial evolution of the gap resonance harmonics along the gap, with new phenomena being observed in terms of the group dynamics within the gap.

Temporal and spatial evolution of the gap resonance along the gap

In this analysis, a set of four focused wave groups are generated using the same paddle signal, but with each Fourier component shifted by a relative phase of 0 • , 180 • , 90 • or 270 • , respectively. These four wave groups correspond to a crest focus, a trough focus and up-and down-crossings, all with the same linear envelope. These four-phase wave group signals can be used to extract the first four harmonic components, i.e. η 1 , η 2+ , η 3+ and η 4+ , which refer to the terms with frequencies around ω, 2ω, 3ω and 4ω, respectively. The extracted harmonics are associated with the Stokes-type expansion for non-linear waves. It should be noted that the second-order difference frequency signal η 2-, arising from the interaction of pairs of linear components, is combined with the η 4+ signal in this methodology, but it is straightforward to separate these through a simple frequency filter as these two terms cover quite different frequency ranges. The same idea holds for the corresponding gap resonant responses, and so we can separate the first four gap resonance harmonics ϕ 1 , ϕ 2+ , ϕ 3+ and ϕ 4+ . For the sake of space, we do not repeat the four-phase decomposition theory here, but details can be found in [START_REF] Fitzgerald | Phase manipulation and the harmonic components of ringing forces on a surface-piercing column[END_REF] and [START_REF] Zhao | Gap resonance and higher harmonics driven by focused transient wave groups[END_REF].

The first four harmonics of the gap resonance in beam sea excitation are extracted through the four-phase decomposition method. As the higher harmonic components of the gap resonance beyond the second are quite small in this test, we only show the first (ϕ 1 ) and the second-order difference frequency (ϕ 2-) and sum frequency (ϕ 2+ ) signals.

Figure 2 shows the harmonics of the surface elevations measured by the seven wave gauges in the gap. Strong gap resonant responses are excited as shown by the linear components (ϕ 1 ) in figure 2. This is because the frequency range of the linear components of the input group contains frequencies corresponding to the first few gap resonant modes. The time when the undisturbed wave component crests focused at the location of the central gauge has been set as t=0 s. As shown in figure 2, the incident transient wave group (η 1 ) only lasts about 6 s after the focal time, while the gap responses last for much longer and show strong beating patterns. The beating pattern of the gap resonance time history is a result of the interference of the different modes set up in the gap, each of which simply decays exponentially in time once the incident wave group has passed by. The second-order difference frequency and sum frequency signals, which are simply the bound wave harmonics of the linear response, are much smaller compared to the linear components. It is interesting to see that the second-order difference frequency term is as significant as the sum frequency term for the gap resonance phenomenon.

The combination of the measured signals from the seven wave gauges provides important information on the spatial structure of the resonances in the gap. At the excitation stage, i.e. around t=0 s, the signal pulse at the two ends of the gap (WG1 and WG7) is small, but they seem to propagate from the ends towards the centre of the gap and induce large response including large set up (blue curve in figure 2) when they meet at the centre of the gap. Then the wave groups seem to continue propagating towards the ends and some of them are reflected back to the gap. This process continues until the waves disappear due to dissipation and radiation. This phenomenon is more clearly demonstrated in the next section where the gap resonance is excited through frequency doubling, a nonlinear process.

When the waves (the same as in figure 2) approach the gap from a head sea, so along the gap from one end to the other, the gap signals show locally very different structure compared to the beam sea condition. As shown in figure 3, it is clear that the wave group propagates from one end to the other, with some energy loss. When it approaches the far end, part of the wave system is reflected and propagates back along the gap in the opposite direction. The process continues until all the wave energy in the gap is lost through dissipation and radiation. It is interesting to see that the largest gap response occurs at the entry area of the gap in the head sea, rather than at the centre of the gap as for the beam sea case. It is worth noting that only odd gap resonance modes are strongly excited for beam sea excitation due to the symmetry of the experimental set-up, whereas both even and odd modes are excited for the head sea excitation where the longitudinal symmetry of the gap response is lost.

We stress that much of the published analysis of gap resonance has concentrated on regular wave excitation. There the group structure in the gap would be regarded as a starting transient during the build-up of steady state oscillation. The only previous study of gap dynamics by wave groups that we know is by Eatock [START_REF] Taylor | Gap resonances in focused wave groups[END_REF] which shows comparable travelling groups in the gap, there computationally using potential flow calculations, here experimentally.

Response Amplitude Operators of the gap resonance and mode shapes

To provide further information on the resonant modes in the gap, we look at the response amplitude operators (RAOs). As an important design parameter, the RAO is the linear transfer function (in the frequency domain) between the input wave signal and the corresponding responses. [START_REF] Molin | Experimental and numerical study of the gap resonances in-between two rectangular barges[END_REF] provided the RAOs of gap resonances at different heading sea excitations with gap width of 12 cm and 31 cm (at model scale), for comparable scaled models. Here, we provide RAOs for a similar set-up but with a narrower gap (6.67 cm) with multiple wave gauge locations along the gap, to complement Molin et al. linear components are extracted through the four-phase decomposition methodology. It is worth mentioning that there is a cross term, assumed to be a (3,1) term -so cubic in amplitude, embedded in the first harmonic component. This cross term has the linear frequency, but a high-order dependence on the wave amplitude, and thus it is negligible for weakly nonlinear waves.

The RAOs obtained in a beam sea are shown in figure 4, with the symbols being the experimental data and curves being numerical fits to these experimental values. The mode shapes, each being close to an integer number of half wavelengths along the gap length, are demonstrated in the figure with the little diagrams next to each spectral peak of the RAOs. The range of frequencies covered by the first few odd gap resonance modes is quite compact, i.e. m= 1 to 7 modes are covered in a narrow frequency range from 1.0 to 1.4 Hz. It is not a surprise that the RAOs measured by WG4 (the centre of the gap) exhibit the largest values, and those measured at WG2 are very similar to those measured at WG6, which is a reflection of the symmetric set-up in the beam sea condition. The experimentally-determined frequencies of the gap resonance modes match well those calculated by the potential flow diffraction code DIFFRACT [START_REF] Sun | First-and second-order analysis of resonant waves between adjacent barges[END_REF], without consideration of any viscous damping. This was demonstrated in [START_REF] Zhao | Gap resonance and higher harmonics driven by focused transient wave groups[END_REF] and we do not repeat the results here.

By analogy, the gap resonance RAOs in head sea excitation are obtained and shown in figure 5. Compared to the beam sea excitation, an obvious difference in the head sea condition is that even gap resonance modes are also driven due to the asymmetry of the excitation. While the RAOs measured at WG2 and WG6 are very similar in beam sea conditions, they are different in the head sea case as shown in figure 5. In particular WG2 shows deeper troughs either side of the m=2 and m=6 modal peaks. Our linear potential flow calculation shows similar behaviour, though with much larger amplitudes as we do not include any viscous damping. This is not shown here. It is worth mentioning that the locations of WG2 and WG6 are close to nodes for the m=4 mode, and thus there is no significant m=4 mode response. The peak RAO value at the frequency of the m=2 mode in the head sea is comparable to those for the m=1 mode in both beam and head sea excitation. The frequency of the m=2 gap mode is very close to that of the m=1 mode, which indicates that both the first two gap resonance modes are likely to be excited to comparable level in a given sea state.

Another interesting phenomenon is that the RAOs at the frequency of the m=1 mode in the head sea excitation are slightly smaller compared to those in the beam sea, while all the other modes are slightly larger. This is consistent with the radiation patterns: linear potental flow calculations show that the m=1 mode radiates most strongly perpendicular to the gap, while the higher modes radiate more energy along the gap direction [START_REF] Wang | Resolving wave and laminar boundary layer scales for gap resonance problems[END_REF].

Gap resonance driven nonlinearly -a frequency-doubling process

In the section above, we discussed the time histories and the RAOs of the resonant responses along the gap under different heading excitations. These gap resonances are driven through a linear process, i.e. the frequency range of the linear incident wave components contains the frequencies of the gap modes, leading to resonant responses. One may note that the m=1 mode frequency is f m=1 =1.02 Hz at lab scale. This corresponds to a period of 7.6 s in the field at a scaling of 1:60. Therefore, we may suppose long period swells at 15.2 s might drive gap resonance through a frequency-doubling process; clearly this is of practical interest for open sea applications of side-by-side operations. We therefore look at the gap resonance excited by wave groups whose underlying spectral peak frequency is half the m=1 mode frequency.

Spectral demonstration of the frequency-doubling excitation

Model tests are conducted using the same set-up as in the linear case. To facilitate the analysis, we plot the spectrum of the undisturbed incident waves in figure 6, together with the corresponding gap resonance spectra under different heading excitations. All the signals in the figure were measured by the central gauge WG4 which was in place throughout the whole test programme.

As shown in figure 6, the spectral peak of the undisturbed incident wave group (black dotted curve) is half the m=1 mode frequency. The most striking observation from figure 6 is that the resonant responses in the gap are significant from 1.0 to 1.4 Hz, where there is very little incident wave energy. The m=1 mode response at the centre of the gap (WG4) seems to be significantly affected by the heading conditions. As noted in the previous section, each mode radiates in a different, rather directional, manner but the second-order excitation is more directional (e.g. cross terms between frequency pairs) than the linear excitation.

Temporal and spatial structure of the gap resonance: frequency doubling

Instead of focusing on the single wave gauge signal at the centre of the gap, this section presents the time histories measured by wave gauges along the gap, to better understand the temporal and spatial structure of the resonant responses in the gap.

Four-phase wave group tests are also conducted for each heading condition, so as to extract the harmonic components of the gap resonance. Using the four-phase decomposition methodology, we obtain the first four harmonics of the gap resonance, where the higher harmonics are quite small except that the second harmonic is now as important as the linear component. Figure 7 shows the first two harmonics of the gap resonance measured at the seven wave gauges, where the gap resonances are driven nonlinearly in a beam sea. The linear response time histories (left of figure 7) are uniform along the gap and are excited simultaneously. In this case, the frequency components of the linear responses are well below the gap resonance frequencies, and thus the long incident waves just pass the gap without exciting resonances. The frequency range of the second harmonics in this case covers the frequencies of the gap modes, and thus drive significant gap resonances. One can see clearly that the waves as a group propagate from the two ends of the gap towards the centre, meet at the centre, then propagate towards the ends, where there is some reflection back to the gap and some radiation to the far field. Indicative blue arrow lines are added on top of the second harmonic signals (in figure 7) to highlight the process.

Figure 8 shows the first two harmonics of the surface elevations in the gap under head sea excitation. As for the beam sea excitation, the frequency components of the linear responses (ϕ 1 ) are well away from the gap resonance frequencies, and thus no resonance is excited. In contrast to the beam sea condition, the linear response here decreases significantly from the upwave to downwave end, which we have found to be entirely consistent with potential flow theory (without additional damping). It is found that the linear response propagates from one end (WG1) of the gap to the other (WG7) at the same speed as the undisturbed incident waves (deep-water free waves). The second harmonic signal (ϕ 2+ ) in figure 8 is obviously not a bound component to the linear response, as it travels much more slowly than the linear component. This leads to a separation between the gap resonance time histories and the incident wave fields, facilitating the analysis of the group structure in the gap. The phase speed and group velocity derived for components in the gap are discussed in detail in the following section.

Phase speed and group velocity of the gap resonance modes

As demonstrated in the previous sections, the gap responses show a strong group structure which propagates along the gap. To explore this phenomenon, we look at the characteristics of the phase speed and group velocity associated with the gap resonance modes and compare these to the behaviour of open sea deep-water waves. The frequencies (ω m = 2πf m ) are taken from the experiments and the wavenumbers of the first nine gap resonance modes are calculated as k m = 2π/(2L/m), where m refers to the m th gap mode and L=3.333 m is the length of the gap. The values are listed in Table 1. Here, we have assumed the gap resonance modes have nodes exactly at the ends of the gapthis is only approximately correct but simplifies the analysis here without losing much accuracy, as the end corrections will be O(gap width) gap length. A Padé approximant polynomial curve is used to fit the relationship between the frequencies and the wavenumbers of the first nine gap resonance modes, as shown in figure 9. The fitted curve (black dotted line) is then used to provide the phase speed (c p = ω/k) and group velocity (c g = ∂ω/∂k, so the slope of the fitted curve) against wavenumber for the gap resonance modes. The group velocity of the gap resonance modes is about 0.35 m/s for the first few and most important modes (see the solid red curve in figure 9). Simply assuming the group velocity of each wave component is around 0.35 m/s, it will take just less than 7 s for wave energy to propagate the distance of 2.43 m from WG1 to WG7. This is consistent with the experimental observations of the group propagation, e.g. figure 8 for the head sea excitation. It is worth emphasizing that the linear response in the gap (the black curves in figure 8, which are not resonant modes) travels the same distance within only about 1.7 s, at the same speed (around 1.4 m/s) as that of deep-water free waves.

As shown in figure 9, the phase speed (solid blue curve) of the gap resonance modes decreases with wavenumber, but group velocity (solid red curve) increases slowly with wavenumber which is the opposite trend to free waves on the open sea (dashed curves). It is worth noting that the group velocity associated with the gap modes is remarkably Figure 9. Phase speed (cp) and group velocity (cg) in the gap, compared to free deep-water waves. The black solid dots and black dotted curve (a numerical fit) are the experimental data for the first nine gap modes, referring to the left vertical axis. All the remaining curves refer to the right vertical axis. The solid blue and red curves are experimentally-determined phase speed and group velocity in the gap. The dotted blue and red curves cp(f ) and cg(f ) are for deep-water free waves, while the dashed curves cp(M ) and cg(M ) are calcuated based on the potential flow model in [START_REF] Molin | Experimental study of the wave propagation and decay in a channel through a rigid ice-sheet[END_REF]. Note the different vertical scales.

small. The very slow variation of group velocity against wavenumber implies that there is little dispersion when a wave packet propagates along the gap. This explains why the observed group structure remains so clear along the gap, e.g. as shown by the second harmonic responses (the red curves) in figures 7 and 8. The phase speed (c p ) is much larger than the group velocity (c g ) in the gap. One consequence of this is that each wave component travels forwards through the group, until it reaches the front of the group, where it disappears. The group structure is then sustained by new waves that are continuously formed at the 'tail' of the group.

One can see in figure 9 that the group velocity of the gap modes tends to be half the phase speed for very short waves. This is not surprising, as very short waves can hardly 'feel' the gap and thus behave in a similar way to deep-water free waves. It would be more interesting to explore the phase speed and group velocity of gap resonant modes for very long waves, so very long gap. To achieve this, we look at the relationship between the frequency ω and the wavenumber k for waves in the gap through a theoretical model. Based on linear potential flow theory, [START_REF] Molin | Experimental study of the wave propagation and decay in a channel through a rigid ice-sheet[END_REF] derived the dispersion equation for waves propagating in an infinitely long and rectilinear channel with width b and draft h, which is formed by barge-like structures with infinite length and beam. The dispersion relationship can be approximated as

ω 2 gk 1 + J0 tanh kh J0 + tanh kh , (5.1) where J0 (kb) = 1 -2 πkb (1 - 1 0 exp (-kb/ √ 1 -u 2 )du).
The group velocity (∂ω/∂k) is obtained as

c g = g 2ω [ 1 + J0 tanh kh J0 + tanh kh - kb J 0 + kh(1 -J2 0 ) ( J0 cosh kh + sinh kh) 2 ], (5.2) where J 0 (χ) = d J0 dχ = 1 χ (1 -J0 (χ)) -2 πχ 1 0 exp(-χ/ √ 1-u 2 ) √ 1-u 2 du.
The phase speed and group velocity based on Molin's approximation are compared with the experimentally-determined values in figure 9. The agreement is reasonably good, given that no end correction is applied for the gap modes in the experimental results and that the box models in the experiments have round bilges. Molin's approximation behaves very similarly to deep-water free waves for large wavenumbers, and the group velocity converges to half the phase speed. The most striking observation is that the phase speed increases continuously as wavenumber decreases, while the group velocity decreases very slowly, leading to increasing deviation, e.g. the phase speed reaches up to 20 times the group velocity. An intuitive explanation of the very slow group velocity of the gap resonances may be related to the fluid kinematics in the effectively unbounded flow field underneath the model. It is also interesting to see that the group velocity increases significantly (without bound) when the wavenumber becomes small enough.

Conclusions

Focusing on the group dynamics of the resonant responses of the fluid in a narrow gap, a series of experiments is conducted. Two identical vessel models forming the narrow gaps are fixed in the wave basin during the tests. Transient wave groups are used to drive the gap resonant responses and the fixed models are rotated to achieve different wave approach directions. Seven wave gauges are deployed in the gap, which allows for the investigation of both the temporal and spatial structure of the gap resonance and the corresponding phase speed and group velocity. Some interesting phenomena are observed.

Experimentally-determined linear transfer functions of the water surface resonance along a narrow gap are provided. Only the odd gap modes are observed at the gap centre as a result of the symmetrical set-up in beam sea tests, while both odd and even gap modes are driven once the symmetry is broken (e.g. in head sea excitation).

How readily each gap mode can be excited is related to how well it radiates energy as free-surface waves outwards once the mode is excited. So this is sensitive to the approach heading of the wave as each mode radiates in a different, rather directional, manner. The m=2 gap mode linear transfer function (in head sea excitation) is observed to be as significant as that of the m=1 gap mode. This suggests that the m=2 mode may play a significant role in the relative yaw motion of two floating vessels, which needs further investigation with freely floating models. In contrast, the m=1 mode will not affect relative yaw of the vessels but it might couple with relative sway, so variation of the gap width with the two vessels remaining parallel along the gap.

The group velocity associated with the gap resonance modes does not vary much between different gap modes. This leads to the strong group structure of the resonant waves when propagating along the gap. These groups show rather smaller frequency dispersion than deep-water free waves. The most striking observation is that the group velocity of the resonant modes is very small. In contrast, the phase speed is large in particular for the first dominant gap modes, larger than for free waves of comparable frequencies.

It should be noted that the two vessel models are fixed during the model tests, and hence we have tackled a pure diffraction problem. However, the tests with the model fixed facilitate the understanding of the group dynamics of gap resonances and the observations drawn from the experiments are insightful. Further studies are needed to investigate the effects of gap resonance on floating structures, where the head sea excitation may see more relative sway and yaw motions between the two vessels. This work was undertaken as part of the Industrial Transformation Research Hub for Offshore Floating Facilities which is funded by the Australian Research Council, Woodside Energy, Shell, Bureau Veritas and Lloyds Register (Grant No. IH140100012). The first author is grateful for the DECRA fellowship (Grant No. DE190101296) awarded by the Australian Research Council.

Figure 1 .

 1 Figure 1. (Colour online) Experimental set-up: (a) sketch (not to scale) of the fixed boxes in different heading excitations, with the red symbols showing the locations of the wave probes; (b) a snapshot of the fixed box hull (yellow) rigidly connected to the gantry (blue) in the wave basin. The end of the narrow gap is marked by two vertical green lines.

Figure 2 .

 2 Figure2. Harmonic components of the gap resonance in beam sea excitation, where undisturbed waves approach the gap from broadside on (see figure1). The central red symbols refer to the location of the wave gauges along the gap. ϕ 1 (black curve), ϕ 2-(blue curve) and ϕ 2+ (red curve) represent the linear component, second-order difference frequency and second-order sum frequency terms of the gap resonance, respectively. Only the linear component (η 1 ) of the incident wave group is shown, as the high harmonics are negligible. Note the different vertical scales of the subplots.

Figure 3 .

 3 Figure 3. Same as in figure 2, but the gap resonance is driven by head sea excitation, where undisturbed waves propagate along the gap from one end (WG1) towards the other (WG7), as presented in Zhao et al. (2017).

Figure 4 .

 4 Figure 4. Experimentally-determined RAOs in beam sea excitation. The smooth curves are fitted based on cubic interpolation. The mode shapes are demonstrated around the corresponding RAO peaks. Note only odd modes of the gap resonance are excitated here as a result of the symmetrical set-up.

Figure 5 .

 5 Figure 5. Same as in figure4, but for head sea excitation. Note that even gap modes are also excited due to the asymmetry of the excitation. The location of WG2 and WG6 is close to a node for the m = 4 mode.

Figure 6 .

 6 Figure6. Amplitude spectra of the undisturbed waves η (black dotted curve) and corresponding gap resonances ϕ (solid curves in blue for the beam sea excitation and in red for the head sea case) measured at the centre of the gap (WG4).

Figure 7 .

 7 Figure 7. Spatial and temporal evolution of the gap resonance harmonics driven in beam sea condition through a frequency-doubling process, where the peak spectral frequency of the undisturbed waves is fp = 1 2 fm=1. The blue lines with arrows on top of the second harmonic signal are used to indicate the propagation of the waves in the gap. The red symbols represent the locations of the seven wave gauges in the gap. t = 0 refers to the time when the undisturbed incident waves focus.

Figure 8 .

 8 Figure8. Same as in figure7, but for head sea excitation where incident waves pass through the gap from upwave (WG1) to downwave end (WG7).

Table 1 .

 1 ). Wavenumbers and frequencies of the first nine gap modes.

	m	1	2	3	4	5	6	7	8	9
	fm(Hz) 1.025 1.071 1.123 1.178 1.238 1.300 1.362 1.426 1.491
	km(m -1 ) 0.943 1.885 2.828 3.770 4.713 5.655 6.598 7.541 8.483

† Email address for correspondence: wenhua.zhao@uwa.edu.au

Appendix A

Focused transient wave groups are adopted to excite the gap resonance in this study. These are generated based on the NewWave theory [START_REF] Jonathan | On irregular, nonlinear waves in a spread sea[END_REF], where the wave surface profile (in time) at the focus point is given by

where k n and f n are the wavenumber and frequency of the spectral components and the variance σ 2 = N n=1 S(f n )∆f . This NewWave profile (η N W ) is the most probable shape in time of an extreme crest event in a linear random Gaussian sea state. One can see that the structure of η N W is defined by the shape of the energy spectrum S(f n ). The most probable maximum elevation α is set by the largest 1 in N linear crest in a random sea state from the Rayleigh distribution, as derived below [START_REF] Newman | Marine Hydrodynamics[END_REF]. The normalised probability density function for the wave amplitude in a narrow-banded sea state is given as

where ζ = α/σ is the normalised amplitude. The peak of the probability density function, which is the most probable extreme wave in N samples, can be approximated as:

One can see that the most probable maximum α defines the amplitude of the NewWave profile η N W .


Hélène Pellissier
email: h.pellissier@univ-amu.fr

Asymmetric Organocatalytic Tandem/Domino Reactions to Access Bioactive Products

Keywords: Total synthesis, bioactive products, enantioselective domino/tandem reactions, organocatalysis, asymmetric catalysis, chirality

Tandem and domino reactions constitute economic methodologies to prepare complex molecules starting from simple materials. Especially, combining these powerful procedures to asymmetric catalysis allows direct access to many elaborated chiral products, including important key intermediates in total syntheses of important biologically active compounds. A range of various types of chiral organocatalysts have already been successfully applied to such syntheses. This review presents major developments in the total synthesis of bioactive products based on the use of enantioselective organocatalytic domino/tandem reactions as key steps. It is divided into three parts, dealing successively with syntheses based on organocatalytic asymmetric Michael-initiated domino reactions as key steps; aldol-initiated domino/tandem reactions and other domino reactions.

INTRODUCTION

By avoiding costly purification of intermediates and protection/deprotection steps, one-pot synthetic procedures, such as domino and tandem processes [1], constitute a challenge in total synthesis. These powerful reactions allow easy and direct access to elaborated molecules starting from simple materials. Especially, a number of asymmetric organocatalytic versions of these economic methodologies have been employed as key steps in the synthesis of many bioactive products [2]. Indeed, organocatalytic processes are particularly adapted for the total synthesis of drugs related to the absence of metal contamination. By means of the impressive advent of asymmetric catalysis, many types of chiral green organocatalysts have been successfully used in such syntheses, spanning from common proline-derived secondary amines to cinchona alkaloids, phosphoric acids, and imidazolidinones, among others. Remarkably, very high enantioselectivities are commonly observed in these single processes. This review aims to summarize the major developments in the total synthesis of important bioactive products based on the use of asymmetric organocatalytic domino and tandem procedures. It is divided into three parts, dealing successively with syntheses based on organocatalytic asymmetric Michael-initiated domino reactions as key steps; aldol-initiated domino/tandem reactions and other domino reactions.

MICHAEL-INITIATED DOMINO REACTIONS AS KEY STEPS

In comparison with metal catalysts [START_REF] Noyori | Asymmetric Catalysts in Organic Synthesis[END_REF] presenting drawbacks such as toxicity, cost, moisture sensitivity, and recoverability, organocatalysts have the serious advantages to be cheaper, robust, non-toxic, more stable, readily available, and inert towards moisture and oxygen [4]. So far, various types of chiral organocatalysts have been applied to the total synthesis of a range of biologically important products, spanning from common proline-derived secondary amines to cinchona alkaloids, phosphoric acids, and imidazolidinones, among others. For example, in 1998, Terashima et al.. applied for the first time the concept of organocatalysis to the total synthesis of a drug, namely (-)-huperzine A, which is a naturally occurring potent reversible acetylcholinesterase inhibitor agent employed for the treatment of Alzheimer's disease [START_REF] Kaneko | Synthetic studies of Huperzine A and its fluorinated analogues. 1. Novel asymmetric syntheses of an enantiomeric pair of Huperzine A[END_REF]. Indeed, the key step of this short synthesis consisted an enantioselective domino Michael/aldol reaction between β-keto ester 1 and methacrolein 2 organocatalyzed by (-)-cinchonidine, leading to chiral key tricyclic product 3 as a mixture of three diastereomers (10:7:1) in 45% yield and 64% ee (Scheme 1). The latter was further converted through six supplementary steps (detailed in Scheme 1) into expected (-)-huperzine A. In the first step, domino product 3 was undergone dehydration in the presence of acetic acid to give product 4 in 77% yield. The second and third steps consisted of a Wittig reaction of 4 with ethylidenetriphenylphosphorane followed by isomerization of the ethylidene moiety to afford (E)-configured ethylenic product 5 in 88% yield (2 steps). Subsequent alkaline hydrolysis of this product led to the corresponding carboxylic acid 6 in 64% yield. Then, a modified Curtius rearrangement of the latter gave amide 7 in 66% yield, which was finally deprotected in the presence of TMSI to provide expected (-)-huperzine A in 81% yield.

In 2007, total synthesis of a natural product (+)-palitantin, exhibiting anti-HIV, antibiotic, and antifungal activities, was disclosed by Hong et al. [6]. It was based on an enantioselective domino Michael/aldol reaction of two equivalents of α,β-unsaturated aldehydes 8 catalyzed by L-proline, which afforded chiral cyclohexadiene carbaldehyde 9 in 70% yield and 95% ee (Scheme 2). This key intermediate was converted into expected (+)-palitantin through nine supplementary steps, beginning with its dihydroxylation into diol 10 achieved with 67% yield. Diol 10 was then pro- chiral proline-derived amine (R)-18 [START_REF] Valero | Highly enantioselective organocatalytic synthesis of piperidines. Formal synthesis of[END_REF]. Among these products, chiral piperidine 19, obtained with 84% yield, 66% de, and 90% ee, was used as a key intermediate in a synthesis of (-)-paroxetine which is a selective serotonine reuptake inhibitor drug. As shown in Scheme 3, domino product 19 was further converted into primary alcohol 20 with 76% yield by treatment with BH 3 . After subsequent protection of the latter into the corresponding mesylate 21 achieved with 97% yield, etherification with sesamol led to product 22 with 79% yield. Final deprotection of the N-benzyl group in 22 through hydrogenation afforded expected (-)-paroxetine in 90% yield.

In 2009, List and Michrowska employed another chiral imidazolidinone catalyst, such as 23, to promote enantioselective domino reductive Michael/Michael cyclization reaction between aldehyde 24 and Hantzsch ester 25 [START_REF] Michrowska | Concise synthesis of ricciocarpin A and discovery of a more potent analogue[END_REF]. This reaction allowed the synthesis of chiral ketoaldehyde 26 to be achieved. The latter was not isolated but directly submitted to Sm(Oi-Pr) 3 , undergoing isomerization followed by a highly diastereoselective Tishchenko reaction, which yielded ricciocarpin A, an anti schistosomiasis agent. Remarkably, this natural product was obtained as a single diastereo-(>99% de) and enantiomer (>99% ee) in 48% yield (Scheme 4). This synthesis of ricciocarpin A is the shortest reported so far.

In 2010, the first total synthesis of a natural and biologically active product (+)-conicol was reported by Hong et al. [START_REF] Hong | Enantioselective total synthesis of (+)-conicol via cascade three-component organocatalysis[END_REF]. The key step of this synthesis consisted in an enantioselective domino oxa-Michael/Michael reaction of 3-methylbut-2-enal 27 with (E)-2-(2nitrovinyl)-benzene-1,4-diol 28 upon catalysis with L-prolinederived secondary amine (S)-18, affording the corresponding enantiopure cycloadduct 29 in 76% yield (Scheme 5). This intermediate was further implicated in a domino Michael/aldol sequence catalyzed by the same organocatalyst through reaction with crotonalde- hyde 30, leading to chiral hexahydro-6H-benzo [c] The antidepressant drug (-)-paroxetine was also synthesized in 2014 by Wang and Sun based on another organocatalytic asymmetric domino sequence [START_REF] Ren | An enantioselective cascade reaction between α,β-unsaturated aldehydes and malonic half-thioesters: a rapid access to chiral δ-lactones[END_REF]. This occurred with 72% yield and 91% ee between α,β-unsaturated aldehyde 38 and malonic half-thioester 39 in the presence of L-proline-derived amine catalyst 40 through successive Michael addition, cyclization, and nucleophilic addition (Scheme 6). The formed chiral lactone 41 could be further converted into (-)-paroxetine in nine supplementary steps. Firstly, lactone 41 was submitted to nickel-catalyzed ring-opening reaction to give aldehyde 42 in 70% yield. A subsequent reduction of 42 afforded the corresponding chiral primary alcohol 43 in 87% yield. According to previously described works [START_REF] Yu | Asymmetric synthesis of (-)-paroxetine using PLE hydrolysis[END_REF], alcohol 43 was me-sylated and then undergone a reaction with benzylamine to give the corresponding lactame 44 in 82% yield. A subsequent carboxymethylation gave 45 in 88% yield, which was further reduced into primary alcohol 46 in 92% yield. Then, mesylation followed by reaction with sesamol afforded ether 47 in 80% yield. The latter was finally hydrogenated with 93% yield into expected (-)paroxetine.

In order to propose a novel route to estrogenic hormone estradiol, Hayashi et al. developed in 2017 an asymmetric total synthesis of estradiol methyl ether based on the use of an organocatalyst [START_REF] Hayashi | Pot Economy in the total synthesis of estradiol methyl ether by using an organocatalyst[END_REF]. Indeed, the first step of the sequence consisted of an enantioselective domino Michael/aldol reaction of nitroalkane 48 with α,βunsaturated aldehyde 49 catalyzed by chiral amine (S)-18 to give the corresponding enantiopure bicyclic product 50. This highly functionalized bicyclo[4.3.0]nonane was not isolated but directly submitted to stereoselective addition of KCN to the aldehyde moiety, followed by the formation of the xanthate ester 51. Again, the latter was not isolated but directly dehydrated upon further addition of SOCl 2 in the presence of pyridine to provide enantiopure cyclopentene 52 in 78% yield (3 steps). Then, reductive removal of both the nitro group and the xanthate ester moiety in 52 was accomplished simultaneously by treatment with HSnBu 3 in the pres- The latter was then submitted to a series of six reactions (detailed in Scheme 7) conducted in a single vessel, involving successively a Kraus-Pinnick oxidation, hydrogenation, an acyl chloride formation, a Friedel-Crafts acylation, a TIPS deprotection, and a reduction of benzyl ketone moiety to afford final enantiopure estradiol methyl ether in 55% overall yield (6 steps). It must be noted that this total synthesis employed a total of only five reaction vessels to be accomplished along with as low as four purification procedures. Later in 2018, the same authors improved this synthesis, increasing the overall yield from 5% to 6.8% [START_REF] Koshino | Total synthesis of estradiol methyl ether and its five-pot synthesis with an organocatalyst[END_REF].

ALDOL-INITIATED DOMINO/TANDEM REACTIONS AS KEY STEPS

In dol/oxa-Michael/hemiacetalization reaction (Scheme 8) [START_REF] Liu | A short route to alpha-tocopherol[END_REF]. Proline-derived amine catalyst 56 was employed to promote this reaction between α,β-unsaturated aldehyde 57 and salicylic acid 58, which led to a 58% yield of chiral tricyclic hemiaminal 59 as almost single diastereomer (97% de). This key product could be transformed into desired α-tocopherol in only four steps. The first one consisted of its oxidation with PCC into lactone 60 achieved with 90% yield. Then, this benzylic lactone was quantitatively hydrogenated into carboxylic acid 61, which was further submitted to a Barton decarboxylation procedure to give α-tocopherol ether 62 in 72% yield and 94% de. Final cleavage of the methyl ether of 62 by treatment with BF 3 (SMe 2 )/AlCl 3 yielded expected αtocopherol with 84% yield.

In 2018, an enantioselective tandem double aldol reaction catalyzed by simple L-proline and achiral thiomorpholinium trifluoroacetate 63 was developed by Aggarwal et al. as a key step in a total synthesis of Δ 12 -prostaglandin J 3 exhibiting anti-leukemic properties [START_REF] Pelšs | Reoptimization of the organocatalyzed double aldol domino process to a key enal intermediate and its application to the total synthesis of δ 12 -prostaglandin J 3[END_REF]. This one-pot two-step aldol dimerization of succinaldehyde 64 followed by hemiacetalization and dehydration led to the corresponding chiral bicyclic enal intermediate 65 in 29% yield, 60% de, and 99% ee (Scheme 9). The synthetic utility of this product was demonstrated in its conversion through ten supplementary steps into Δ 12 -prostaglandin J 3 . The sequence began with the oxidation of the aldehyde group in 65 into carboxylic acid 66 with a 74% yield. Then, the latter was converted into acyl azide 67 in 80% yield. Heating 67 in toluene affected a Curtius rearrangement leading to an isocyanate, which was trapped with benzyl alcohol to give carbamate 68 in 90% yield. The latter was then reduced to hemiacetal 69 in the presence of DIBAL with a 98% yield. Then, Wittig reaction of 69 with phosphonium salt 70 provided the corresponding enamide, which was not isolated but directly hydrolyzed and then dehydrated to afford enone 71 in 81% yield. The latter was further converted into t-butyl ester 72 in 83% yield. This product subsequently underwent aldol condensation with β-boryl aldehyde 73 to give alcohol 74 as a mixture of epimers. The latter was treated with MesCl and TEA to afford the corresponding mesylate, which underwent elimination in the presence of DBU to produce the corresponding E-configured elimination product exclusively. The resulting boronic ester was oxidized into secondary alcohol 75 using NaBO 3 (H 2 O) in 23% overall yield (3 steps). Finally, treatment of 75 with HBF 4 yielded an expected Δ 12 -prostaglandin J 3 in 75% yield.

OTHER DOMINO REACTIONS AS KEY STEPS

Later in 2006, chiral phosphoric acid 76 was applied by Rueping et al. to promote the key step of the synthesis of three bioactive tetrahydroquinoline alkaloids, such as (+)-cuspareine, (+)galipinine, and (+)-angustureine [START_REF] Rueping | A highly enantioselective Brønsted acid catalyzed cascade reaction: organocatalytic transfer hydrogenation of quinolines and their application in the synthesis of alkaloids[END_REF]. Indeed, Brønsted acid 76 was found to catalyze highly enantioselectively, the double transfer hydrogenation of 2-substituted quinolines 77a-c with Hantzsch ester 78. As shown in Scheme 10, this one-pot double-transfer hydrogenation afforded the corresponding chiral tetrahydroquinolines 79a-c in both high yields (79-89%) and enantioselectivities (90-91% ee). The latter were further N-methylated to give expected (+)cuspareine, (+)-galipinine, and (+)-angustureine in excellent yields (90-95%).

2-methyl-2-butene t-BuOH/H 2 O, 0 °C 2) H 2 , Pd(OH) OH 55% (6 steps) MeO H H H estradiol methyl ether 3) (COCl) 2 /CH 2 Cl 2 4) AlCl 3 /CH 2 Cl 2 5) MeOH 6) H 2 ,
In 2006, Itoh et al. reported synthesis of the highly toxic alkaloid (+)-coniine, which is known to induce curare-type paralysis [START_REF] Nagata | Enantioselective syntheses of ent-sedridine and (+)-coniine via proline-catalyzed Mannich reaction[END_REF]. The synthesis included an asymmetric three-component Mannich reaction organocatalyzed by L-proline. It involved acetone 80, p-anisidine 81, and 5-hydroxypentanal 82 as substrates, leading to chiral Mannich product 83 in 76% yield and 91% ee (Scheme 11). The conversion of this key product into desired (+)-coniine was achieved through seven steps, beginning with its cyclization into piperidine 84 through Mitsunobu reaction followed by reduction of the latter with NaBH 4 to give 85 in 66% yield (2 steps). Subsequently, intermediate 85 was mesylated and then reduced with LiAlH 4 to give 86 in 82% yield (2 steps). Then, CAN oxidation of 86 followed by Cbz protection led to product 87 in 86% yield (2 steps). Finally, catalytic hydrogenation of 87 afforded (+)-coniine hydrochloride in quantitative yield.

The indole skeleton is widely expanded in medicinal chemistry [START_REF] Chadha | Indoles as therapeutics of interest in medicinal chemistry: bird's eye view[END_REF]. In 2009, MacMillan et al. reported total synthesis of natural and biologically active (-)-minfiensine, the key step of which was a highly enantioselective organocatalytic domino Diels-Alder/amine cyclization reaction building the central tetracyclic pyrroloindoline framework of (-)-minfiensine [START_REF] Jones | Nine-step enantioselective total synthesis of (+)-minfiensine[END_REF]. As illustrated in Scheme 12, in the presence of chiral imidazolidinone catalyst 88, 2-vinylindole 89 reacted with propynal 90 to give the corresponding chiral tetracyclic pyrroloindoline 91 in 87% yield and 96% ee. This carbamate was further converted through only five steps into (-)-minfiensine. dary amine 92 with butynal t-butyl sulfide was performed in the presence of NaBH(OAc) 3 to give intermediate 93 in 96% yield. The latter was further undergone to a radical cyclization, affording al-lene 94 with a 61% yield. Hydrogenation of this allene followed by deprotection in the presence of TFA led to final (-)-minfiensine in 90% yield and >20:1 E/Z diastereoselectivity.

CONCLUSION

This review collects major advances in the total synthesis of bioactive products using enantioselective organocatalytic domino/tandem processes as key steps. It demonstrates that a variety of one-pot asymmetric reactions catalyzed by chiral green organocatalysts have already allowed a diversity of biologically important products and drugs to be economically synthesized. The diversity of these single vessel reactions reflects that of the catalysts employed to promote them. Indeed, various chiral organocatalysts have already been successfully applied to the total synthesis of pharmaceutical and bioactive products. The most employed are prolinederived secondary amines which allow the syntheses of products as different as (+)-conicol with >99% ee, (+)-coniine with 91% ee, (+)-paroxetine with 91% ee, estradiol methyl ether with >99% ee, Δ 12 -prostaglandin J 3 with 99% ee, (+)-palitantin with 95% ee, and α-tocopherol with 97% de. Other chiral amine catalysts, such as imidazolidinones, have been used in the key steps of total syntheses of (+)-minfiensine with 96% ee, and (+)-ricciocarpin A with >99% ee. Chiral phosphoric acids were successfully applied in the total syntheses of (+)-cuspareine, (+)-galipinine, and (+)-angustureine with 91% ee, while cinchona alkaloids were employed to promote the key steps in the synthesis of (-)-huperzine A with 64% ee. In accordance with the huge advent of asymmetric catalysis, more and more organocatalyzed asymmetric domino and tandem methodologies will undoubtedly be applied as economic key steps in the total synthesis of other bioactive products in the near future.

LIST OF ABBREVIATIONS

AIBN

  Scheme 1. Synthesis of (-)-huperzine A.

  Scheme 2. Synthesis of (+)-palitantin.

Scheme 3 .

 3 Scheme 3. Synthesis of (-)-paroxetine.

Scheme 5 .

 5 Scheme 5. Domino oxa-Michael/Michael reaction of 3-methylbut-2-enal with (E)-2-(2-nitrovinyl)-benzene-1,4-diol as key-step of synthesis of (+)-conicol.

Scheme 6 .

 6 Scheme 6. Synthesis of (-)-paroxetine.

Scheme 7 .

 7 Scheme 7. Synthesis of estradiol methyl ether.

Scheme 8 .

 8 Scheme 8. Synthesis of α-tocopherol.

10 .Scheme 11 .

 1011 Scheme 9. Synthesis of Δ 12 -prostaglandin J3.

  Scheme 12. Synthesis of (-)-minfiensine.

Please provide corresponding author(s) photograph size should be 4" x 4" inches Hélène Pellissier

tected into acetonide 11 with 85% yield, and then hydrogenation yielded aldehyde 12 in 65% yield. Wittig reaction of the latter with (2E)-hexenyl triphenylphosphonium bromide led to diene 13 in 85% yield. Further hydrolysis of 13 followed by the protection provided alcohol 27 in 83% yield. Subsequent oxidation of 14 by Dess-Martin periodinane, followed by deprotection of the TBS ether, provided acetonide 15 with 79% yield. Finally, deprotection of acetonide 15 afforded (+)-palitantin in 95% yield.

In 2009, Rios et al. described a highly enantioselective synthesis of piperidines through domino Michael/cyclization reaction of α,β-

unsaturated aldehydes 16 with amidomalonates 17 catalyzed by

  of AIBN to afford intermediate 53 in 59% yield. Subsequently, diastereoselective reduction of the ketone moiety in 53 and conversion of the nitrile group into a formyl moiety were conducted in a single pot by successive treatment with LiBHEt 3 and DIBAL to give hydroxy aldehyde 54 in 34% yield. The next step was the protection of 54 into the corresponding silyl ether 55 with a 59% yield.

		CHO O	O		N
		O	Bn	H N	HCl	t-Bu
	+	24	23 (20 mol%)	CHO O
	t-BuO 2 C	CO 2 t-Bu	dioxane, 22 °C
						26	O
		N H
		25				O
		Sm(Oi-Pr) 3				O
						O
					(+)-ricciocarpin A
				48%, >99% de, >99% ee
	mechanism for domino reductive Michael/ Michael reaction:
		CHO
		O
			O
		24		reductive Michael	O CHO
		+
		t-BuO 2 C	CO 2 t-Bu			23
						O
		N H
		25
			Michael			CHO O
						26	O
	Scheme 4. Synthesis of ricciocarpin A.

ence

  The first step consisted of the treatment of 91 by TESOTf to provide silyl ether 92 in 84% yield. Reductive amination of this secon-

												OH
						1)	H N	CO 2 H	O
						L-proline (2 mol%)
							AcOEt, r.t.
				64 (2 equiv)	F 3 C 2)	O	O	H 2 N		S	H	O 65
							63 (2 mol%) 65 °C		29%, 60% de, 99% ee
												O
					O							O
												O
	NaClO 2 , NaH 2 PO 4		O	ClCO 2 Et, TEA				O
	2-methyl-2-butene					THF, -10 °C					toluene, 80 °C
	t-BuOH, H 2 O, r.t.	HO	66	O	then acetone, NaN 3 , r.t.	N 3	67	O	then BnOH, r.t.	HN O	68 OBn
			74%	OH	Br				80%	90%
				O		Ph 3 P				CO 2 H
	DIBAL/CH 2 Cl 2					KOt-amyl, THF, 0 °C		CO 2 H t-BuOH, DMAP
	-78 °C		HN	OBn	then H 2 O, p-TSA, r.t.			O	81% 71	Boc 2 O
				O	69
					98%
					CO 2 t-Bu			1) LDA/THF, -78 °C	CO 2 t-Bu
	O	72 83%				2) OHC		BPin	O	OH	BPin
												74
	1) MesCl, TEA CH 2 Cl 2 , then DBU						CO 2 t-Bu		HBF 4 /H 2 O MeCN, 10 °C	CO 2 H
	2) NaBO 3 (H 2 O) 4 THF/H 2 O	O			OH						O	OH
						75						Δ 12 -Prostaglandin J 3
					23% (3 steps)

ACKNOWLEDGEMENTS

This work was supported by the National Centre for Scientific Research: CNRS.

FUNDING

None.

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