Ashod Aradian

Philippe Barois

Olivier Mondain-Monval

Virginie Ponsinet

Alexandre Baron

The bottom-up approach towards artificial optical magnetism in metastructures

The generation of artificial optical magnetism (AOM) in engineered composites has been the major concept that led to the emergence of the field of metamaterials at the turn of the millennium. Indeed, the proven possibility to manipulate the magnetic permeability of materials at microwave frequencies induced a considerable excitement in the scientific community as it opened the way to the design of unprecedented tools and devices for the control of light propagation. Extensions to higher frequencies of IR and visible light were soon proposed and tested by downsizing the artificial structures. The fabrication of negative index materials, optical cloaks or hyper-lenses seemed within reach. Two decades later, and after considerable research efforts, the applications of the AOM are still scarce and the concept seems to face a number of fundamental physical limits. We review in this chapter the state-of-the-art of the bottom-up approach whereby nanochemistry and colloidal physics are used to engineer hybrid metastructures exhibiting AOM in visible light or near IR.

-Introduction

 . Today, it is clear that AOM is an essential, if not necessary, ingredient for the development of metasurfaces. This chapter focuses on the complementary bottom-up approach, whereby colloidal chemistry is used to synthesize the magnetic resonators. In contrast to top-down approaches, bottom-up fabrication often builds metamaterials in two steps, first synthesizing the basic building blocks (meta-atoms) that are subsequently assembled into a 2D or 3D material. Considering the huge number of nano-objects required, on the order of 10 8 /mm² on a surface or 10 12 /mm 3 in bulk, self-assembly appears as an efficient strategy for the realization of macroscopic materials. We review the most recent achievements of the bottom-up approach combining wet-chemistry

and self-assembly for the generation of AOM, after outlining in section 2 the optical characterization techniques.

-Optical detection of AOM

-AOM detection in Meta-atoms

In the bottom-up approaches, meta-atoms usually consist in single nanoparticles or ensembles of nanoparticles arranged to exhibit a specific optical response (see examples in Section 3). The physical observables that characterize this response are contained in the scattering matrix of the system. For the sake of simplicity, we shall describe the characterization of isotropic systems, such that the scattering matrix is assumed to be diagonal with components S 1 and S 2 . The components parallel () and orthogonal () to the scattering plane are expressed as:   with θ the scattering angle,  the polarization angle and 0 the incident field. The scattering coefficients can be expressed as a function of the Mie multipolar coefficients a n and b n [START_REF] Bohren | Absorption and scattering of light by small particles[END_REF] . From these, the extinction ( e ), scattering ( s ), and absorption cross-sections can be classically calculated [START_REF] Bohren | Absorption and scattering of light by small particles[END_REF] . Extinction spectra are usually retrieved by measuring the absorbance of a suspension of metaatoms, using Beer's law. Alternatively,  e can be measured directly on a single particle by spatially modulating the position of the particle in the kHz range in the focal plane of a tightly focused light beam 18,[START_REF] Muskens | Quantitative absorption spectroscopy of a single gold nanorod[END_REF] .

The scattering spectrum can be measured in several ways. At the single particle level, darkfield spectroscopy enables a measurement of the differential scattering cross-section integrated over the numerical aperture of the microscope objective used to collect the scattered light. Dark-field spectroscopy enables a qualitative comparison between experimental particles and numerical or theoretical designs, because the scattered signal is not altered by polydispersity.

Importantly, since the electric and magnetic responses of the meta-atom are carried by the a n and b n coefficients respectively, most techniques exposed thus far do not actually measure AOM directly, but rather the total scattering or extinction, i.e. a superposition of the fields radiated by magnetic and electric modes. Consequently, most of these optical characterizations usually require a theoretical or numerical model to interpret the spectral features of the measured quantities.

Another possibility for characterizing the scattering cross-section is to resort to polarization-resolved static light scattering spectroscopy (SLS) of suspensions of metaatoms [START_REF] Sheikholeslami | A metafluid exhibiting strong optical magnetism[END_REF][START_REF] Ponsinet | Resonant isotropic optical magnetism of plasmonic nanoclusters in visible light[END_REF] . This enables a direct measurement of the differential scattering cross-section and has been used to characterize AOM (see Fig. 1). The differential scattering-cross section D  can be decomposed into two components, parallel and orthogonal to the scattering plane. Assuming the system to be purely dipolar, we may write at a scattering angle of 90°:

   
with the wavevector and Λ an experimental (generally unknown) constant. Hence, electric and magnetic dipoles are obtained separately, and can be fully determined only if a reference is measured. However, the magnetic-to-electric ratio is always accessible 20,22,23, :

   
R ME may be used as a figure of merit to maximize AOM with respect to the electric response of the meta-atom. When R ME = 1, the magnitude of the electric and magnetic dipoles are equal and the so-called Kerker regime is reached. The first Kerker condition is reached when a 1 = b 1 and ensures that the meta-atom is a purely forward-scattering dipole (zero back-scattering), also known as a Huygens dipole. The second Kerker condition is reached when a 1 =  b 1 and corresponds to a meta-atom that maximizes the backward scattering.

Under the condition that the meta-atoms remain dipolar and that the volume fraction of meta-atoms remains small enough, assembling meta-atoms with R ME larger than 1 should produce metamaterials with  > , and R ME = 1 should produce a metamaterial with  = , that is, impedance-matched to free-space.

In the multipolar regime, D   (90°) and D   (90°) remain interesting observables as they enable distinguishing between even and odd-parity modes in the scattering:

   
They may be used to engineer specific scattering properties that depend on the interference of odd and even modes. For instance, the first generalized Kerker condition (GKC) occurs when the superposition of even modes is equal in amplitude and in phase to that of odd modes. Similarly to the dipolar case, this produces a situation where back-scattering is suppressed. Then, we have D   (90°)  D   (90°). Though not exactly equivalent to the GKC, this approximation is a good indication toward an effective Huygens multipole [START_REF] Lermusiaux | Toward Huygens' Sources with Dodecahedral Plasmonic Clusters[END_REF] .

Most experimental meta-atom results described in Section 3 follow one of the optical detection schemes of AOM exposed above. scattering. The incident electric field E 0 is parallel to (Oxy) and  is the polarization angle with respect to (Ox). The scattering plane (Oyz) contains both k (incident wavevector) and k s (scattered wavevector). The scattering angle  is the angle between k and k s . In the scattering direction, the orthogonal (e  ) and parallel (e // ) components are represented. The top-right inset considers two specific situations where ( = 0°;  = 90°) and ( = 90°;  = 90°), which allow to separate the electric dipole contribution to the scattering from the magnetic dipole contribution.

-AOM in assembled metamaterials

From a suspension of meta-atoms synthesized to exhibit specific scattering properties, metastructures can be assembled, as two-dimensional metasurfaces (monolayers), structures with a few layers, up to bulk three-dimensional metamaterials. The characterization and measurement of electromagnetic constitutive properties, including artificial magnetism, is a difficult task where one should be wary of numerous pitfalls.

In principle, the most straightforward approach is to measure the complex reflection r and transmission t coefficients of a metastructure slab, to achieve some form of unambiguous determination of AOM, namely of  . This is hard experimentally in the optical range, but numerically straightforward: many metamaterial characterizations actually compute r and t through a rigorous full-wave simulation and retrieve both  and  in a first step, then comparing experimentally the measured reflectance R = |r| 2 and transmittance T = |t| 2 with those computed to justify indirectly the presence of artificial magnetism [START_REF] Smith | Composite medium with simultaneously negative permeability and permittivity[END_REF][START_REF] Smith | Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients[END_REF][START_REF] Smith | Electromagnetic parameter retrieval from inhomogeneous metamaterials[END_REF] .

Alternatively, measuring  and  is equivalent to measuring the refractive index  and the impedance   of the metamaterial. Across a single interface between two materials, the reflection and transmission coefficients for p-and s-polarized waves are expressed according to Fresnel's laws [START_REF] Jackson | Classical electrodynamics[END_REF][START_REF] Flamant | Direct retrieval method of the effective permittivity and permeability of bulk semi-infinite metamaterials by variable-angle spectroscopic ellipsometry[END_REF] : knowing the incident medium impedance Z 1 , and the angles of incidence and refraction, a simple measurement of R and T is sufficient to find Z 2 in the metamaterial. The index of refraction of the metamaterial can be measured by resorting to interferometry using the field transmitted (or reflected) through a metamaterial slab of length small compared to the penetration depth in the metamaterial [START_REF] Shalaev | Negative index of refraction in optical metamaterials[END_REF][START_REF] Dolling | Simultaneous negative phase and group velocity of light in a metamaterial[END_REF][START_REF] Dolling | Negative-index metamaterial at 780 nm wavelength[END_REF] .

Finally, variable-angle spectroscopic ellipsometry can be used to measure AOM. Ellipsometry usually measures the complex ratio  , where and are referred to as the ellipsometric angles. A first indirect measurement scheme consists in fitting and assuming Lorentzian models for both  and . This ensures that the optical parameters used for the spectral fitting are physical [START_REF] Grigorenko | Nanofabricated media with negative permeability at visible frequencies[END_REF] and is well-suited to metamaterial slabs. In addition, Mueller-ellipsometry can provide access to permittivity, permeability, and chirality in thin nanostructures [START_REF] Guth | Optical properties of metamaterials: Influence of electric multipoles, magnetoelectric coupling, and spatial dispersion[END_REF] .

A strong word of caution is required here: despite abundant use in the literature, the above methods are of limited applicability for metastructures comprised of one or a few layers of resonators only. The extracted material parameters will depend on the angle of incidence, the slab thickness, and lose most of their predictive power for situations outside the measurement configuration [START_REF] Simovski | On electromagnetic characterization and homogenization of nanostructured metamaterials[END_REF][START_REF]Publications Office of the European Union[END_REF][START_REF] Menzel | Validity of effective material parameters for optical fishnet metamaterials[END_REF][START_REF] Alu | First-principles homogenization theory for periodic metamaterials[END_REF] .

One favorable case is a 3D, isotropic, semi-infinite metamaterial. Using spectroscopic ellipsometry, an analytical expression allows to obtain  and  from the experimental ratio and the incidence angle  1 , following a simple linear regression model: with  is a solution to a second-order polynomial equation = 0

And µ follows from

Imposing that the metamaterial be dissipative singles out the physical solutions and unambiguously determines both  and  [START_REF] Gómez-Graña | Hierarchical self-assembly of a bulk metamaterial enables isotropic magnetic permeability at optical frequencies[END_REF][START_REF] Flamant | Direct retrieval method of the effective permittivity and permeability of bulk semi-infinite metamaterials by variable-angle spectroscopic ellipsometry[END_REF] . The quality of this method is asserted by the quality of the linear regression and fails when spatial dispersion becomes important. In that case, the metamaterial can no longer be described by simply an electric permittivity and a magnetic permeability (see Section 4).

3: Synthetic meta-atoms for AOM:

Meta-atoms for AOM generation should exhibit a strong enough optical response, with dimensions noticeably shorter than the operating wavelengths to enable homogenization. For visible or near-IR light, dimensions should not exceed ~100nm typically. These two requirements are generally antinomic: small objects produce small optical effects. Optical resonators appear as the best opportunity to reconcile these two constraints, since resonances induce a significant amplification of the fields. Two classes of optical resonances are well known: plasmons, linked to the negative value of the dielectric permittivity in conductors, and Mie resonances which are cavity-type resonances mainly controlled by the morphology.

Exploiting these natural resonances to induce an artificial magnetization requires specific designs [START_REF] Monticone | The quest for optical magnetism: from split-ring resonators to plasmonic nanoparticles and nanoclusters[END_REF] , described below.

3-1-Plasmonic magnetic meta-atom:

3-1-1-Theoretical background:

Localized surface plasmon resonances (LSPR) occur in metallic nanoparticles, and the nature and size of the particle and surrounding materials determine their frequency. For instance, the resonance wavelengths are 550 nm and 440 nm for gold and silver nanoparticles of 10 nmradius in water. Plasmonic resonances of metallic nanoparticles can trigger magnetization, when the particles are organized in nano-circuits, as suggested in early models illustrated in figure 3.1.a [START_REF] Alù | Negative effective permeability and left-handed materials at optical frequencies[END_REF][START_REF] Alù | Dynamical theory of artificial optical magnetism produced by rings of plasmonic nanoparticles[END_REF][START_REF] Alu | The quest for magnetic plasmons at optical frequencies[END_REF] . The circular plasmonic current generates the wanted local magnetization, which oscillates at the frequency of the light wave. The plasmonic ring model has been further improved to promote an isotropic response of the magnetic meta-atoms by distributing the nanoparticles in a 3D symmetric cluster (figures 3.1.b-c). Metallic satellites are randomly distributed around a central dielectric core to form the so-called "plasmonic raspberry" nanostructure [START_REF] Simovski | Model of isotropic resonant magnetism in the visible range based on core-shell clusters[END_REF] . Fully ordered structures were also imagined by locating the metallic nanoparticles on the faces of a Platonic solid, e.g. six particles placed at the faces of a cube 41 (figure 3.1.c). In the example shown in figures 3.1.d-e, twelve silver satellites are located at the vertices of an icosahedron [START_REF] Vallecchi | Collective electric and magnetic plasmonic resonances in spherical nanoclusters[END_REF] . Numerical simulations reveal that the optical response of both the raspberry and icosahedral clusters is dominated by only three multipoles, namely the electric dipole (ED), the targeted magnetic dipole (MD), and the electric quadrupole (EQ) appearing at higher frequency. In computations on a bulk material made of a dense cubic lattice of such resonators, a sharp resonant behavior of was found with extreme values reaching a few negative and positive units [START_REF] Simovski | Model of isotropic resonant magnetism in the visible range based on core-shell clusters[END_REF] .

3-1-2-Experimental realizations: raspberry-like nanoclusters (R-NC)

The Simovski-Tretyakov model [START_REF] Simovski | Model of isotropic resonant magnetism in the visible range based on core-shell clusters[END_REF] of raspberry-like nano-clusters (R-NC) proved highly stimulating for nanochemists, who came up with many realizations summarized in Figure 3.2.

The basic strategy consists in attaching metallic nanoparticles (satellites) onto a dielectric nanosphere (core), self-assembled with the help of simple colloidal forces (i.e. electrostatic and Van der Waals) or more specific chemical bonds (after proper surface functionalization). Silica or polystyrene are commonly used for the core, gold or silver for the satellites. Although silver is preferable for its lower level of losses, gold satellites were often used as a proof of concept for their higher chemical stability and easier surface functionalization. The first bottom-up realization of R-NCs is illustrated in figure 3.2.a-b [START_REF] Cunningham | Selfassembled plasmonic core-shell clusters with an isotropic magnetic dipole response in the visible range[END_REF] . 275 to 320 gold satellites of radius 10 ± 1nm are electrostatically assembled around silica cores of radius 130 ± 10nm. The extinction spectrum measured on a collection of such clusters (panel 3.2.b) exhibits a broad resonance at 670 nm, which is not present in the suspension of free satellites. This pioneering work reveals some features that will be found in all other systems: The subwavelength ratio, which we define as the outer diameter of the clusters divided by the resonant magnetic mode wavelength is hardly lower than 1.

Replacing gold by silver in the satellites gives the hope of a higher magnetic response for smaller clusters. Figure 3.2.c-d shows R-NCs made of a polystyrene core (D core = 90nm) surrounded by about thirty silver satellites of diameter 36 nm attached by a thiol linker [START_REF] Sheikholeslami | A metafluid exhibiting strong optical magnetism[END_REF] . A fine scattering study of these silver R-NCs provided a direct identification of the magnetic dipolar response. Dark-field spectroscopy on a single R-NCs on the one hand, and polarized static light scattering on a population on the other hand, enabled to unambiguously distinguish the electric and magnetic scattering modes. The next step in the characterization of AOM of R-NCs was obtained by measuring the magnetic-to-electric ratio across the whole visible spectrum in order to determine its maximum value and to localize the wavelength of the multipolar resonances. The polarized static light scattering method was implemented with a white light source, to study R-NCs made of 30nm gold [START_REF] Ponsinet | Resonant isotropic optical magnetism of plasmonic nanoclusters in visible light[END_REF] or 25nm silver satellites [START_REF] Gómez-Graña | Hierarchical self-assembly of a bulk metamaterial enables isotropic magnetic permeability at optical frequencies[END_REF] Ref. [START_REF] Cunningham | Selfassembled plasmonic core-shell clusters with an isotropic magnetic dipole response in the visible range[END_REF] . Copyright 2011 American Chemical Society). (c) TEM (top) and SEM (bottom) images of clusters of silver nanospheres covalently attached to a polystyrene core as shown in (d) (Reprinted with permission from Ref. [START_REF] Sheikholeslami | A metafluid exhibiting strong optical magnetism[END_REF] . Copyright 2013 American Chemical Society). (e) TEM micrographs of gold-on-core R-NCs. (f) Plots of the orthogonal (red) and parallel (blue) scattering corresponding mainly to the electric dipole and magnetic dipole contributions (Reprinted with permission from Ref. [START_REF] Ponsinet | Resonant isotropic optical magnetism of plasmonic nanoclusters in visible light[END_REF] . Copyright 2015 by the American Physical Society.). (g-h) similar to (e-f) with silver satellites. Inset in (h) shows the strength of the three scattering modes, ED, MD and EQ (Reproduced from Ref. [START_REF] Gómez-Graña | Hierarchical self-assembly of a bulk metamaterial enables isotropic magnetic permeability at optical frequencies[END_REF] with permission from The Royal Society of Chemistry) (i) R-NCs with a thicker layer of gold satellites. (j) Experimental (top) and simulated (bottom) extinction spectra showing the first dipolar resonances in the near IR (Reprinted with permission from Ref. [START_REF] Qian | Raspberry-like metamolecules exhibiting strong magnetic resonances[END_REF] . Copyright 2015 American Chemical Society). (k) TEM micrographs of clusters made of gold nanorods attached on silica microspheres. (l) Extinction spectra revealing the electromagnetic couplings of the nanorods in an assembled surface (Reprinted with permission from Ref. [START_REF] Grillo | Self-Assembled Arrays of Gold Nanorod-Decorated Dielectric Microspheres with a Magnetic Dipole Response in the Visible Range for Perfect Lensing and Cloaking Applications[END_REF] . Copyright 2020 American Chemical Society).

Replacing the spherical satellites by metallic nano-rods provides also an interesting structural option as it enables some tuning of the resonance frequency by simply adjusting the aspect ratio of the nano-rods [START_REF] Grillo | Self-Assembled Arrays of Gold Nanorod-Decorated Dielectric Microspheres with a Magnetic Dipole Response in the Visible Range for Perfect Lensing and Cloaking Applications[END_REF] . Note that magnetic dipoles based on plasmonic current loops were also observed in colloidal nanoarchitectures on surfaces [START_REF] Fan | Self-assembled plasmonic nanoparticle clusters[END_REF][START_REF] Roller | DNA-assembled nanoparticle rings exhibit electric and magnetic resonances at visible frequencies[END_REF] .

3-1-2-Experimental realizations: Platonic nanoclusters (P-NC)

The perfect organization of a well-defined number of metallic satellites on the faces of a Platonic solid is a smart way to produce clusters with isotropic optical properties. Figure 3.1.c shows the example of a cluster made of six identical spheres sitting on the vertices of an octahedron. It is remarkable that bottom-up synthetic methods not only can produce random organization of the satellites as in the R-NC model, but also such quasi-perfect platonic-like nanoclusters (P-NCs) with a large-scale output. In figure 3.3.a, gold nanospheres are attached to thiol groups at predefined locations on the surface of a genetically engineered cowpea mosaic virus with icosahedral symmetry [START_REF] Fontana | Virus-templated Plasmonic nanoclusters with icosahedral symmetry via directed self-assembly[END_REF] . Optical resonances are observed in the visible, with a 10-fold enhancement of the local field. The next examples are based on the concept of "patchy" particles whereby well-defined areas of a core nanoparticle are decorated with specific chemical functions, which will subsequently be used to attach or grow the metallic satellites [START_REF] Désert | High-yield preparation of polystyrene/silica clusters of controlled morphology[END_REF] . Figure 3.3.b. illustrates the multistep "patchy" particle strategy and a remarkable set of P-NCs of tetrahedral, octahedral and icosahedral symmetry [START_REF] Chomette | Colloidal alchemy: conversion of polystyrene nanoclusters into gold[END_REF] . [START_REF] Many | High optical magnetism of dodecahedral plasmonic meta-atoms[END_REF] ).Transmission electron micrographs of silica/gold P-NCs four, six or twelve satellites (scale bars 100 nm) and 3-D reconstruction of a dodecapod obtained by electron tomography (bottom) (Reprinted with permission from Ref. [START_REF] Chomette | Colloidal alchemy: conversion of polystyrene nanoclusters into gold[END_REF] ), (c) scheme and TEM images of a dodecapod and the steps of silver satellite growth (scale bars 100 nm) (top) and spectral variation of the magnetic-to-electric ratio along the satellite growth (bottom) (Adapted with permission from Ref. [START_REF] Lermusiaux | Toward Huygens' Sources with Dodecahedral Plasmonic Clusters[END_REF] . Copyright 2021 American Chemical Society).

An optical study of gold dodecapods of icosahedral symmetry revealed a magnetic-to-electric ratio of the dipolar scattering of 0.15, well above the value 0.045 obtained for the R-NC form of equivalent size and gold amount [START_REF] Many | High optical magnetism of dodecahedral plasmonic meta-atoms[END_REF] . The same "patchy particle" strategy was used with silver satellites to further enhance the AOM [START_REF] Lermusiaux | Toward Huygens' Sources with Dodecahedral Plasmonic Clusters[END_REF] . Figure 3.3.c presents a series of silver dodecapods of increasing satellite size preserving the icosahedral symmetry. The polarized scattering study (bottom) shows that the parallel-to-transverse scattering ratio

   
increases with the amount of silver to reach a record value higher than 1, definitely higher than the value 0.28 obtained for silver R-NCs of similar size. The numerical multipole analysis indicates that the generalized Kerker condition is fully or nearly satisfied across the visible range, which is confirmed experimentally by an angular scattering study evidencing a strongly dominant forward scattering: these resonators are examples of Huygens multipoles as described in section 2.1.

3-2-Dielectric Mie-resonant magnetic meta-atom:

The advantage of Mie-resonant particles made of transparent dielectrics has been long recognized for the reduction of optical losses [START_REF] Jahani | All-dielectric metamaterials[END_REF][START_REF] Baranov | All-dielectric nanophotonics: the quest for better materials and fabrication techniques[END_REF] . Upon increasing frequency, the two dipolar resonances of the Mie expansion appear first. For a sphere of refractive index n, the magnetic resonance, naturally of interest for the AOM quest, occurs for a wavelength   n close to the diameter D. The additional requirement of sub-wavelength size D <<  implies the search of transparent materials of high refractive index. Available high-index materials are shown in figure 3.4.a: the highest possible values do not exceed 4 to 5. Bottom up approaches have investigated two materials, titanium dioxide (TiO 2 ) with an index of 2.6 and crystalline silicon that has an index close to 4 (Fig. 3.4.b) [START_REF] Aspnes | Dielectric functions and optical parameters of si, ge, gap, gaas, gasb, inp, inas, and insb from 1.5 to 6.0 ev[END_REF] . Amorphous silicon is less desirable for its higher absorption coefficient k. TiO 2 nano and microparticles can be produced by sol-gel chemistry, but the effective refractive index of the particles is generally disappointing, about 1.6 instead of 2.6 for the anatase crystalline phase. Synthesizing crystalline silicon (c-Si) nanospheres is more challenging, but more rewarding. The laser ablation is undoubtedly excellent to produce perfectly calibrated c-Si nanospheres, though in limited amount. On the other hand, the mass-production of silicon nano-spheres of well-controlled size and internal structure by chemical synthesis from a silicon-rich precursor is a tough challenge 58 : Figures 3.6 [START_REF] Hinamoto | Colloidal Solutions of Silicon Nanospheres toward All-Dielectric Optical Metafluids[END_REF] . Copyright (2020) American Chemical Society).

In the above examples, the electric and magnetic dipolar resonances occur at different wavelengths, in agreement with the Mie-theory for high-index spheres. Merging these two resonances is desirable to produce broad-band Huygens' sources with applications to perfect absorption [START_REF] Dezert | Complete multipolar description of reflection and transmission across a metasurface for perfect absorption of light[END_REF] . Coating a silicon core with a dielectric shell allows controlling the relative frequencies of the two dipolar resonances [START_REF] Liu | Broadband unidirectional scattering by magneto-electric core-shell nanoparticles[END_REF] , as was experimentally demonstrated on Si particles made by laser ablation and subsequently oxidized to grow a silica shell [START_REF] Tsuchimoto | Fano resonant all-dielectric core/shell nanoparticles with ultrahigh scattering directionality in the visible region[END_REF] . The massproduction of similar core-shell structures was made possible 66 by adapting the solvo-thermal synthesis (Figure 3.7.a-b). Dark-field studies evidenced the full overlap of the electric and magnetic dipole resonances with equal strength (Fig. 3.7.c). Numerical simulations show that the electric and magnetic dipoles are located respectively in the shell and in the core (Fig.

3.7.d).

These last works [START_REF] Cha | Large-scale and low-cost fabrication of silicon mie resonators[END_REF][START_REF] Hinamoto | Colloidal Solutions of Silicon Nanospheres toward All-Dielectric Optical Metafluids[END_REF][START_REF] De Marco | Broadband Forward Light Scattering by Architectural Design of Core-Shell Silicon Particles[END_REF] announce the upcoming large-scale availability of crystalline silicon nanospheres, which opens the way to future applications of AOM in metasurfaces or metamaterials.

3-3-Plasmon-assisted Mie-resonators:

The choice of high-index dielectrics is limited in visible light (Figure 3.4.a), and even more so for nanochemistry synthetic approaches. An alternative consists in using the plasmonic resonance of a metal-dielectric composite to generate an effective material with a high effective index, which itself is subsequently shaped in spheres subject to Mie resonances [START_REF] Rockstuhl | Design of an artificial three-dimensional composite metamaterial with magnetic resonances in the visible range of the electromagnetic spectrum[END_REF] . This hierarchical approach was realized using small crosslinkers between particles to produce quasispherical aggregates, inducing a magnetic mode visible in the extinction spectra for large enough nanoparticles (20 nm) [START_REF] Bourgeois | Self-Assembled plasmonic metamolecules exhibiting tunable magnetic response at optical frequencies[END_REF] . More monodisperse clusters were targeted with emulsion processes. ) (e-g) Realization of spherical gold clusters by drying a water-in-oil emulsion. (f) Cryo-TEM images recorded at different angles proving the spherical shape of the clusters. Scale bar is 100 nm (g) Measurements (left) and simulations (right) of the magnetic-to-electric dipolar ratio. (e-f-g reprinted from Ref. [START_REF] Elancheliyan | Tailored self-assembled nanocolloidal Huygens scatterers in the visible[END_REF] with permission from The Royal Society of Chemistry).

These emulsion processes are efficient and cost-effective for a large-scale production of resonators in a solvent. Moreover, numerical simulations [START_REF] Dezert | Isotropic Huygens dipoles and multipoles with colloidal particles[END_REF] and measurements [START_REF] Elancheliyan | Tailored self-assembled nanocolloidal Huygens scatterers in the visible[END_REF] show that their optical properties can be finely tuned via structure control.

3-4-Conclusion:

This section shows that bottom-up approaches offer a large variety of AOM meta-atoms. In many cases, the magnetic response is of the same order as the electric one, opening the way for efficient Huygens' source production for forward-only scattering. The size of the magnetic meta-atom is mostly in the 100-200 nm range, only moderately sub-wavelength for visiblelight applications, and often polydisperse. Optical applications may require post-synthesis size-sorting for a finer control of the properties. Tunability was demonstrated, and the toolbox of the classical colloidal physical-chemistry offers the variability for exploring resonance engineering.

-4-Self-assembled materials

-1 -2D assemblies, metasurfaces:

AOM studies in metasurfaces fabricated by self-assembly are scarce, compared to the abundant literature dealing with the top-down approach [START_REF] Glybovski | Metasurfaces: From microwaves to visible[END_REF] , more powerful indeed for a perfect surface ordering of meta-atoms. Nevertheless, self-assembly can for example produce an excellent organization of spheres of uniform diameter on a substrate 59 (see Figure 4.1a): a hundred percent transmission band is found in experiments and FDTD numerical simulations in the near IR, and attributed to impedance-matching caused by both the magnetic and the electric dipole interactions. [START_REF] Grillo | Self-Assembled Arrays of Gold Nanorod-Decorated Dielectric Microspheres with a Magnetic Dipole Response in the Visible Range for Perfect Lensing and Cloaking Applications[END_REF] . Copyright 2020 American Chemical Society) (e-f) Design of a perfect absorber using the multipolar behavior of individual metaatoms. (e) Wavelength dependence of the sum of even and odd multipole coefficients of a single SiO2 microsphere in vacuum (D=4.3µm) (f) Spectra of R, T and A calculated for an infinite square array of SiO 2 microspheres with a surface fill fraction of 0.7. (Reprinted with permission from Ref. 63 © The Optical Society.) Interestingly, a monolayer of R-NCs can be prepared in two steps [START_REF] Grillo | Self-Assembled Arrays of Gold Nanorod-Decorated Dielectric Microspheres with a Magnetic Dipole Response in the Visible Range for Perfect Lensing and Cloaking Applications[END_REF] by adsorbing the metallic satellites onto the previously deposited regular array of dielectric spheres. Figure 4.1d shows a triangular lattice of silica beads decorated with gold nanorods. The extinction spectrum of the array (Fig. 3.2.l) is consistent with the presence of magnetic multipoles as shown by numerical simulations in figures 4.1e.

The design of the meta-atoms can actually be adjusted in numerical simulations to promote perfect reflection, transmission or absorption. In this latter case, two conditions should be met simultaneously, namely the extinction of the reflected wave (generalized Kerker's condition) and a -phase shift of the transmitted wave for destructive interference with the incident light [START_REF] Dezert | Complete multipolar description of reflection and transmission across a metasurface for perfect absorption of light[END_REF] . Figures 4.1g-h show an example of a 2D array of meta-atoms made of 13 spheres of germanium of 75 nm radius producing perfect absorption in the visible at a wavelength of 790 nm. In this study, numerical simulations point out the significant contribution of scattering multipoles for each meta-atom, and the importance of the inter-particle coupling in the array. Reducing the AOM to the effect of the sole magnetic dipole would be insufficient.

Very few experimental examples of self-assembled metasurfaces operating in visible light have been reported so far, but the recent availability of a large number of magnetic metaatoms should enable and stimulate new realizations. Several self-assembly techniques are commonly available to deposit nanoparticles on a substrate like spin-coating [START_REF] Pichumani | Dynamics, crystallization and structures in colloid spin coating[END_REF] , dip-coating [START_REF] Berteloot | Dip coating with colloids and evaporation[END_REF] , blade-coating [START_REF] Yang | Large-scale colloidal self-assembly by doctor blade coating[END_REF] or Langmuir-Blodgett transfer [START_REF] Meldrum | Utilization of surfactant-stabilized colloidal silver nanocrystallites in the construction of mono-and multiparticulate Langmuir-Blodgett films[END_REF][START_REF] Malassis | Bottom-up fabrication and optical characterization of dense films of meta-atoms made of core-shell plasmonic nanoparticles[END_REF] .

-2 -3D assemblies: bulk magnetic metamaterials

The ability of the bottom-up route to synthesize a huge number of magnetic meta-atoms enables bulk metamaterials fabrication. Figure 4.2 illustrates the realization of a bulk magnetic metamaterial by aggregating the R-NCs shown in figure 3.2g in a micro-channel evaporator 77 78 . A slow evaporation of the solvent across a thin membrane drags a dilute suspension of R-NCs to the channel dead-end (Fig. 4.2a) and aggregates the particles into a dried 3D material [START_REF] Gómez-Graña | Hierarchical self-assembly of a bulk metamaterial enables isotropic magnetic permeability at optical frequencies[END_REF] , presenting a random, close-packed, isotropic nanostructure ((Figs. 4.2bc and 3.2g). The typical dimensions of a crack-free piece of metamaterial are 5 × 100 × 500 µm 3 gathering about 2.10 7 R-NCs for a filling fraction estimated at 40%. Spectroscopic ellipsometry enabled the determination of the effective optical parameters reproduced in figures 4.2d-g, using the analysis method described in section 2.2 for semiinfinite materials. The electric permittivity and the magnetic permeability exhibit a resonant behavior around 400 nm, close to the free R-NC resonance (Fig. 3.2h). In particular, the real part µ' of the magnetic permeability explores values from 0.8 to 1.45. This composite constitutes the first example of a 3D isotropic metamaterial exhibiting reflection properties consistent with an effective magnetic permeability significantly different from the natural value µ r =1 across the visible spectrum, and independent of the angle of incidence. This simple result however may hide the complexity of the magnetic behavior. The negative values of the imaginary part µ" of the permeability for instance, reveals that the electric and magnetic responses are inextricably linked. The material is indeed dissipative if the electric and magnetic processes are considered together. Moreover, close to the resonance wavelength, some data points do not satisfy the linear relationship Y=AX+B introduced in section 2, which denotes an angular variation of the coefficients A and B. This is a clear evidence of the phenomenon of spatial dispersion, which may preclude the extraction of valid effective optical parameters. Such theoretical limitations have been amply discussed in the literature [START_REF] Alu | First-principles homogenization theory for periodic metamaterials[END_REF][START_REF]Publications Office of the European Union[END_REF][START_REF] Simovski | Material parameters and field energy in reciprocal composite media[END_REF]80 Finally, it should be noted that the full characterization of the optical parameters would require measurements of the reflected and transmitted waves, the latter being inaccessible yet.

-5-Conclusion

The various works reported in this chapter clearly demonstrate that the bottom-up approach brings a significant contribution to the design and generation of AOM and other properties. The main advantage of this approach is its ability to produce large amounts of magnetic metaatoms, larger than the top-down techniques by several orders of magnitude. Moreover, the self-assembly techniques are generally and energy saving as they do not require costly equipment such as electron beam lithography or ion-beam etching. The profusion of magnetic meta-atoms enables the production of metasurfaces of large area and of bulk magnetic materials of macroscopic size. They can be dispersed in aqueous or organic solvents to form "meta-inks" which can be conveniently implemented in various self-assembly techniques.

The newest plasmonic and all-dielectric designs provide magnetic and electric responses of equivalent magnitude, in narrow or broad frequency bands, opening the way to directional scattering. Scattering efficiencies significantly higher than 1 are obtained for typical sizes of order 100 to 200 nm, which is great for applications in monolayers in metasurfaces. The wavelength to diameter ratio however hardly exceeds 3 at resonance, which may not be optimal to warrant homogeneity. A trade-off has to be adjusted between homogeneity and efficiency: smaller sizes imply weaker optical response. Disorder or inaccuracy, inherent of the bottom-up methods, are often seen as limitations for applications. It is true that the fabrication processes often result in some distribution of the sizes of the meta-atoms, implying variations of the optical properties. For applications requiring an accurate design, the usual methods of size-sorting of nanoparticles like centrifugation, viscosity gradient centrifugation [START_REF] Qiu | Viscosity gradient as a novel mechanism for the centrifugation-based separation of nanoparticles[END_REF] , or gel electrophoresis [START_REF] Surugau | Electrophoretic methods for separation of nanoparticles[END_REF] are available. The self-organization of the meta-atoms may also lead to disordered materials, although monolayer of monodisperse spheres can self-organize in excellent triangular lattices as shown in figure 4.1. The relevant question is after all: what kind of order is required for a given application or property? For a 2D structure, certain types of correlated disorder, like hyperuniformity may be just as good as a regular lattice [START_REF] Torquato | Local density fluctuations, hyperuniformity, and order metrics[END_REF][START_REF] Leseur | High-density hyperuniform materials can be transparent[END_REF] . Many questions related to the effect of disorder remain open that should be addressed in the future. Finally, we note that the realization of 3D magnetic materials offers the unique opportunity to investigate experimentally the subtle and complex effects of non-locality and spatial dispersion and explore the limits of validity of an effective magnetic permeability parameter.

Figure 2 . 1 :

 21 Figure 2.1: (a) Sketch of a polarization-resolved static light scattering setup (adapted from Ref.22 with permission from The Royal Society of Chemistry). It consists of two broadband polarizers (P 1 and P 2 ); a Fresnel rhomb tandem (FR); a focusing (L 1 ) and collection (L 2 ) lenses, two pinholes (PH 1,2 ) and a spectrometer (SP). (b) Illustration of the vector fields involved in the illumination and

Figure 3 . 1 :

 31 Figure 3.1: (a) Original model of plasmonic nano-ring 40 . (b) Raspberry-like magnetic nanocluster model 43 (c) Cube-based isotropic model 41 . (d-e) Sketches showing the plasmonic currents (red arrows) in the electric (d) and magnetic (e) resonant modes 44 .

  around a 100nm-silica sphere (figures 3.2.eg). The scattering cross sections recorded along the two principal output polarizations reveal two resonant features (figure 3.2.f and h). Numerical simulations confirm the contribution of only three significant modes in the visible spectrum, namely ED, MD and EQ in decreasing strength. For silver satellites, the magnetic-to-electric dipole ratio reaches the highest value R ME = 0.26. Interestingly, the resonances of the three contributing modes largely overlap, which enables the simultaneous presence of electric and magnetic optical responses in the same wavelength range. In an attempt to increase the magnetic optical response of the R-NC designs, Qian et al. investigated variations of the structural parameters by changing the core diameter and the size and number of metallic satellites 46 . Figures 3.2.i shows nanoclusters made of several layers of gold nanoparticles wrapping up the silica core. Experimental and simulated extinction spectra reveal dipolar resonances shifted towards the near IR domain (figure 3.2.j), while higher multipoles are present in the visible.

Figure 3 . 2 :

 32 Figure 3.2: Raspberry-like magnetic nanoclusters (R-NCs). (a) SEM picture of gold-on-silica R-NCs. (b) Extinction spectrum showing the magnetic resonance at 680 nm (Reprinted with permission from

Figure 3 . 3 :

 33 Figure 3.3: Platonic nano-clusters (P-NCs) (a) Virus model and TEM picture of P-NCs with 30nm-silver satellites (top). Normalized absorbance spectra comparing the experimental (purple) and averaged simulation (black) (bottom) (Reproduced from Ref. 50 with permission). (b) Schematic process for the synthesis of gold dodecapods ).(top) (Reprinted with permission from Ref.[START_REF] Many | High optical magnetism of dodecahedral plasmonic meta-atoms[END_REF] ).Transmission electron micrographs of silica/gold P-NCs four, six or twelve satellites (scale bars 100 nm) and 3-D reconstruction of a dodecapod obtained by electron tomography (bottom) (Reprinted with permission from Ref.[START_REF] Chomette | Colloidal alchemy: conversion of polystyrene nanoclusters into gold[END_REF] ), (c) scheme and TEM images of a dodecapod and the steps of silver satellite growth (scale bars 100 nm) (top) and spectral variation of the magnetic-to-electric ratio along the satellite growth (bottom) (Adapted with permission from Ref.[START_REF] Lermusiaux | Toward Huygens' Sources with Dodecahedral Plasmonic Clusters[END_REF] . Copyright 2021 American Chemical Society).

Figure 3 . 4 :

 34 Figure 3.4: (a) Refractive indices of materials available for dielectric nanophotonics from visible to mid-IR spectral ranges (Reprinted with permission from Ref. 54. © The Optical Society). (b) Optical index 55 of crystalline (blue) and amorphous (red) silicon. Solid (dashed) lines represent real (imaginary) part. Si nanospheres have been produced by laser ablation of Si 56 or silicon-on-insulator targets 57 , collected on a glass slide, laser-recrystallized and optically characterized by dark field optical microscopy. Their dipolar magnetic and electric Mie resonances in the visible are found in full agreement with the Mie theory (Fig. 3.5).

Figure 3 . 5 .

 35 Figure 3.5. (a) Schematic presentation of laser induced production of silicon nanospheres. (b) SEM image of a Si sphere of radius R = 104 nm. Inset shows the corresponding dark-field images. (c)

  .a-b illustrate two recent chemical paths based on solvothermal synthesis[START_REF] Shi | Monodisperse silicon nanocavities and photonic crystals with magnetic response in the optical region[END_REF] and thermal decomposition ,60 of various silane precursors. Interestingly, a large-scale and low-cost production of crystalline, spheroidal silicon nanoparticles (100-200nm) exhibiting magnetic dipolar scattering in the visible was obtained by physically grinding silicon lumps in a kitchen blender[START_REF] Cha | Large-scale and low-cost fabrication of silicon mie resonators[END_REF] (fig.3.6.c). More recently, perfectly spherical crystalline silicon was produced from silicon oxide (SiO) lumps, annealed at high temperature to induce spherical Si inclusions, which are then extracted and size-sorted by centrifugation 62 (figure 3.6.d). Their magnetic dipolar resonance was observed throughout the visible for diameters ranging from 90 to 200 nm.

Figure 3 . 6 .

 36 Figure 3.6. (a) SEM picture of silicon nanospheres made by solvothermal synthesis from a trisilane precursor (top). Extinction spectrum revealing the magnetic and electric dipoles in the infrared (bottom) (Reprinted by permission from Nature Publisher from Ref. 59 . Copyright 2013). (b) Silicon nanospheres synthesized from Hydrogen Silsesquioxane precursor (top). X-ray diffraction diagrams evidencing the crystalline structure (bottom) (Reprinted with permission from Ref. 60 Copyright (2019) American Chemical Society). (c) Kitchen-blender fabrication of crystalline silicon spheroids (top). Scattering spectra showing the size-dependent electric and magnetic dipolar resonances (bottom) (Reprinted with permission from Ref. 61 . Copyright (2019) American Chemical Society). (d) Crystalline silicon nanospheres produced by thermal annealing and etching of SiO lumps (top). Extinction spectra showing the two dipolar resonances (bottom) (Reprinted with permission from Ref.[START_REF] Hinamoto | Colloidal Solutions of Silicon Nanospheres toward All-Dielectric Optical Metafluids[END_REF] . Copyright (2020) American Chemical Society).

Figure 3 . 7 .

 37 Figure 3.7. (a) SEM micrographs of silicon nanospheres made by solvothermal synthesis from two different mixtures of trisilane and bis-amidinate precursors (bar = 1µm). (b) STEM-EDX elemental analysis evidencing the core-shell structure Si@SiO x N y (bar = 200nm). (c) Experimental (solid line) and simulated (dots) dark-field spectra showing the overlapping electric (blue) and magnetic (red) dipolar scattering. (d) Electric (left) and magnetic (right) field maps. (Reprinted from Ref. 66 with permission from Wiley and Sons Publisher).

  Figures 3.8.b-d show spherical clusters of silver nanoparticles encapsulated in oilin-water emulsions and aggregated by dithiol linkers 69 , which display dipolar Mie resonances in extinction spectra. Figures 3.8.e-g show clusters of gold nanoparticles synthesized in a water-in-oil emulsion, where water evaporation confines the nanoparticles into controlled aggregates, which were shown to have a strong magnetic dipolar resonance 22 .

Figure 3 . 8 :

 38 Figure 3.8: (a) Hierarchical model of a Mie-resonant sphere made of an artificial Lorentz-resonant high-index material (Reprinted with permission from Ref. 67 Copyright (2007) by the American Physical Society). (b-d) Realization by silver nanoparticles aggregation in an oil-in-water emulsion (c) SEM images of the raw emulsion showing the polymeric nanocapsules (left) and TEM images of the NP-clusters (right) (d) Extinction measurements and simulations showing the magnetic resonance. (bc-d reprinted with permission from Ref 69 © The Optical Society.) (e-g) Realization of spherical

Figure 4 . 1 :

 41 Figure 4.1: (a-b) 2D photonic crystal of silicon microspheres (a) SEM image (scale bar, 500 nm). (b) Transmission (red) and reflection (blue) spectra at normal incidence obtained from the experiment (solid lines) and the FDTD simulation (dotted lines) (Reprinted by permission from Nature Publisher from Ref. 59 . Copyright 2013)). (c-d) Array of silica microspheres decorated with gold nanorods (c) SEM micrograph. (d) Computed contribution of the different multipole moments to the extinction spectra for an isolated cluster. (Reprinted with permission from Ref. 47 . Copyright 2020 American Chemical Society) (e-f) Design of a perfect absorber using the multipolar behavior of individual metaatoms. (e) Wavelength dependence of the sum of even and odd multipole coefficients of a single SiO2 microsphere in vacuum (D=4.3µm) (f) Spectra of R, T and A calculated for an infinite square array of

Figure 4 . 2 :

 42 Figure 4.2: (a) Schematic view of the 3D assembly of R-NCs in a microfluidic evaporator. (b-c) SEM views of the assembled material at different magnification.(d-g) Experimental values of the complex electric permittivity ('+i") and magnetic permeability ('+i"). Blue and red data points correspond to two different samples. (Reprinted from Ref.[START_REF] Gómez-Graña | Hierarchical self-assembly of a bulk metamaterial enables isotropic magnetic permeability at optical frequencies[END_REF] with permission from The Royal Society of Chemistry).

Acknowledgement:

The authors acknowledge the support of the LabEx AMADEus (ANR-10-LABX-42) in the framework of IdEx Bordeaux (ANR-10-IDEX-03-02), France


Léo Berline

Andrea Michelangelo Doglioli

Anne Petrenko

Stéphanie Barrillon

Boris Espinasse

Frederic A C Le Moigne

François Simon-Bot

Melilotus Thyssen

François Carlotti

Particle transport in the central Ionian Sea

Introduction Methods

Ionian Sea considered as oligotrophic, but at the crossroad of 3 main water masses, with complex surface circulation. Few data on horizontal particle distribution.

-High resolution sampling using MVP mounted with CTD-LOPC-Fluorometer (end of May 2017) -Hull mounted ADCP -Regular CTD stations and underway flow cytometry -Backward Lagrangian tracking w/geostrophic velocity -Satellite SST and Chl-a -High resolution sampling using MVP mounted with CTD-LOPC-Fluorometer -Hull mounted ADCP -Regular CTD stations and underway flow cytometry -Backward Lagrangian tracking w/geostrophic velocity -Satellite SST and Chl-a

Fig 3 .

 3 Fig 3. Backward Lagrangian simulations. Seeding in white polygon. Positions of numerical particles one month before sampling (black dots), and trajectories splitted by main origin (colors)

Fig

  Fig 2. Distribution of variables along ION-Transect

Chl-a


Romain Pertschi

Solène Miaskiewicz

Nicolas Kern

Jean-Marc Weibel

Patrick Pale

Aurélien Blanc1
email: ablanc@unistra.fr

Gold(I)-Catalyzed Divergent and Diastereoselective Synthesis of Azepines by Ammoniumation/Ring-Expansion Reactions

Keywords: Catalysis, Gold(I), Ammoniumation, Ring Expansion, Azepines, and Azetidines

Gold(I) catalysts enable the chemoselective addition of tailor-made N-sulfonylated azetidine derivatives onto alkynes affording bicyclic vinyl-ammonium gold intermediates. Intramolecularly intercepted by a nucleophilic carbonate or ester function adequately positioned, these ammoniums efficiently lead to ring-expanded azepine products which are important pharmacophore fragments. Depending on the substitution pattern of the starting material, divergent deauration pathways occur, stereoselectively producing monomeric or original dimeric nitrogenated seven-membered rings in good to excellent yields, such as cis-tetrahydroazepin-4,5-diol carbonate, (E)-alkylidene tetrahydroazepin-4-yl ester, and cis-bis(azepinyl)cyclobutane derivatives. One of the synthetic methods were extended to the formation of dihydrobenzazepines of high pharmaceutical value. A mechanistic study, including kinetics and labeled experiments allows to fully understand the origin of the high chemo-and diastereoselectivity of these rearrangements. Overall, this work demonstrates the underlying synthetic potential of the ammoniumation catalyzed by gold for the future developments of reaction cascades and the preparation of bioactive compounds.

INTRODUCTION

Azepine and its saturated derivatives are important pharmacophore fragments1 present in various natural products and in a wide range of bioactive compounds (Figure 1A).2 For example, sevenmembered aza-ring systems can be found in the structure of balanol,3 a potent inhibitor of protein kinases, or in (-)-cobactin T,4 a siderophore growth promoter isolated from mycobacteria. N-Sulfonyl hydroazepine motif can also be found in the synthetic relacatib,5 a potent inhibitor of human cathepsin K. The (hydro)benzazepine core is also quite common in drug structures, as exemplified by the commercial benazepril6 drug, which is an angiotensin-converting-enzyme inhibitor used to treat renal insufficiency or hypertension. Considering the high pharmaceutical value of the (hydro)azepine derivatives, various routes to produce them have been developed (Figure 1B).7 Nevertheless, the required conditions usually do not allow for structural variations and functionalizations. Therefore, the development of flexible methodologies for their synthesis stands as an important and timely needed task.8

In the course of our studies on complexity-generating rearrangements of aza-rings, we recently outlined a versatile ammoniumation strategy based on the ability of gold(I) to promote the addition of N-sulfonylated cyclic amines on alkynes leading to vinyl-ammonium gold species (See blue arrow on 1 and intermediate A, Figure 1C).9 Selective interception of these intermediates by external and protic nucleophiles open new routes to important N-heterocycles such as pyrroles, pyrrolinones, benzosultams, and various 1-azabicyclo[m.n.0]alkane derivatives. Therefore, we wondered whether a complementary strategy could be designed for the synthesis of valuable azepine derivatives.10 With this aim, N-sulfonyl 1-(azetidin-2-yl)propargyl carbonates or esters 1 were devised as potential precursors for a gold-catalyzed cyclization/transannular ring opening11 process (Figure 1C). We indeed reasoned that a carbonate or an ester group, appropriately positioned at the propargylic position, may be prone to act as an internal aprotic nucleophile able to open intermediate A, thus providing the azepine intermediate B. The evolution of the latter, and especially its ability to release gold(I) to render the whole process catalytic, would be critical for the reaction outcome. In view of the rich gold-catalyzed chemistry12 of propargylic carbonates and esters, competing pathways could also be expected (red dotted arrows on 1 in Figure 1C), since the latter are known to rearrange into 4-alkylidene-1,3-dioxolan-2-ones13 or undergo 1,2-and 1,3-carbonate14 or -ester15 migrations with variable outcomes depending on substitution patterns and conditions.

We report herein the feasibility of such rearrangements as well as their extension to cascade reactions. These studies highlight the facile sulfonyl azetidinium generation even in a complex setup, but also unveil a new deauration pathway. Overall, complex azepines 2 or 3 embedding rich substitution patterns (Figure 1C), hardly accessible via conventional methods,7,8 can readily be produced through the present process.

RESULTS AND DISCUSSION

Gold(I)-Catalyzed Ammoniumation/Ring-Expansion Reactions

We first selected the azetidine carbonate 1a, i.e. tert-butyl (1-(1-tosylazetidin-2-yl)non-2-yn-1-yl) carbonate (Table 1) as model substrate for the envisioned ring expansion. The choice of tert-butyl carbonate ester (R=OCO2tBu) was guided by the possible elimination of isobutene from the tertbutoxydioxolanium moiety in intermediate B (Figure 1C) and the expected protodemetalation induced by the so-released proton.13 Such a sequence would directly lead to the azepinyl carbonate 2.

This carbonate 1a and its analogs were conveniently obtained from N-sulfonyl 2-azetidinecarboxylate methyl esters, the protected form of the naturally occurring aminoacid Aze. Although commercially available, the latter and more importantly its substituted analogs are readily available on multigram scale in a few steps (Scheme 1).16 These building blocks provide a flexible access to various Nsulfonyl-1-(azetidin-2-yl) propargyl alcohol derivatives (see Supplemental Information). Scheme 1. Convenient route to the required azetidine precursors.

The transformation of 1a was first examined in the presence of 5 mol % of Gagosz catalyst (Ph3PAuNTf2) in dichloromethane at room temperature (Table 1, entry 1). After 24 h, only 50% conversion was obtained, but the formation of the expected N-tosyl tetrahydroazepin-4,5-diol carbonate 2a, as the single cis diastereomer17 was observed in the 1H crude NMR spectrum. Switching from bistriflimide to hexafluoroantimonate counterion strongly improved the activity of the gold catalyst as full conversion was reached after only 4 h of reaction (Entry 2). However, compound 2a was formed along with degradation products. The use of electron-withdrawing ligands improved the efficiency of the reaction up to 64% yield but again with the formation of a significant number of unstable side-products (Entries 3 and 4). Therefore, electron-donating ligands were surveyed. Carbenic gold(I) complex only led to low reactivity and conversion (Entry 5). Biarylphosphine gold(I) complexes induced cleaner conversion and consistently led to better yields (Entries 6-8). The CyJohnPhos variant showed a slightly superior activity compared to the standard JohnPhos ligand (Entry 6 vs 7), which can be attributed to the more confining character of the latter. [START_REF] Christian | Uncovering subtle ligand effects of phosphines using gold(I) catalysis[END_REF] The silver salt (AgSbF6) used to prepare the catalytically active gold(I) complexes proved to be unsuitable for this transformation as shown by control experiment (Entry 9). From this optimization, the CyJohnPhosAuSbF6.MeCN complex (5 mol %) was selected as the best catalyst and used for the evaluation of the reaction scope. It is noteworthy that despite the presence of two diastereomers in the starting carbonate 1a, both were consumed, leading to the exclusive formation of cis-tetrahydroazepin-4,5-diol carbonate 2a. Ts = para-toluenesulfonyl; Mbs = para-methoxybenzenesulfonyl.

We first examined the effect of alkyne substitution with substrates 1a-f (R1 on Scheme 2). The reaction proceeded in good yields with primary alkyl (2a) and alkoxy sidechains (2b). Incorporation of cyclic moieties, such as cyclohexyl or cyclopropyl R1 substituents, improved the efficiency of the reaction. A longer reaction time was however required, in line with the increase in steric hindrance. cis-Tetrahydroazepin-4,5-diol carbonates 2c and 2d could thus be obtained in excellent yields when compared to 2a and 2b. Further increase of the congestion by capping the alkyne with a tert-butyl group (1e) completely inhibited the reaction, even upon heating (70 °C).

Interestingly, the presence of an isopropenyl group was well tolerated, and the hydroazepine 2f embedding a potentially useful dienyl unit was formed with reasonable efficiency. Aryl substituents at the R1 position, independently of their electron donating or withdrawing nature, were perfectly compatible, leading to compounds 2g-k in excellent yields (81-93%). Moreover, the rearranged product 2h furnished suitable crystals for X-ray diffraction, which confirmed the relative cis configuration of diol carbonates 2 (See structure of 2h on Scheme 2). Introduction of methyl, allyl or phenyl groups at the propargylic position (R2, Scheme 2) was well tolerated and the hydroazepines 2l-o could be obtained in good to moderate yields, albeit requiring longer reaction times with sterically demanding groups. The variation of the sulfonyl moiety did not affect the rearrangement course, as attested by the formation of 2p bearing a para-methoxybenzenesulfonyl group in excellent yield. To briefly look at the possible influence of substituent on the azetidine ring (R3, Scheme 2), we prepared and evaluated the behavior of the spiroazetidine 1q. Under our standard conditions, the densely substituted spirohydroazepine 2q was formed in a modest 42% yield while recovering the starting material left, and doubling the catalyst loading only slightly increased yield (45%), even after prolonged reaction time. 1H NMR monitoring of this reaction revealed that only one of the diastereomers of 1q was converted to the expected product, while the other led to degradation products.

Reasoning that cis-tetrahydroazepin-4,5-diol carbonates 2 incorporate an enesulfonamide moiety potentially able to react further as π-nucleophiles, we envisaged a cascade involving a second cyclization step. Substrate 1r carrying a diyne chain (Scheme 3) was therefore devised. Under standard conditions, the latter led within 4 h to the tetrahydroazepine 2r, which could be isolated at that stage in modest yield. However, if not isolated, this compound evolved towards the formation of the dihydrobenzazepine 2r' as expected. Indeed, 2r could undergo another cyclization on the second alkyne moiety, which was followed by tautomerization of the so-formed iminium-vinylgold intermediate, demetallation and subsequent elimination of carbon dioxide and water (See Figure S1 in Supplemental Information). It is worth mentioning that once isolated, 2r replaced under reaction conditions provided the benzazepine 2r'. This sequence thus enabled a benzannulation cascade starting from 1r, yielding the benzazepine derivative 2r' in 63% yield after 8 h. Scheme 3. Gold-catalyzed cascade rearrangement of azetidine carbonate derivative 1r into benzazepine derivative 2r'.

At this stage, the influence of the internal nucleophile moiety was surveyed by switching the carbonate group for a pivalate ester. In the previous tert-butyl carbonate series (substrates 1a-r), catalytic turnover was enabled by the release of a tert-butyl cation, precursor of isobutene and a proton which allowed the pivotal demetallation step.13 However, with an ester function as internal nucleophile, such deauration19 step would require an alternative elimination pathway to afford the desired azepine derivative while maintaining a viable catalytic cycle. We thus investigated the capability of azetidinyl propargyl pivaloyl ester 1s to rearrange upon gold activation (Table 2). Unfortunately, conditions determined for the carbonate series only led to disappointing results. Azepine derivative 3s was rapidly obtained at room temperature in dichloromethane, but in low yield along with several side-products (Table 2, entry 1). Applying another classical gold catalyst also provided similar results (entry 2). Among side-products, the alkyne hydration derivative 3s' was clearly identified by 1H NMR as the major compound. To avoid its formation, molecular sieves (4 Å) were added in the reaction mixture. This modification drastically changed the reaction efficiency. 3s was interestingly obtained as a single diastereomer in 66% yield in 4 h with triphenylphosphine as ligand, but when CyJohnPhos was used instead, a modest yield of 54% was still observed (entries 3 and 4). Electronic effects of various gold(I) ligands were then evaluated, in view of their strong influence on catalyst activity.20 With an electron-rich tricyclohexylphosphine ligand, 3s was obtained with a slightly lower yield, whereas a marked improvement was observed with the electron-poor trispentafluorophenylphosphine ligand (entries 5-6 vs 4). Switching to a phosphite derivative did not improve this outcome further (entry 7). Counterions21 and solvents22 are also known to influence gold catalyst selectivity and efficiency; however, additional screening of both parameters did not lead to a sensible improvement, the best combination remaining hexafluoroantimonate anion in dichloromethane (See Table S1 in Supplemental Information). As for carbonate-tagged substrates, a control experiment showed that AgSbF6 alone was inefficient in this transformation (entry 8).

Notably, the obtained azepine derivative 3s possesses an exocyclic double bond, in contrast to the regular outcomes starting from carbonates. The (E)-stereochemistry of this unusual alkylidene tetrahydroazepine structure was unambiguously established by NOESY NMR experiment. With the best conditions in hand (Table 2, entry 6), we then explored the scope of this second unprecedented transformation (Scheme 4).23 We first surveyed the effect of the internal nucleophile, i.e. the ester moiety, on the reaction efficiency. Changing the nature of the ester influenced the yield, an unsurprising trend given its expected role within the rearrangement (see Figure 1C). The less bulky iso-butyryl and acetyl groups provided compounds 3t and 3u in lower yields compared to the pivaloyl (Piv) derivative 3s. Such difference could be attributed to the steric hindrance of the tert-butyl group, pushing the nucleophilic oxygen closer to the transient C-ammonium bond. Benzoyl groups also led to azepines 3v-x in lower yields, in line with their lower nucleophilicity, but also due to stability problems under these conditions. Such reduced propension to undergo the cascade rearrangement was even more apparent in the case of an appended 3,5-dinitrobenzoyl group: here, heating to 70 °C was required to generate 3x in a modest yield of 57%. Nevertheless, 3x provided crystals suitable for X-ray diffraction.

The resulting structure matched our previous assumptions from NMR data and confirmed the (E)geometry of the exocyclic alkene. Variation of the N-sulfonyl protecting group (SO2Ar) proved fully compatible with the rearrangement conditions. Indeed, using N-para-methoxybenzenesulfonyl (Mbs) group instead of N-tosyl group allowed the formation of 3y in a similar yield. Alkyne substituents R2 were also tunable as demonstrated by the formation of azepines 3s, 3z and 3aa bearing alkyl or protected hydroxyl groups. The marked sensitivity of compound 3aa, due to the presence of a benzyloxy functional group at the allylic position, could explain the lower yield obtained in that case. Substitutions of the azetidine moiety (1ab) as well as of the propargylic position (1ac) were also compatible with the reaction conditions, although the expected azepines 3ab and 3ac were obtained in lower yields.23

Interestingly, the analog 1ad carrying a CH2OMe group did lead to the expected product 3ad as shown by NMR, but the latter cannot be isolated. Instead, the dihydroazepine 2-carbaldehyde 4 was obtained, although with a modest 47% yield (Scheme 5, Eq 1). Such compound could originate from the expected azepine 3ad after pivaloyl elimination and proton loss driven by the conjugation of the final product 4 during the purification step (See Figure S2 in Supplemental Information).

The outcome of this new gold-catalyzed rearrangement depends on the final deauration step. This requirement was ensured by the presence of a methylene link between the alkyne and its R2 substituent (See Scheme 4), from which a proton shift would selectively form an exocyclic E-double bond. Such requirement was highlighted by the lack of azepine formation with substrates bearing a tert-butyl or a phenyl group directly linked to the alkyne moiety. In these cases, degradation mostly occurred (See Figure S3 in Supplemental Information).

In sharp contrast, compound 1ae bearing a terminal alkyne evolved through an alternative and unprecedented deauration pathway, affording the unexpected compound 5ae as a mixture of three diastereomers. A high yield was achieved using the CyJohnPhosAuSbF6.MeCN complex (Scheme 5, Eq 2). The compound structure, established from extensive NMR investigations, proved to be a dimeric bis(azepinyl)cyclobutane24 with a cis stereochemistry of the cyclobutane moiety (see below).

Scheme 5. Gold-catalyzed rearrangement of azetidine derivatives 1ad and 1ae.

Considering its original nature, we briefly evaluated the scope of this dimerization reaction (Scheme 6). As for the formation of hydroazepines 3, modulation of the ester function as well as the sulfonyl group was perfectly tolerated in this transformation, leading to compounds 5af-ak in high yields (73-97%). All dimers 5 were obtained as a mixture of only 3 diastereomers in similar ratios (~4.5:1.7:1) which could be separated by flash column chromatography. Two of them were symmetrical compounds as hinted by their relatively simple 1H and 13C NMR spectra. For all of them, nOe experiments revealed the proximity of the two cyclobutane protons, and thus suggested the cis stereochemistry of the central cyclobutane. To determine their relative stereochemistry, crystals of major diastereomers 5af and 5ah were grown, and X-ray diffraction confirmed the cis stereochemistry of the cyclobutane hydrogens and established the syn relationship for the two ester substituents. These data allowed assigning the relative stereochemistry of each diastereomer (Scheme 6). Of note, the same result was obtained with the azetidine carbonate 1ak bearing a terminal alkyne, affording the dimeric cis-bis(azepinyl)cyclobutane dicarbonate 5ak in high yield as a mixture of 3 diastereomers as well. Such unexpected cis-cyclobutyl structure clearly arose from a diastereoselective homodimerization process.

6. Diastereoselective Synthesis of cis-bis(azepinyl)cyclobutane derivatives 5.

aStick representation of major diastereomer 5af XRD structure.

Ts = para-toluenesulfonyl; Mbs = para-methoxybenzenesulfonyl.

Mechanistic Studies and Hypothesis

The large set of results obtained from these gold-catalyzed rearrangements tends to support the proposed mechanism25 through the opening of an ammonium bicyclic intermediate (A on Figure 1C). Nevertheless, they also raised several questions.

-How is such an intermediate formed? Does it arise either from direct nucleophilic addition of the aminosulfonyl group or from a cascade initiated through an ester or carbonate addition? -In the former case, why is the aminosulfonyl group more nucleophilic than an ester or carbonate carbonyl?

-Why a single stereoisomer is produced starting from a mixture of diastereomers?

As mentioned above, propargylic esters or carbonates, such as derivatives 1, are well-known to undergo 1,2-or 1,3-oxo-migrations as a starting point for many cascade transformations.14,15 To get clues on these alternatives and decipher the actual mechanistic pathway, substrates labeled at specific positions were prepared and submitted to our standard reaction conditions (Figure 2A). Both tert-butyloxycarbonyl and pivaloyl derivatives 1al and 1am D-labeled at the propargylic position afforded the hydroazepines 2al and 3am still mono-deuterated at the same position (Eq. 1 & 2 on Figure 2A). Moreover, compound 1an, 17O-enriched at the carbonyl oxygen, provided a single isotopomer 3an, in which this oxygen atom became the alkoxy group of the ester moiety, as revealed by 17O NMR analysis (Figure 2A, Eq. 3). Therefore, these results excluded any cascade initiated by propargylic 1,2-or 1,3-oxo-shift,15 and confirmed that the carbonyl oxygen is acting as nucleophile as expected.

These results also imply that the aminosulfonyl group would be more nucleophilic than the carbonyl oxygen from an ester or a carbonate. The nitrogen lone pair in sulfonamides could be -conjugated with vacant sulfur orbitals, in a planar arrangement, and thus be less nucleophilic than in amines. However, pyramidalization often occurred and especially in N-sulfonyl azetidines,26 rendering the amino part of sulfonamide more nucleophilic. As N-sulfonyl pyrrolidines are less pyramidalized,26 competition between N-and O-cyclization should occur. To confirm such effect, we prepared the five-membered ring analogs 6a-b from proline and submitted them to the corresponding standard conditions (Figure 2B). This pyrrolidinyl propargylic carbonate 6a did not provide the possible azocine derivative, but only the product 7 resulting from Meyer-Schuster rearrangement through 1,3-oxo addition,27 in modest yield (Eq. 5). Similarly, the pyrrolidinyl propargylic ester 6b only gave a complex mixture, in which any azocine could be detected (Eq. 6). aCalculated yield relative to an internal standard (dimethylterephthalate).

bThe relative configuration of each diastereomer was established from the X-ray structure of the corresponding propargylic alcohol of the major diastereoisomer of 2g (See compound IIg in Supplemental Information).

(A) Labeling experiments.

(B) Rearrangement of pyrrolidine derivatives 6a and 6b.

(C) Kinetics experiments.

As mentioned above, the starting material was used as a mixture of diastereomers, but both were converted into a single product isomer, in the carbonate as well as in the ester series. This is particularly prevailing in the carbonate rearrangement, and the production of a single cis carbonate starting from two diastereomers suggests epimerization and equilibration along the reaction pathway.

Furthermore, discrepancies in terms of reactivity were notable when comparing the evolution of each starting diastereomers in some cases (see i.a. the formation of 2q, Scheme 2). To address and understand the stereochemical course of both reactions, kinetic experiments were performed on substrate 1h and 1s (Figure 2C). For the -OBoc derivative 1h, the minor diastereomer (red dots) was consumed significantly faster than the major one (blue triangles) (Figure 2C, left). Both diastereomers reacted according to an exponential decay fitting first-order kinetics. A similar behavior could be observed in the case of the ester derivative 1s. At the beginning of the reaction, the concentration of the major diastereomer (blue triangles) only slowly decreased, whereas the concentration of the minor diastereomer (red dots) rapidly decreased following an exponential regime (Figure 2C, right). After 25 min, the major diastereomer adopted a similar exponential regime.

Again, these profiles agreed with first-order kinetics. In both carbonate and ester series, the minor diastereomer (cis) was the more reactive, the carbonate being more reactive than the ester. Such reactivity difference probably reflects different pathways involving stereochemical constraints. This could arise at the opening of the bicyclic ammonium intermediate A, which must exist as a mixture of cis and trans diastereomers (Acis and Atrans), depending on the stereochemistry of the starting material 1. In the case of Acis the carbonyl function is appropriately placed to interact with the bridging C-N bond of the bicyclic ammonium. The oxygen lone pair is indeed almost perfectly aligned with the C-N * orbital, as shown by preliminary calculations (see Figure 3A and Figure S4 in Supplemental Information). Thus, ring expansion could rapidly occur via intramolecular nucleophilic substitution affording the dioxolanium intermediate Bcis. For the intermediate Atrans, the carbonyl group of the ester or carbonate moiety cannot be properly aligned to allow the opening of the azetidinium ring (see Figure 3A and Figure S4 in Supplemental Information). Moreover, the ring expansion should lead to dioxolanium Btrans with conformational constraints. The latter could drive a ring-opening/ring-closing equilibrium via the ene-iminium intermediate C, a process that would lead to epimerization to Bcis. These various factors probably account for the slower conversion of the major diastereomer. Overall, these data suggest that the azetidinium opening is the driving force due to the four-membered ring strain release.

Considering such features as well as the results of the labeling experiments, the following mechanisms can be postulated (Figure 3A). Nucleophilic addition of the strongly pyramidalized sulfonylated nitrogen to the gold(I)-activated alkyne should furnish cis and trans vinyl-ammoniumgold bicyclic intermediates (Acis and Atrans), which could evolve to an equilibrated mixture of cis and trans azepinyl carbonates and azepinium ester (Bcis, Btrans, and C respectively). The final step is the crucial deauration.

In the Boc series (1a-q, R = OtBu), the Bcis intermediate affords the cis-tetrahydroazepin-4,5-diol carbonate 2 by elimination of isobutene and a proton, which allowed deauration.13 This eliminationdeauration process seems to be faster for the Bcis intermediate than for the Btrans intermediate, as only the cis hydroazepinyldiol carbonate 2 is produced. It seems also faster than any other deauration pathway (see below).

In the ester series (1s-ac, R = Alkyl, Aryl), the demetallation step depends on the R1 substituent. With at least a methylene group (R1 = CH2R2 on Figure 4A) adjacent to the vinyl or iminium group in B or C respectively, protodeauration would occur via a diastereoselective proton elimination from this methylene unit (B1 or C1, Figure 4A), followed by an electrophilic cleavage of the C-Au bond, leading to compounds 3. Molecular modeling of simplified C1 intermediate, (see Figure S5 in Supplemental Information) highlighted that only the exocyclic E double bond can be formed considering the steric clash between the side chain (R2) and the sulfonyl moiety (SO2R). The formation of degradation products with ester substrates bearing a tert-butyl or a phenyl group directly linked to the alkyne moiety supported the latter protodeauration pathway (See Figure S3 in Supplemental Information).

To further corroborate this mechanism, substrate 1ao deuterated at the C-4 position (80%) was prepared and submitted to a pre-activated catalyst to limit adventitious presence of water brought by silver salt (Figure 2B, Eq. 4). Deuterium incorporation was observed at C-2 (37%) and C-4 (92%; starting material numbering) in the resulting product 3ao. The C-2 deuteration strongly supports protodeauration at that position through the proposed mechanism.

With terminal alkynes 1af-ak (C2, R1 = H on Figure 3B), a totally different process occurred leading to diastereomeric cis-bis(azepinyl)cyclobutane derivatives 5 (See Scheme 6). Such compounds could only arise from homodimerization. The latter could be due to the addition of the vinyl gold moiety of the azepinium C2 to the iminium moiety of another C2 monomer (D1 on Figure 3B).28 The resulting adduct still containing a vinyl gold and an iminium able to react intramolecularly to provide dimer 5 (D2 on Figure 3B). The always cis stereochemical outcome revealed that this dimerization is a stepwise process; a concerted reaction would indeed give the trans cyclobutane analog. The observed diastereomers resulted from the syn or anti relationship of the carbonate or ester substituents and this could be explained by addition on one face or the other of the azepinium C.

Deauration was thus achieved in this series by an unprecedented process. Interestingly, this also confirmed the above proposed mechanism (Figure 3A) through the azepinium intermediate C. (B) Proposed mechanism for the dimerization leading to 5.

Conclusion

In conclusion, we developed a modular and efficient ring-expansion of readily available N-sulfonyl-1-(azetidin-2-)yl propargyl alcohol derivatives 1 catalyzed by gold(I). cis-Tetrahydroazepin-4,5-diol carbonates 2 (17 examples, 45-95%) were obtained from tert-butyl N-sulfonyl 1-(azetidin-2yl)propargyl carbonates catalyzed by gold (I), while N-sulfonyl 1-(azetidin-2-yl)propargyl esters afforded E-2-alkylidenyltetrahydroazepin-5-ol esters 3 (12 examples, 11-77%). These synthetic methods were extended to the formation of dihydrobenzoazepine 2r' and cisbis(azepinyl)cyclobutane derivatives 5 (7 examples, 73-97%) by varying the functionalization pattern of the starting materials. Finally, a rigorous mechanistic study allowed us to fully understand the origin of the high chemo-and stereoselectivity of these gold-catalyzed rearrangements. Further investigations to extend such strategy to other cyclic or acyclic secondary sulfonamides are ongoing in our laboratory.

(

  A) Examples of important azepine derivatives. (B) Main synthetic routes to azepines. (C) The proposed gold-catalyzed ammoniumation/ring expansion strategy towards azepine derivatives from azetidines.

Scheme 4 .

 4 Scheme 4. Diastereoselective Synthesis of various N-sulfonyl E-alkylidene tetrahydroazepines 3. aIsolated yield. bCalculated yield relative to an internal standard (dimethyl terephthalate). cReaction run at 70 °C in dichloroethane (DCE) for 2 h. dEllipsoid representation of compound 3x XRD structure. eReaction run with 10 mol % of catalyst. fReaction run at 0 °C. Ts = para-toluenesulfonyl; Mbs = para-methoxybenzenesulfonyl.

Figure 2 .

 2 Figure 2. Mechanistic Study.

Figure 3 .

 3 Figure 3. Proposed Mechanism. aSimplified Molecular Modeling (MMFF) of the Postulated Vinyl-ammonium-gold(I) Intermediates Acis and Atrans. (A) Proposed formation of the azetidinyl carbonates 2 and esters 3.

Table 1 .

 1 Screening of reaction conditions for the formation of the N-tosyl cis-tetrahydroazepin-4,5diol carbonate 2a from azetidine carbonate 1a.

	Entry Catalyst (5 mol %)	Time (h)	Yielda 2a (%)
	1	Ph3PAuNTf2 24	50b
	2	Ph3PAuCl/AgSbF6	4	47
	3	LAuSbF6.MeCNc	4	64
	4	(p-CF3Ph)3PAuCl/AgSbF6	4	62
	5	IPrAuPF6.MeCN	24	29b
	6	JohnPhosAuSbF6.MeCN	6	72
	7	CyJohnPhosAuSbF6.MeCN	4	74
	8	CyJohnPhosAuNTf2	6	70
	9	AgSbF6 24	-d
	Ts = para-toluenesulfonyl; IPr = 1,3-bis(2,6-bis(diphenylmethyl)-4-methylphenyl)imidazo-2-ylidene;
	JohnPhos = (2-biphenyl)di-tert-butylphosphine ; CyJohnPhos = 2-(biphenyl)dicyclohexylphosphine.
	aYield calculated by integration of the 1H NMR spectrum of the crude product relative to an internal
	standard (dimethyl terephthalate).
	b50% of conversion.
	cL = tris(2,4-di-tert-butylphenyl)phosphite.
	dNo conversion.

Table 2

 2

	Entry Catalyst (5 mol %)	Time (h)	Yielda (%)
						3s	3s'
	1	CyJohnPhosAuSbF6.MeCN	2	32b	18
	2	Ph3PAuCl/AgSbF6	2	5b	19
	3	CyJohnPhosAuSbF6.MeCN	4	54	-
	4	Ph3PAuCl/AgSbF6	4	66	-
	5	Cy3PAuCl/AgSbF6	4	52	-
	6	(C6F5)3PAuCl/AgSbF6 4	80	-
	7	LAuSbF6.MeCNc	4	59	-
	8	AgSbF6 24	-d	-

. Screening of reaction conditions for the formation of N-tosyl (E)-2-hexylidene tetrahydroazepine 3s from azetidine 1s. Ts = para-toluenesulfonyl; CyJohnPhos = 2-(biphenyl)dicyclohexylphosphine. aYield calculated by integration of the 1H NMR spectrum of the crude product relative to an internal standard (dimethyl terephthalate). bReaction carried out without molecular sieves (MS). cL = tris

(2,4-di-tert-butylphenyl)

phosphite. dNo conversion.

ACKNOWLEDGMENTS

We gratefully acknowledge the French Ministry of Research and the CNRS for financial support. R.P., S.M. and N.K. thank the French Ministry of Research for PhD fellowships. The authors thank Dr Pierre de Frémont for crystallographic structure refinements of compounds 2g, 2h, 3x, 5af, 5ah and IIg.

EXPERIMENTAL PROCEDURES

Resource Availability Lead Contact Further information and requests for resources should be directed to and will be fulfilled by the Lead Contact, Aurélien Blanc (ablanc@unistra.fr).

Materials Availability

This study did not generate new unique reagents.

Data and Code Availability

Crystallographic data for 2g, 2h, 3x, 5af, 5ah, and IIg have been deposited in the Cambridge Crystallographic Data Center (CCDC) under accession numbers CCDC: 1936619, 1936620, 1848775, 1862796, 1862856 and 1936597. These data can be obtained free of charge from the CCDC at http://www.ccdc.cam.ac.uk/data_request/cif.

Representative Experimental Procedures for Gold(I)-Catalyzed Reactions Synthesis of cis-tetrahydroazepin-4,5-diol carbonates 2: To the appropriate 1-(1-sulfonylazetidin-2yl)yn-1-yl carbonate 1 (1 eq.) in anhydrous CH2Cl2 (c = 0.1 M) was added [CyJohnPhosAu(MeCN)]SbF6 (5 mol %). The reaction mixture was stirred at room temperature until completion (typically 4 h). The solvent was then removed under reduced pressure and the crude residue was purified by chromatography (SiO2, Et2O/heptane) leading to the desired cistetrahydroazepin-4,5-diol carbonate derivative 2.

Synthesis of E-2-alkylidenyltetrahydroazepin-5-ol esters 3: The appropriate 1-(1-sulfonylazetidin-2yl)yn-1-yl ester 1 (1 eq.) and 4 Å molecular sieves were dried under reduced pressure and placed under argon atmosphere, then anhydrous CH2Cl2 (c = 0.2 M) was added. Chloro[tris (2,3,4,5,6pentafluorophenyl)phoshine]gold(I) (5 mol %) and AgSbF6 (5mol %) were dissolved in anhydrous CH2Cl2 (c = 0.2 M). The reaction mixture was stirred at room temperature for 15 min shielded from light. This solution was added to the solution of 1-(1-sulfonylazetidin-2-yl)yn-1-yl esters 1. The reaction mixture was stirred at room temperature shielded from light until completion (typically 4 h). The solvent was then removed under reduced pressure and the crude residue was purified by chromatography using Et3N deactivated silica (SiO2, Et2O/heptane) leading to the desired E-2alkylidenyltetrahydroazepin-5-ol derivative 3.

Synthesis of cis-bis(azepinyl)cyclobutane Derivatives 5:

To a solution of the appropriate 1-(1sulfonylazetidin-2-yl)prop-2-yn-1-yl ester 1 (1 eq.) in anhydrous CH2Cl2 (c = 0.1 M) at room temperature was added the gold catalyst [CyJohnPhosAu(MeCN)]SbF6 (5 mol %). The reaction mixture was stirred at room temperature until completion (typically 3 h). The solvent was then removed under reduced pressure and the crude residue was purified by flash chromatography (SiO2, EtOAc/heptane) leading to the desired cis-bis(azepinyl)cyclobutane derivative 5.

SUPPLEMENTAL INFORMATION

Supplemental Information can be found online at … Document S1. Supplemental Experimental Procedures, Table S1, and Figures S1-S5.

Table S1. Full Optimization of the Formation of Compound 2s.

DECLARATION OF INTERESTS

The authors declare no competing interests.