# Tandem InCl3-Promoted Hydroperoxide Rearrangements and Nucleophilic Additions: A Straightforward Entry to Benzoxacycles

Alexandra Bosnidou, Agathe Fayet, Cristina Cheibas, Oscar Gayraud, Sophie Bourcier, Gilles Frison, Bastien Nay

► To cite this version:

Alexandra Bosnidou, Agathe Fayet, Cristina Cheibas, Oscar Gayraud, Sophie Bourcier, et al. Tandem InCl3-Promoted Hydroperoxide Rearrangements and Nucleophilic Additions: A Straightforward Entry to Benzoxacycles. Journal of Organic Chemistry, 2023, 88 (13), pp.9277-9282. 10.1021/acs.joc.3c00845. hal-04239627

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# Tandem InCl₃-promoted hydroperoxide rearrangements and nucleophilic additions, a straightforward entry to benzoxacycles

Alexandra E. Bosnidou,<fnref n="1" /> Agathe Fayet,<fnref n="1" />,<fnref n="2" /> Cristina Cheibas,<fnref n="1" /> Oscar Gayraud,<fnref n="1" /> Sophie Bourcier,<fnref n="3" /> Gilles Frison*,** and Bastien Nay*,<fnref n="1" />

*Keywords:* Hydroperoxide; Rearrangement; Benzoxacycles; Indium(III) catalysis; Tandem reactions

<figure><img src="image_2.png" /></figure>

**ABSTRACT:** The acid-catalyzed rearrangement of organic peroxides is generally associated to C-C-bond cleavages (Hock and Criegee rearrangements), with the concomittent formation of an oxocarbenium intermediate. This article describes the tandem process between a Hock or Criegee oxidative cleavage and a nucleophilic addition onto the oxocarbenium species (in particular a Hosomi-Sakurai-type allylation), under InCl₃ catalysis. It was applied to the synthesis of 2-substituted benzoxacycles (chromanes, benzoxepanes), including a synthesis of the 2-(aminomethyl)chromane part of sarizotan, and a total synthesis of erythrococcamide B.

<footnote n="1">¹ Laboratoire de Synthèse Organique, Ecole Polytechnique, CNRS, ENSTA, Institut Polytechnique de Paris, F-91128 Palaiseau, France</footnote>

<footnote n="2">² Sorbonne Université, CNRS, Laboratoire de Chimie Théorique, F-75005 Paris, France</footnote>

<footnote n="3">³ Laboratoire de Chimie Moléculaire, Ecole Polytechnique, CNRS, Institut Polytechnique de Paris, F-91128 Palaiseau, France</footnote>
INTRODUCTION

The oxidative cleavage of organic hydroperoxides (Hock rearrangement¹) and related peresters (Criegee rearrangement²) constitutes a straightforward route to carbonyl and phenol derivatives.³ Important applications of the Hock cleavage concern the industrial cumene process, which allows the synthesis of millions tons of phenol and acetone each year (Scheme 1a),⁴,⁵ and the synthesis of artemisinin, a major antimalarial compound.⁶ It was also used to transform complex terpenoids, like cholesterol⁷ or diterpenic acids,⁸ in a bio-inspired manner. The Hock rearrangement involves a Brønsted or a Lewis acid catalysis that triggers the heterolytic cleavage of the C<sub>α</sub>-C<sub>β</sub> bond adjacent to the peroxide function, with concomitant 1,2-migration of the β carbon onto the nearest peroxide oxygen (Scheme 1b).³,⁹,¹⁰ Alternatively, the Criegee rearrangement relies on the activation of the hydroperoxide through a perester formation, weakening the O-O bond. These mechanisms are related to that of the Baeyer-Villiger rearrangement.¹¹⁻¹⁴ The peroxide cleavage is expected to form a transient oxocarbenium species, which is usually hydrolyzed (route A) into two carbonyl derivatives (or phenols), possibly through an acylal species that can be hydrolyzed in the Criegee mechanism¹⁵ (route B).

a The Hock (cumene) process

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b Mechanism of peroxide rearrangements, rationalizing possible interruption with a nucleophile (M = H⁺ or Lewis acid)

<figure><img src="image_12.png" /><figcaption>**Scheme 1.** Hock and Criegee oxidative cleavages: (a) The cumene process; (b) Mechanism ration-
alizing a possible oxocarbenium interception by a nucleophile.</figcaption></figure>
Recently, we investigated the mechanism of the InCl₃-catalyzed Hock rearrangement through theoretical chemistry, detailing the formation of the oxocarbenium intermediate through a Wheland intermediate.¹⁶ Considering the electrophilicity of hypothetical oxocarbenium intermediates, the Hock and Criegee rearrangements can be considered as potential candidates to design interrupted versions by tandem additions of various nucleophiles¹⁷⁻²⁰ (route C).

Brønsted or Lewis acids (e.g. TFA, TfOH, BF₃·OEt₂, AlCl₃, SnCl₄ and more occasionally lanthanide triflates) have been used to catalyze the Hock cleavage.³ The industrial production of phenol mainly used mineral acids (e.g. H₂SO₄) and zeolites.⁴,⁵ However, there have been scarce systematic report on catalyst screening and applications.³,⁹,²¹ Interestingly, the selectivity of the Hock and Criegee rearrangements is strongly influenced by strain relief²² and by the electronic properties of substituents.¹⁰,²³⁻²⁵ The use of tandem and interrupted Hock reactions in the development of synthetic methodologies has been limited to few examples of allylation,⁹ oxindole rearrangements,²⁶⁻²⁸ an intramolecular Paal-Knorr synthesis of furans²⁹,³⁰ or a synthesis of carbazoles.³¹ The main drawback of such tandem reactions could be the critical competition with the hydrolysis resulting from the addition of a hydroxide residue (H₂O or MOH⁻ released during the hydroperoxide cleavage) onto the oxocarbenium intermediate. The Criegee rearrangement, which avoids the release of water, could provide a flexible solution to this problem.¹⁵,³² Herein, to develop these hypotheses, easily accessible indane and tetralin hydroperoxide substrates were used to afford the respective chromane and 1-benzoxepane products upon acid catalyzed rearrangements with a large scope of substituents.³³ The reactive oxocarbenium species formed in situ were expected to react with a series of nucleophiles to install substituents (allyl, cyano, azido or hydrogen upon reduction). This strategy was finally applied to the synthesis of valuable compounds, especially the natural product erythrococcamide B³⁴ and the 2-(aminomethyl)chromane part of sarizotan, an experimental drug tested to treat the breathing problems of the Rett syndrome (Figure 1).³⁵,³⁶

<figure><img src="image_13.png" /><figcaption>**Figure 1.** Examples of biologically significant benzoxacycles.</figcaption></figure>
RESULTS AND DISCUSSION

The tandem Hock rearrangement–Hosomi-Sakurai allylation³⁷ was first investigated with indanyl
hydroperoxide **1a** in presence of an acid catalyst and allyltrimethylsilane, to furnish 2-allylchrom-
ane **2a** (Table 1) [*Note that although the following organic peroxides were stable in our hands, it must
be reminded that the manipulation of such reactive species must always be undertaken with great
care³⁸*]. Decomposition was observed in the presence of BF₃·OEt₂ (2 equiv) at 0 °C (entry 1), while
lowering the temperature at –78 °C afforded alkyl peroxide **3a** with no sign of Hock rearrangement
 entry 2). The use of catalytic amounts of BF₃·OEt₂ (0.1 equiv) was inefficient (no reaction, entry 3).
Although the Hock rearrangement was observed with pTsOH (entry 4) or TMSOTf³⁹ (entry 5), only
bis(peroxyacetal) **4a** was identified (see reference 16 for a discussion of the structure determina-
tion), demonstrating the elimination and recombination of peroxide species during these reaction,
while no reaction occurred with catalytic amounts of (PhO)₂PO₂H (entry 6). Catalytic amounts of
Sn(OTf)₂, In(OTf)₃, Sc(OTf)₃ and AlCl₃ mostly led to complex mixtures of products (entries 7-10),
but traces amounts of **2a** (3%) could be detected with In(OTf)₃. Copper(II) salts (entries 11 and 12)
were able to promote the Hock cleavage, mainly resulting in peroxyacetal **4a**, while only Cu(ClO₄)₂
provided allylation product **2a**. To complete this catalyst screening, we were pleased to observe sig-
nificant amounts of **2a** in presence of FeCl₃ and indium halides (entries 13-16), the most efficient
catalyst being InCl₃ (0.1 equiv) with 62% of 2-allylchromane **2a**. Additional solvent screening
showed that toluene (entry 17) and a coordinating solvent such as CH₃CN (entry 18) gave poor re-
sults compared to CH₂Cl₂. Overall, we observed that the Hock rearrangement can be promoted by
most of the catalysts, especially InCl₃ and with the exception of BF₃·OEt₂, but only a few of them
were able to perform the tandem Hosomi-Sakurai reaction (FeCl₃, Cu(ClO₄)₂ and In³⁺ salts in non
coordinating solvent). Furthermore InCl₃ had previously been described by Baba and co-workers to
be unable to perform the Hosomi-Sakurai allylation of aldehydes, unless a co-catalyst was added
(TMSCl).⁴⁰ Interestingly, InCl₃ was recently used by Ferrié and co-workers to promote the Hosomi-
Sakurai allylation of 1,2-dioxolan-3-yl acetates without affecting the endoperoxide group.⁴¹
<figure><img src="image_14.png" /><figcaption>**Table 1.** Optimization of the tandem Hock/Hosomi-Sakurai reaction towards 2-allylchromane (2a).</figcaption></figure>

<table><thead><tr><th>Entry</th><th>Catalyst or reagent (equiv), other remark</th><th>Ratio 1a:2a:3a:4a (yield of 2a, %)<sup>a</sup></th></tr></thead><tbody><tr><td>1</td><td>BF<sub>3</sub>·OEt<sub>2</sub> (2)</td><td>Complex mixture</td></tr><tr><td>2</td><td>BF<sub>3</sub>·OEt<sub>2</sub> (2), starting at -78 °C</td><td>0:0:100:0 (0)</td></tr><tr><td>3</td><td>BF<sub>3</sub>·OEt<sub>2</sub> (0.1)</td><td><sup>-b</sup></td></tr><tr><td>4</td><td>pTsOH (0.1)</td><td>0:0:0:100 (0)</td></tr><tr><td>5</td><td>TMSOTf (2)</td><td>0:0:0:100 (0)</td></tr><tr><td>6</td><td>(PhO)<sub>2</sub>PO<sub>2</sub>H (0.1)</td><td><sup>-b</sup></td></tr><tr><td>7</td><td>Sn(OTf)<sub>2</sub> (0.1)</td><td>15:0:70:15 (0)</td></tr><tr><td>8</td><td>In(OTf)<sub>3</sub> (0.1)</td><td>0:7:81:12 (3)</td></tr><tr><td>9</td><td>Sc(OTf)<sub>3</sub> (0.1)</td><td>Complex mixture</td></tr><tr><td>10</td><td>AlCl<sub>3</sub> (0.1)</td><td>Complex mixture</td></tr><tr><td>11</td><td>Cu(OTf)<sub>2</sub> (0.1)</td><td>0:0:30:70 (0)</td></tr><tr><td>12</td><td>Cu(ClO<sub>4</sub>)<sub>2</sub> (0.1)</td><td>0:35:0:65 (22)</td></tr><tr><td>13</td><td>FeCl<sub>3</sub> (0.1)</td><td>0:100:0:0 (30)</td></tr><tr><td>14</td><td>InBr<sub>3</sub> (0.1)</td><td>0:70:0:30 (22)</td></tr><tr><td>15</td><td>InI<sub>3</sub> (0.1)</td><td>0:100:0:0 (40)</td></tr><tr><td><b>16</b></td><td><b>InCl<sub>3</sub> (0.1)</b></td><td><b>0:100:0:0 (62)</b></td></tr><tr><td>17</td><td>InCl<sub>3</sub> (0.1) in PhMe</td><td>55:45:0:0 (n.d.)<sup>c</sup></td></tr><tr><td>18</td><td>InCl<sub>3</sub> (0.1) in CH<sub>3</sub>CN</td><td>0:0:50:50 (n.d.)</td></tr></tbody></table>

The best condition (0.1 equiv of InCl<sub>3</sub>, 2 equiv of allyltrimethylsilane, CH<sub>2</sub>Cl<sub>2</sub>, 0 °C to room temperature, hereafter Method A) was applied to various 1-indanyl hydroperoxides (Scheme 2), including tertiary hydroperoxides, all synthesized from the corresponding indanones through a two-step sequence of reduction or Grignard addition<sup>42</sup> on the ketone, and acid-catalyzed hydroperoxidation (see supporting information). With secondary hydroperoxides **1a-1n** (R<sup>1</sup> = R<sup>3</sup> = H), the reaction was successful with various substituents on the aromatic ring. π-Donors in position 5 are favorable, especially halides. The presence of a strong π-donor like OMe led to higher reactivity, leading us to avoid any isolation of **1j** since the Hock reaction was partially observed during the

<footnote><sup>a</sup> Ratio based on NMR integrations, and NMR yield relatively to internal standard 1,2-dichloroethane. <sup>b</sup> Mostly no reaction, with traces (<5%) of 2a, 4a, and decomposition products. <sup>c</sup> Not determined.</footnote>
hydroperoxidation step. Thus, performing the allylation on a crude hydroperoxide extract of **1j** led to product **2j** in 46% yield. On the contrary, a strong π-acceptor like a CN group was detrimental to the tandem reaction, leading to **2k** with a low yield only (5%). In that case, a lactol side product (compound **S2** in the Supporting Information) was nevertheless isolated in 21% yield along with 22% of recovered starting material, showing the low performance of the Hock reaction on electron-deficient substrates like **1k**. Biphenyl derivatives (**1l-1n**) were tested with different *para*-substituents, showing a similar reactivity trend in presence of a OMe (54% of **2m**) or a CN (49% of **2n**) resulting from a "shielding" effect of the phenyl ring towards the substituent electronic properties.

<figure><img src="image_15.png" /><figcaption>**Scheme 2.** Tandem Hock/Hosomi-Sakurai reactions of 1-indanyl hydroperoxides through method</figcaption></figure>

A. <sup>a</sup> The *tert*-butyl peroxide of **1** gave a similar yield of 64%. <sup>b</sup> Lactol side product **S2** was also isolated in 21% yield, along with 22% of starting material **1k** (see the Supporting Information). <sup>c</sup> From *tert*-butyl peroxide **1x** (R<sup>3</sup> = *t*-Bu).
Furthermore, we observed that tertiary hydroperoxides **1o-1v** (R¹ = Me; R³ = H) performed well to provide the allylation products. The presence of a methyl substituent in position 2 of the indane core (**1w**) led to a diastereomeric mixture (55% yield) with a 46:54 ratio in slight favor of *anti* compound **2w**. The tandem reaction was also applicable to tertiary fluorenyl *tert*-butyl peroxide **1x** (R³ = *t*-Bu) to give tricyclic chromane **2x**. Finally, it was possible to perform the allylation with branched allylsilanes (R⁴ = CH₂OAc or CH₂Cl), though in lower yields, giving allyl acetate **2y** and chloride **2z** in only 22% and 45% yields. Incidentally, in the same conditions, the 1-indanyl *tert*-butyl peroxide of **1a** (R¹ = R² = H, R³ = *t*-Bu) afforded chromane **2a** in 64% yield, showing a similar reactivity as the hydroperoxide substrate (R³ = H).

Starting from 1-tetralinyl hydroperoxides **5a** and **5b** (Scheme 3), method A quantitatively gave typical Hock cleavage products (**7a** and **7b** in *ca.* 40%). These products result from the formal addition of a hydroxide group released during the Hock cleavage onto the oxocarbenium intermediates, followed by the rapid opening of the resulting seven-membered lactols **6a** and **6b** (Scheme 3). Unfortunately, we never observed any allylation under these conditions, leading us to investigate an alternative method.

<figure><img src="image_16.png" /><figcaption>**Scheme 3.** Application of method A to 1-tetralinyl hydroperoxides, showing no tandem allylation.</figcaption></figure>

To avoid the opening of lactol intermediates **6a/b**, we envisaged to apply the Criegee rearrangement in a tandem process with the Hosomi-Sakurai allylation. According to Kishi,¹⁵ the Criegee rearrangement can be performed in presence of a carboxylic anhydride to activate the hydroperoxide, releasing a carboxylate that can react back onto the oxocarbenium intermediate, thus affording a transient acylal product (see Scheme 1B). In presence of a nucleophile and an appropriate catalyst, this acylal could thus lead to the coupling product in a one-pot process. Testing the reaction on 1-indanyl hydroperoxide **1a** in presence of trifluoroacetic anhydride in CH₂Cl₂ and in the absence of nucleophile, it was possible to isolate *O*-trifluoroacetyl lactol **8** in 76% yield, in accordance with Kishi's report (Scheme 4).¹⁵ Under similar conditions, after completion of the Criegee rearrangement revealed by thin layer chromatography, the addition of allyltrimethylsilane to the reaction mixture did not afford the allylation product (**2a**), but a complex mixture. Compound **2a** was however cleanly obtained in 70-80% yields when a Lewis acid catalyst was added concomitantly with the nucleophile, here InCl₃ (0.1 equiv, Method B) or BF₃·OEt₂ (1.6 equiv, Method C).
<figure><img src="image_17.png" /><figcaption>**Scheme 4.** Reactivity and allylation of 1-indanyl hydroperoxide under Criegee reaction conditions.</figcaption></figure>

Methods B and C were applied to 1-tetralinyl hydroperoxide substrates (5, Scheme 5). The 2-alkylbenzoxepane derivatives (9a-9i) could be obtained in moderate to good yields (50-80%) in all cases. Although method B is better than method C in terms of reagent economy and should be preferred for larger scale applications, method C offers some advantages to improve yields with a few substrates (9e, 9i). Furthermore, the transformation was applicable to a tertiary hydroperoxide (giving 9b), and to substituted or branched allyltrimethylsilanes (9g-9i).

<figure><img src="image_18.png" /><figcaption>**Scheme 5.** Application of the tandem Criegee/Hosomi-Sakurai reaction to the synthesis of benzoxepanes.</figcaption></figure>
Finally, we transposed this one-pot sequence to the tandem addition of other nucleophilic partners¹⁷⁻²⁰ like Et₃SiH (hydride donor), Me₃SiCN (cyanide donor) and Me₃SiN₃ (azide donor), giving the corresponding chromane and benzoxepane products in generally good yields (Scheme 6). These additional nucleophiles were only applicable to methods B and C. Other nucleophiles like 1,3,5-trimethoxybenzene or indole derivatives were unfortunately unsuccessful, unlike other studies.²⁶,²⁷ Interestingly, differences could be observed between the two sets of conditions, suggesting their complementarity. In particular, the azidation sequence was only possible with InCl₃, giving satisfying yields ca. 70%, while BF₃·OEt₂ always led to decomposition, supposedly due to BF₃-promoted azide rearrangements.⁴³ Finally, it must be mentioned that the presence of the TMS group on all these nucleophiles is required for the success of the reaction.

<figure><img src="image_19.png" /><figcaption>**Scheme 6.** Tandem reactions with other nucleophilic silanes: Et₃SiH, Me₃SiCN, Me₃SiN₃. a Decomposition was observed.</figcaption></figure>

Benzoxacycles are important building blocks in natural products and are considered as privileged structures in medicinal chemistry (Figure 1).⁴⁴ The chromane scaffold is the lead-core of flavonoids, vitamins E, or of synthetic drugs like sarizotan.³⁵,³⁶ The benzoxepane core is also frequently found in biologically active natural products like heliannuols or radulanines.⁴⁵,⁴⁶ To demonstrate the interest of these tandem reactions, we applied method A to the total synthesis of erythrococcamide
B³⁴ (22, Scheme 7a), and method C to the synthesis of the 2-(aminomethyl)chromane moiety of sarizotan (23, Scheme 7b). The hydroperoxide 19, made from indanone 18, was submitted to the tandem Hock/Hosomi-Sakurai reaction using method A to give chromane 20 in 50% yields (1.17 mmol scale). The KMnO₄-mediated oxidative cleavage of the double bond to form carboxylic acid 21, followed by the formation of the isobutyl amide, finally afforded natural product 22. Concerning sarizotan chromane 23, it was synthesized by the reduction of cyanide 13, available from 1-indanyl hydroperoxide (1a) through the tandem Criegee rearrangement/cyanation protocol, following method C in presence of Me₃SiCN. Comparatively, the synthesis of 23 was previously achieved from chromane-2-carboxylates.⁴⁷⁻⁴⁹

**a. Total synthesis of erythrococcamide B**

<figure><img src="image_20.png" /></figure>

**b. Synthesis of the 2-(aminomethyl)chromane part of sarizotan**

<figure><img src="image_21.png" /></figure>

**Scheme 7.** Synthetic applications of tandem oxidative cleavage/nucleophile addition.

From a mechanistic point of view regarding the InCl₃-promoted Hock rearrangement, this experimental study opens interesting questions on the influence of the substituents on the hydroperoxide rearrangement, the catalytic character of InCl₃ and the nature of the active metallic species, or the preferential migration of the sp² carbon compared to the sp³ carbon. These questions, of a more fundamental nature have been the subject of a theoretical investigation in a separate article.¹⁶ Based on this study and previous hypotheses concerning the Hosomi-Sakurai allylation,¹⁷ we propose a mechanism for the present tandem transformation (Scheme 8). The rearrangement would start with the O–O bond cleavage and the concommittant formation of a Wheland intermediate (A to B). The C–C bond cleavage of B would result in the rearomatisation and the formation of an electrophilic species (C) capable to react with the nucleophile, finally leading to the allylchromane product 2a through E.
<figure><img src="image_22.png" /><figcaption>**Scheme 8.** Proposed mechanism of the InCl₃-promoted Hock rearrangement¹⁶ and Hosomi-Sakurai allylation. <sup>a</sup>Note that InCl₃ is always coordinated and does not exist in a free monomeric form (see ref. 16 for details).</figcaption></figure>

## CONCLUSION

In conclusion, we developed a straightforward route to synthesize chromanes and benzoxepanes from indanyl or tetralinyl hydroperoxides, respectively. The general strategy was based on a tandem Hock or Criegee rearrangement coupled to nucleophilic additions, and was efficiently promoted by InCl₃. In general, we demonstrated the superiority of InCl₃ over other Lewis acids in this transformation. Various nucleophiles, all being activated as trialkylsilanes, allowed the addition of allyl, hydride, cyanide or azide on the oxocarbenium species generated in situ. The method was successfully applied to the total synthesis of the natural product erythrococcamide B and the chromane core of the drug sarizotan. Owing to the important place of the Hock rearrangement in the chemical industry, and that of benzoxacycles in medicinal chemistry, we expect these results could have a significant impact in drug development and fine chemistry.

## Supporting Information

Description of experimental procedures including copies of NMR spectra (PDF).

## AUTHOR INFORMATION

### Corresponding Authors

**Bastien Nay** – Laboratoire de Synthèse Organique, Ecole Polytechnique, CNRS, ENSTA, Institut Polytechnique de Paris, F-91128 Palaiseau, France;
orcid.org/0000-0002-1209-1830;
Email: bastien.nay@polytechnique.edu

**Gilles Frison** – Sorbonne Université, CNRS, Laboratoire de Chimie Théorique, F-75005 Paris,
France;
[orcid.org/0000-0002-5677-3569](http://orcid.org/0000-0002-5677-3569)
Email: gilles.frison@cnrs.fr

## Authors

**Alexandra E. Bosnidou** – Laboratoire de Synthèse Organique, Ecole Polytechnique, CNRS, ENSTA,
*Institut Polytechnique de Paris, F-91128 Palaiseau, France*;
[orcid.org/0000-0001-9240-5598](http://orcid.org/0000-0001-9240-5598)

**Agathe Fayet** – Sorbonne Université, CNRS, Laboratoire de Chimie Théorique, F-75005 Paris,
*France*;
*Laboratoire de Synthèse Organique, Ecole Polytechnique, CNRS, ENSTA, Institut Polytech-
nique de Paris, F-91128 Palaiseau, France*
[orcid.org/0009-0005-4211-1432](http://orcid.org/0009-0005-4211-1432)

**Cristina Cheibas** – Laboratoire de Synthèse Organique, Ecole Polytechnique, CNRS, ENSTA, Institut
Polytechnique de Paris, F-91128 Palaiseau, France
[orcid.org/0009-0002-8762-4088](http://orcid.org/0009-0002-8762-4088)

**Oscar Gayraud** – Laboratoire de Synthèse Organique, Ecole Polytechnique, CNRS, ENSTA, Institut
Polytechnique de Paris, F-91128 Palaiseau, France;
[orcid.org/0000-0002-0923-1118](http://orcid.org/0000-0002-0923-1118)

**Sophie Bourcier** – Laboratoire de Chimie Moléculaire, Ecole Polytechnique, CNRS, Institut Polytech-
nique de Paris, F-91128 Palaiseau, France;
[orcid.org/0000-0001-6914-3956](http://orcid.org/0000-0001-6914-3956)

## Funding Sources

Agence Nationale de la Recherche (ANR-19-CE07-0012)
Labex CHARM3AT

## ACKNOWLEDGMENT

This work was supported by the French *Agence Nationale de la Recherche* and by Labex CHARM3AT.
The CNRS, I'X, Sorbonne Université are acknowledged for hosting and funding.

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