David Méndez-Acuña
email: david.mendez-acuna@inria.fr

Variability Management in Domain-Specific Languages

Domain-specific languages (DSLs) have demonstrated their capability to reduce the gap between the problem domain and the technical decisions during the software development process. However, building a DSL is not an easy task because it requires specialized knowledge and skills. Moreover, the challenge becomes even more complex in the context of multi-domain companies where several domains coexist across the business units and, consequently, there is a need of dealing not only with isolated DSLs but also with families of DSLs. To deal with this complexity, the research community has been working on the definition of approaches that use the ideas of Software Product Lines Engineering (SPLE) for building and maintaining families of DSLs. In this paper, we present a PhD thesis that is aimed to contribute to this effort. In particular, we explain the challenges that need to be addressed during the process of going from a family of DSLs to a software language line. Then, we briefly discuss the state of the art, and finally we introduce a research plan.

Motivation

Domain-specific languages (DSLs) allow domain experts the expression of solutions directly in terms of relevant domain concepts and, for example, use generative mechanisms to transform specifications of DSLs into software artifacts (e.g. code, configuration files or documentation). Thus, abstracting away from the complexity of the rest of the system and the intricacies of its implementation. As a result, the construction of DSLs is becoming a recurrent activity during the development of software intensive systems [START_REF] Jézéquel | When Systems Engineering Meets Software Language Engineering[END_REF]. However, the engineering of DSLs is a complex task in the context of large companies such as Thales where the users often have different -and sometimes conflicting-requirements on the same DSL. For example, certain user may require a textual concrete syntax while another user prefers a graphical concrete syntax. Worst, for two different users, the meaning (or semantics) of a particular concept of the language may differ. When this occurs, we have a set of different DSLs that share some commonalities and that are distinguished each other by some particularities. In the literature this is known under the term of families of DSLs [START_REF] Liebig | Feature-oriented language families: A case study[END_REF].

Figure 1 illustrates this situation by presenting a segment of the family of DSLs for modeling finite state machines deeply studied in [START_REF] Crane | Uml vs. classical vs. rhapsody statecharts: not all models are created equal[END_REF] and composed of: Rhapsody [START_REF] Harel | The rhapsody semantics of statecharts (or, on the executable core of the uml)[END_REF], Classical statecharts [START_REF] Harel | The statemate semantics of statecharts[END_REF], and UML state machines diagrams [START_REF] Group | Uml specification[END_REF]. In this case, the commonalities among the three DSLs are the basic concepts of states and transitions. In turn, the differences are focused on the concepts of timed transitions and simultaneous events; while Rhapsody and UML include the notion of timed transitions, it is not supported in classical statecharts. On the other hand, classical statecharts support simultaneous events whereas both Rhapsody and UML adopt to the idea of run-to-completion i.e., each event is attended after processing the precedent one. Note that the second difference corresponds to a conflict in the semantics of the events dispatching functionality; all languages support that functionality but its semantics varies. Although the problem of dealing with families of DSLs is becoming more and more recurrent, currently there is little support for their implementation. Usually, each DSL member of the family is developed in isolation and from scratch what is not convenient because the construction of DSLs is a challenging task; to successfully perform such activity, an engineer must own not only quite solid modeling skills but also the technical expertise for conducting the definition of specific artifacts such as grammars, metamodels, compilers, and interpreters, among others. Nevertheless, as remembered by J.M. Favre in [START_REF] Favre | Empirical language analysis in software linguistics[END_REF] software languages are software too and, consequently, there is room for application of software engineering techniques that facilitate their construction process (i.e., software languages engineering [START_REF] Kleppe | Software Language Engineering: Creating Domain-Specific Languages Using Metamodels[END_REF]). In particular, the research community has realized that the ideas behind Software Product Lines Engineering (SPLE) can be used for facilitating the construction of families of DSLs. This paper presents a PhD thesis aimed to contribute in this effort. To do so, we briefly discuss the challenges that should be addressed during the process of going from a family of DSLs to a software languages line. Then, we discuss the state of the art, and finally we present a research plan.

Problem Statement

We have identified three challenges towards the construction software languages lines.

-Languages modular design. The main purpose of an approach for wellengineering families of DSLs is to increase the reuse in the sense that those language segments that are shared between two or more members of the family can be easily shared without being implemented independently and from scratch. To do so, it is necessary to separate those shared segments and encapsulate them in such a way that their specification artifacts can be actually used as part of the specification of the languages that require it. This separation implies a mechanism that allows to specify a language in different modules (a.k.a. language units) that can be later composed together to provide a complete language specification.

-Multi-dimensional variability modeling. It is worth noting that differences and particularities among members of a family of DSLs can be found in one or several dimensions of the specification. Indeed, the work presented in [START_REF] Cengarle | Variability within modeling language definitions[END_REF] provides a classification of the possible types of variability that can be found within families of DSLs. A brief summary of this classification is introduced below; the challenge in this case is to be able to propose an approach that supports these types of variability.

• Functional variability: One of the motivations for implementing families of DSLs is to offer customized languages that provide only the constructs required by certain type of users. The hypothesis is that the user will adopt the language easier if the language only offers the constructs he/she actually needs. If there are additional concepts the complexity of the language (and the tools) needlessly increases and "the users are forced to rely on abstractions that might not be naturally part of the abstraction level at which they are working" [START_REF] Zschaler | Vml* ? a family of languages for variability management in software product lines[END_REF]. Functional variability refers to the capability of selecting the desired language constructs for a particular type of user. Because of the abstract syntax of the language is the base of the specification -i.e., there can not be definitions neither in the concrete syntax nor the semantics for concepts that do not exist in the abstract syntax-the functional variability relies on the activity of selecting the subset of the abstract syntax required for a particular user.

• Syntactic variability: Depending on the context and, again, on the type of user, the use of certain types of concrete syntax may be more appropriate than other one. Consider for example the dichotomy between textual or graphical notations. Empirical studies such as the presented in [START_REF] Mora | Graphical versus textual software measurement modelling: an empirical study[END_REF] show that, for a specific case, graphical notations are more appropriate than textual notations whereas other evaluation approaches argue that textual notations have advantages in cases where models become large [START_REF] Eichelberger | A systematic analysis of textual variability modeling languages[END_REF]. More intermediate perspectives (e.g., [START_REF] Heidenreich | Derivation and refinement of textual syntax for models[END_REF]) state that graphical and textual notations more that mutually exclusive are complementary. Syntactical variability refers to the capability of supporting different representations for the same language construct. In terms of the specification, the syntactical variability can be viewed as different implementations of the concrete syntax specification unit for a given abstract syntax specification unit.

• Semantic variability: Another problem that has gained attention in the literature of software languages engineering is the semantic variation points existing in software languages. A semantic variation point appears where the same construct can have several interpretations. Consider for example the semantics differences that exist between state machines languages explored in [START_REF] Crane | Uml vs. classical vs. rhapsody statecharts: not all models are created equal[END_REF]. For example, the construct fork can be interpreted as a concurrency point where all the output transitions are dispatched simultaneously or simply as a bifurcation point where the output transitions are dispatched sequentially. Semantic variability refers to capability of supporting different interpretations to the same language construct. In terms of the specification, semantic variability can be viewed as different implementations of the semantic specification unit for a given abstract specification unit.

-Language units composition. After successfully modeling the variability, the next challenge is to compose a concrete DSL from a configuration of the family. In other words, after selecting the required language units, they have to interact each other for constituting a DSL that actually works. To do so, a mechanism for language unit composition is required. The main requirement on this composition mechanism is that allows to select from a set of language units the ones that should be combined. To do so, an external language that allows to express the composition is needed. In the context of software architecture that should be an architectural description language that allows to select a set of given components and compose them together. Note that this requirement is strongly related with the modularization mechanism.

Related work

The idea of families of languages has already been discussed in the software engineering literature. We can find "integral approaches" that propose an integral solution to the problem by addressing the three challenges presented above. Besides, there are "partial approaches" that deal only with one or two of these challenges (e.g., approaches for components-based DSLs development deal with languages modular design but do not consider variability management). In this section, we briefly discuss the strengths and weaknesses of integral approaches. Partial approaches will discussed in a publication currently in progress.

In the work presented in [START_REF] Vacchi | Variability support in domainspecific language development[END_REF] the modularization problem is treated by using Neverlang [START_REF] Cazzola | Domain-specific languages in few steps: The neverlang approach[END_REF] i.e., a tool that allows the expression of a software language in separate language units that can be later composed for generating an interpreter. In turn, the variability management mechanism is addressed by using the Common Variability Language (CVL). The main advantage of that work is that there is a clear mapping between the variability modeling approach with the modularization tool. The specifically the authors present the notion of "slices" as the mechanism for composing certain features of a language in Neverlang, then, providing support for functional and semantical variability. However, in Neverlang the abstract and the concrete syntax of language units are defined in the same artifact (i.e., a BNF-like grammar). As a result, it is not possible to support syntactical variability. Besides, there is not any support for static validation of compatibility between different language units. Hence, compatibility problems can only be detected in composition time by reading the errors produced by the composition tool.

The work presented in [START_REF] Liebig | Feature-oriented language families: A case study[END_REF] introduces the concept of crosscutting modularization, that is, the capability of decomposing a language not only into different language units but also decomposing a language feature into several tool features in order to support not only functional variability but also syntactical and semantical variability. Each tool feature represents a dimension of the language specification (e.g., syntax, semantics, constraints, documentation). The weaknesses of this approach are fundamentally the lack of static verification of composability and the lack of support for the definition of constraints in the variability model. Using this approach, the language engineer may produce invalid configurations by selecting, for example, a semantic feature that requires a nonselected abstract syntax feature. To void this, the variability model should be annotated with dependency constraints -what may produce as many constraints as existing features in the model-. We claim that this process can be facilitated by considering the definition of a staged processes where each dimension of the variability is defined in a different variability model and they are presented in order to the user in such a way that each step only includes selectable features.

Finally, work presented in [START_REF] Cengarle | Variability within modeling language definitions[END_REF] is a formalization of the foundations for managing variability managment in software languages lines. It considers the notions of functional, semantic, and syntactic variability. Besides, the authors present a languages benchmark called MontiCore [START_REF] Krahn | Monticore: a framework for compositional development of domain specific languages[END_REF] that supports modularization of modeling languages. Although there is not a technical impediment for implementing a family of DSLs using this variability modeling mechanism in junction with MontiCore, to the best of our knowledge, there is not a concrete implementation of an approach that includes both functionalities at the same time.

Proposed approach

Our solution approach includes one solution strategy for each one of the aforementioned challenges. These strategies are summarized below:

-Components-based DSLs' development. We propose to address languages modularization by means of an approach for components-based DSLs' development where the main concept is the notion of language units that interact each other by means of languages interfaces. The idea is that dependencies between language units are expressed as software interfaces that offer capabilities for compatibility checking and, in a latter phase, languages composition. Our preliminary results, suggest the need of the definition of different types of languages interfaces that support different scenarios for languages modularization such as languages embedding or languages extension.

-Multi-dimensional CVL for variability modeling: To deal with variability modeling within families of DSLs, we propose to enhance the CVL (Common Variability Language) with capabilities for multi-dimensional variability modeling. We choose CVL because it provides support not only for variability models but also for implementation models which facilitate the mapping between language features and language units. Besides, it introduces the notion realization models constitute a mechanism for configuring a DSL by offering multi-staged variability.

-Language units composition: In order to perform the composition of several language units we explore two strategies: compilation based composition and interpretation based composition. In the first case, the idea is to compose the language units specifications and produce a complete specification that can be latter used for automatically generating language tooling such as editors or type-checkers. In the second case, the idea is to maintain specification separated and generate the corresponding tooling for each one. After that, the services of each of tooling are orchestrated to offer an infrastructure for the DSL. Each strategy presents advantages and disadvantages. For example, whereas interpretation based composition may impact the performance of the language, it enables variability at runtime.

Evaluation & validation plan

Currently, the plan for the evaluation of the approach is based on two case studies. The first one is a family of languages for finite state machines that presents the syntax and semantics variation points that can be found in languages for expressing state machines and that have been largely studied in the literature (e.g., [START_REF] Crane | Uml vs. classical vs. rhapsody statecharts: not all models are created equal[END_REF][START_REF] Fecher | 29 new unclarities in the semantics of uml 2.0 state machines[END_REF]). It is worth to mention that this is a real-world case study that can be found in the context of Thales. The second case study is a family of languages for extended feature models that shows the different interpretation that constructs such as feature attributes have received.

The two case studies include the three dimensions of the variability. However, whereas the former requires the implementation of operational semantics the second one requires the implementation of translational semantics. Like this, we validate that our ideas are useful not only for executable DSLs but also for generative approaches that use transformations.

Fig. 1 :

 1 Fig. 1: A family of DSLs for finite state machines

6

  Current status and planned time-linePlanned time-line in terms of the expected contributions and current status (red line) is shown in Figure2.

Fig. 2 :

 2 Fig. 2: Planned time-line and current status

Acknowledgments

The research presented in this paper is supported by the European Union within the FP7 Marie Curie Initial Training Network "RELATE" under grant agreement number 264840 and VaryMDE, a collaboration between Thales and INRIA.


& +, -,+ +*. % ! / +, -,+ ' & ) % * & & % % % Scheme 3. First example of oligomeric organometallic Co(III) and Fe(II) complexes M-(-)-10a,b bearing bis-η 5 -helicenic ligands. i) CoBr2, oxidation, then NH4PF6; ii) t BuLi, FeCl2. 21

Nidal Saleh, a Chengshuo Shen, a and Jeanne Crassous* ,a

In honour of Prof. Thomas J. Katz.

π

[n]Helicenes † are inherently chiral polycyclic molecules formed of ortho$fused aromatic rings that become configurationally stable when n ≥ 5. Since the first synthesis of aza [5]helicenes in 1903, a large panel of organic carbo [n]helicenes and hetero [n]helicenes have been prepared either in their racemic or in their enantioenriched forms. 1 In addition, their helical topology combined with their extended π$ conjugated system provides helicenes with large optical rotation values and strong responses in electronic circular dichroism (ECD) as well as other properties such as non polarized and circularly polarized luminescence (CPL), conductivity, self$assembly, biological activity, catalytic activity, to name a few. 2 Potential applications in materials science are non linear optical (NLO) devices, chiral wave$ guides, chiroptical switches, molecular motors, metamaterials, macroscopic fibers, 3D displays, transistors, [START_REF] Amabilino | Chirality at the Nanoscale, Nanoparticles, Surfaces, Materials and more[END_REF][START_REF] Feringa | Molecular Switches[END_REF] ... The chemistry of these compounds has recently grown from the stage of an academic curiosity to an important field of research and several reviews have been dedicated to purely organic carbohelicenes or heterohelicenes. 1,2,5$12 At the same time, transition metal$ based helicenes are emerging as novel attractive chiral molecules for several reasons. Firstly, metals are powerful templates for assembling π-conjugated ligands into well defined molecular structures, simply by using the basic concepts of coordination and organometallic chemistry. 13 Secondly, novel properties may appear when metallic ions are grafted onto π$helical structures. [START_REF] Bozec | Molecular Organometallic Materials for Optics[END_REF] Finally, coordination and organometallic chemistry offer simple ways to tune the optical, chiroptical and electronic properties of the π$ligands since the topology together with the nature of the metal$ligand and ligand$ligand interactions can be readily modified by varying the metal center, its associated coordination sphere geometry, its redox state, ... This review is divided into two parts: organometallic helicenes, i.e. helicenes bearing metal$carbon σ bonds, and heterohelicene ligands for coordination chemistry. We focus here on molecular systems; examples involving deposition of organic helicenes onto metal surfaces or nanoparticles are not presented.

Organometallic helicene derivatives, i.e. helicenes bearing a C$M σ bond, are becoming more and more attractive molecules in materials science. 13,[START_REF] Bozec | Molecular Organometallic Materials for Optics[END_REF] For instance, original carbon$rich architectures such as organometallic polymers can be targeted. In addition, the incorporation of heavy metal centers within the helical π$conjugated system can significantly modify the photophysical properties of the helicene derivative due to strong spin$orbit coupling. Finally, the helicene core can adopt a non$innocent behaviour when grafted to a redox$active metal possessing efficiently interacting orbitals. As explained in the following examples, all these aspects lead to innovative applications such as responsive chiral polymers, circularly polarized phosphorescence emitters, or chiroptical switching devices.

A.1.1. Transition metal complexes with η 5 helicenic ligands

The organometallic chemistry of helicenes was pioneered by Prof. Thomas Katz and coworkers in the late 1970's. The original idea was to synthesize helical metallocene oligomers by reacting either cobalt or iron ions with helicene ligands of appropriate lengths and bearing terminal cyclopentadiene moieties. In 1978, they showed that achiral bis$cobaltocenium$ type ( ) and bis$ferrocene$type ( ) closed structures were formed instead of oligomers when using respectively short [4] or [5]helicene proligands (Scheme 1). [START_REF] Katz | [END_REF] Longer racemic [7]helicene proligand possessed the appropriate size to place the two cyclopentadienyl rings in front of each other thanks to a full turn of the helix. Then, reaction with FeCl 2 led to the formation of closed structure (Scheme 1) 16 in which the two terminal five$membered rings coordinate an iron atom in between. The X$ray crystallographic structure of complex was reported in 1983. 17 Compared to the ligand, it showed a dramatic decrease of the dihedral angle between the two terminal rings from 69.1° to 19.8°. In 1986, enantioenriched proligand M$($)$ , [START_REF] Furche | Note that the absolute configurations P$(+) and M$($) can be usually assigned to helicene derivatives from their strong typical signature in their circular dichroism spectra[END_REF] a structural isomer of , was prepared by a diastereoselective photocyclization process of a precursor bearing a chiral silyl ether in one of the terminal rings, followed by dehydration (Scheme 2). 18 Then, reacting enantioenriched M$($)$ with either FeCl 2 or CoBr 2 /oxidation yielded enantioenriched helical ferrocene M$($)$ ( [ ] D α = $3700, ee 62%, THF, C 0.022,) and the cobaltocenium analogue M$($)$ [ ] 578 α = $7100, * acetone, C 0.0045, ee 95%). Such complexes display huge specific rotations, probably as a consequence of the unbroken conjugation throughout the whole molecule. Their ECD spectra also display strong molar ellipticities corresponding to the classical strong CD$active band around 330 nm (molar ellipticities for M$($)$ : [ ] 335 θ = $1. 82 10 5 deg.cm 2 /dmol at 335 nm in THF, for M$($)$ : [ ] 330 θ = $2. 33 10 5 deg.cm 2 /dmol at 330 nm in CH 3 CN) accompanied with lower energy ECD$active bands probably corresponding to charge transfer transitions involving the metallic ion. 18 Iron and cobalt complexes bearing a bis$η 5 $[7]helicenic † ligand were the first examples of non racemic organometallic helicenes described in the literature. Note that such conjugated arrays with a helical structure might display interesting electrical conducting properties.

Scheme 2. Synthesis of enantioenriched organometallic Fe(II) (M-(-)-4) and Co(III) (M-(-)-5) helicenic complexes. i) hν, I2, propylene oxide; ii) TsOH, C6H6; iii) t BuLi, FeCl2; iv) CoBr2, oxidation, then NH4PF6.

18

In 1993, Katz's group reported three other cobalt helicene complexes, i.e. the Co III $ [8]helicene P$(+)$ , the Co 2 III $ [9]helicene P$(+)$ and the Co III $bis [8]helicene M$($)$ (Figure 1). 20 The specific rotation of P$(+)$ is 4500, * which is lower than for its [8]helicene proligand (6300), while that of (M,M)$($ )$ is $13600, slightly more than twice the specific rotation of the proligand. Complex P$(+)$ was prepared from enantioenriched [9]helicene P$(+)$ (see M$($)$ on Scheme 3) capped with two cyclopentadiene terminal rings synthesized via a diastereoselective double photocyclization of an appropriate chiral bis$ether. 21 Its specific rotation (8200), is similar to that of its bis$indenyl$ [9]helicene precursor (7800). However, in order to be able to compare different organometallic helicenes with different constitutions, one needs to consider the molar rotation (MR) * which takes into account the molecular weight of the compounds (see Table 1). Doing this, one can see that the influence of the metallic center on the chiroptical properties is significant. This increase in the MR values upon cobalt complexation can be explained by the presence of ECD$active bands in the low$energy region (> 480 nm) that involve charge transfers between the metal orbital and the π$ligand (vide infra) and that significantly contribute to the MR value. Cyclic voltammetry of complex was used in order to see if a communication existed between the two Co ions through the helicenic bridge. Two reversible Co III /Co II reduction waves separated by 130 mV were observed, indicating a possible weak interaction. However UV$vis, CD and EPR spectroscopies of one$electron reduced species revealed that the delocalization through the whole molecule is almost ineffective and that near$ infrared inter$valence transitions were absent. 22 " # $ " # $ Figure 1. a) Chemical structures of diverse cobaltocenium complexes based on [8] and [9]helical mono-or bis-indenyl ligands. 20 ! . Specific and molar rotations * of selected helicenic ligands and complexes. 21,23 $7800 $35460 P$ 23 +4500 +33975 P$ 23 +8200 +92740 M$ 23 $13600 $140760

Sample/length (n) [ ] D α * [ ] max , D φ a,* M$
a Considering 100% enatiopurity.

Katz et al. finally succeeded in preparing helical metallocene oligomers M$ or P$ " ,! from [9]helicene M$ or P$ (Scheme 3). 21 Indeed, the short oligomeric colbatocenium complex ($)$ " containing 2 to 4 helicenic units and linked by Co III atoms, as identified by fast atom bombardment mass spectrometry and elemental analyses (average molecular weight 1.9 10 3 g.mol $1 ), was prepared from bis$indenyl [9]helicene † M$ ($)$ and its chiroptical properties were studied. This optically active oligomer displays a very large [ ] D α ($26000 for 100% ee), * which is 4.1 times greater than the proligand M$($)$ . Its circular dichroism was also investigated and the molar ellipticities at 474 and 263 nm ([θ] = $8.4 10 5 deg.cm 2 /dmol and $3.3 10 5 deg.cm 2 /dmol, assuming the molecular weight to be 1.9 10 3 ) were found 7.2 and 6.0 times larger than the corresponding ECD$active bands in M$($)$ . Isoelectronic ferrous complex (+)$ "! was also prepared and showed huge specific rotation ( [ ] D α = 27000, benzene, C 0.1), * but it was impossible to obtain it in chemically pure form. 23 The cobaltocenium oligomers such as " were extensively studied and it was shown that oligomers of different lengths can be obtained depending on the solvent used for the oligomer synthesis. Toluene gave heptamers, the longest systems obtained due to increased solubility. These compounds exhibited strong chiroptical responses, with specific rotations reaching 32000$34000 (acetone, C 0.002) and strong CD active bands with ε values between 300$1200 M $1 cm $1 . 23 However, these values corresponded to no more than the addition of several cobaltocenium units, which suggested that no efficient electronic interaction occured between each unit (not a mixed$ valence system). 21 This was further confirmed by the cyclic voltammetry which displayed a large Co III /Co II reduction wave at a potential similar to the corresponding mononuclear and dinuclear species. However and very interestingly, the electrolytic reduction of cobaltocenium oligomers in acetonitrile on a Pt electrode yielded the formation of a film which appeared conductive. This film could be reversibly oxidized and dissolved. Another interesting aspect is the reversible reduction and oxidation of these oligomers in solution using respectively cobaltocene in excess and air. Significant changes were observed in the CD spectrum of " which interconverts between the fully oxidized and the fully reduced species with the presence of several isosbestic points (Figure 2). In fact, it can be considered as the first example of helicene$based redox$triggered CD$active switch (vide infra)! Organometallic pentahelicene analogues $ were prepared by Thiel et al. from dibenzo[c,g]fluorenide (Dbf $ ) acting as a cyclopentadienide ligand (Figure 3). However, these ferrocene, cobaltocenium and ruthenocene$type complexes were not resolved into pure enantiomers and their configurational stability was not studied. 24 28 By reacting these helicenes with [Cp*IrCl 2 ] 2 , the η 6 $iridium complexes were obtained as isomeric mixtures $ , $ and " $ , as evidenced by 1 H and 1 H$ 1 H NOESY NMR experiments, which after several days led to the more thermodynamically stable complexes , , and " . In all cases, it was therefore observed that the metal fragment coordinates to the terminal ring of the helicene ligand, with a clear preference to coordinate to the # ring at the beginning of the reaction. Furthermore, while the coordination to ring # was fast (a few seconds), the isomeric process leading to complexation to ring was slow (several days). Such movement along the helical backbone was proposed to proceed via two routes: either through a migration of the metal cationic unit walking over the helix surface or through a dissociation/association process. DFT calculations showed that the migration of iridium walking over the surface involves a haptotropic rearrangement from η 6 $arene to η 3 $C=C$C followed by a new haptotropic migration to another η 6 $arene on the exo side. An earlier theoretical study by Sola et al. on the migration of tricarbonylchromium on a tetrahelicene also suggested this haptomigration and showed the preference for the metal to bind to the outer rings which are less substituted and more aromatic. 29 From a general viewpoint, the presence of an alkyl substituent in the helicene ligand facilitates the coordination and the formation of η 6 $arene complexes. By following the same synthetic strategy with more equivalents of [Cp*IrCl 2 ] 2 , the bimetallic η 6 $Ir complex (Figure 4) was obtained; it corresponds to the maximum number of metal units that could be bonded. Finally, the reaction of ligand with [(η 6 $ cymene)RuCl 2 ] 2 yielded the monometallic η 6 $Ru complex whose structure was ascertained by X$ray crystallography which showed a decrease of the helicene's helical pitch when coordinating the metal. 28

A.1. 3. Helicenes acting as molecular tweezers

The ability of carbo [7]helicene to act as a chiral "molecular tweezer" was examined by several groups. In 2006, Saini and Deb reported a computational study of the interaction of carbo [7]helicene with alkali cations. The two terminal benzene rings were reported to act as "crocodile's jaws" that can chelate a cation. The stability of complexes increased with the order Na + >K + >Cs + . 30 Later on, Johansson and Patzschke theoretically investigated the trapping of metallic ions (Cr, Mo, W) by carbo [7]helicene. 31 The same year, an Ag(I) complex of carbo [7]helicene was prepared by Fuchter et al.. 32 This complex was characterized by X$ray crystallography of a racemic sample (Figure 5a) which evidenced that the Ag + cation binds at the edge of the two terminal rings of the helicene through η 2 $C=C binding modes. Such kind of complexes may have potential interest for the construction of solid$state devices such as electric conductors.

+ + + + + ) + * - !) +* -0 ) + * / " !" ! / 1 + + " !" ! / 1 + !" ! / 1 ) + * - ) +* -0 ) + * / ) + * - ) +* -0 ) + * / ) + * - ) +* -0 ) + * / " # $ &
In 2009, a hypothetical ferrocene formed from a polycyclic hydrocarbon ligand bearing 10 fused cyclopentadiene rings was considered as a potentially stable helicoid complex (Figure 5b). 34 Note that the ferrocene and cobaltocenium described on Scheme 1 were actually the first examples of helical molecular tweezers.

$% % & ' % &

Aromatics grafted with appropriate metal centers such as Fe(II) and Ru(II) through a bridging π$system (alkynyl, vinyl, aryl) are known to exhibit efficient electronic metal$ligand interaction and interesting electronic and optical properties. 22,35 In 2012, our group prepared a carbo [6]helicene bearing one or two vinyl$ruthenium moieties. 36 These enantiopure helical organometallic species M$($)$ and P$(+)$ ,! (Scheme 5) were readily prepared by simple hydroruthenation of enantiopure mono$ and bis$2$ethynyl$carbo [6]helicenes M$($)$ and P$(+)$ ,! and displayed several interesting and innovative features. First of all, it was observed that the MR values are doubled upon grafting of the organometallic moiety (P$

: [ ] 23 D α = +3133, [ ] 23 D φ = +11030 (CH 2 Cl 2 , C 5 10 $5 M), P$ : [ ] 23 D α = +2850, [ ] 23 D φ = +23770 (CH 2 Cl 2 , C 5 10 $5 M
). * Similarly, the CD spectra are significantly modified with the appearance of new bands at longer wavelengths in ,! compared to ,! due to extended π$conjugation along the Ru$vinyl$helicene backbone. This efficient interaction between the metal center and the π$ helical core is clearly seen in the molecular orbitals, such as in the HOMO of ,!, and makes the vinyl$helicene behave as a non$innocent ligand. 36 As a consequence, upon oxidation of M$ or P$ to M$ or P$[ ] •+ , the chiroptical properties are greatly modified (Figure 6). Furthermore, the reversibility of the oxidation/reduction process and the possibility to read$out the ECD response enabled us to conceive a helicene$based redox$triggered chiroptical switch. 36 Also interesting is the fact that the two Ru centers are not independent in ! since stepwise mono$ and bis$oxidation was observed (two oxidation waves separated by 130 mV). Note that in ,! the Ru are not stereogenic centers.

More recently, enantiopure vinyl$osmium$helicene complexes M$($)$ and P$(+)$ (Scheme 6) were prepared by hydro$osmylation of enantiopure M$($)$ and P$(+)$ 37 and enabled access to carbene$osmium$helicene M$($)$ and P$(+)$ by using HCl. In these unprecedented helicenic osmium$ carbenes the electronic interaction between the organometallic moiety and the helicene core was broken, which modified the MR values and ECD intensities. Interestingly, we were able to perform the reverse → transformation with NEt 3 , potentially leading to a helicene$based acid$base chiroptical switch. This example illustrates the inspiration from simple and well$known organometallic chemistry for the design of new kinds of helicene$based molecular switching systems.

& - , # # 0 , # # 0 & , # # 0 , # # 0 ! & Scheme 6.
Synthesis of enantiopure helicene-grafted vinyl-osmium complex P-25 and osmium-carbene P-26 from enantiopure P-23a. i) HOs(CO)Cl(P i Pr3)2, CH2Cl2, r.t., Ar, 3 days. ii) HCl, toluene. iii) NEt3, CH2Cl2.

37

In 2012, Licandro and coworkers reported the synthesis of racemic tetrathia [7]helicene$based complexes substituted with either a ferrocene ( $ , Figure 7) or a (η 5 $cyclohexadienyl)$ tricarbonylmanganese ( ,!). 38 The effective conjugation of the ferrocene moieties with the helicene system through the alkynyl bridges was ascertained by electrochemical and spectroscopic studies. For example, a systematic bathochromic

- + # # 0 , # # 0 + -'# # 0 & ! -! ! -! ! - - + # # 0 , # # 0 + # # 0 , # 0 # + -'# # 0 & !
shift of the π$ π* transitions was observed in the UV$vis spectra of the complexes as compared with their corresponding proligands. Furthermore, the reversible oxidation wave corresponding to the Fc couple in $ was found to be shifted to more positive values, meaning that the Fc moiety was more difficult to oxidize when conjugated with the ethynyl$ thiahelicene moiety. Interestingly, an electroactive conductive film, probably constituted of dimers of , could be prepared on a glassy carbon electrode, upon several cyclings around the first oxidation peak. 38 Note that no electronic communication between the two Fc moieties was observed in !.

#%

Up to now, the synthesis and properties of heterohelicenes, i.e. helicenes bearing heteroatoms, have been thorougly studied. 1,2,5$12 In 2010, our group prepared the first class of organometallic helicenes incorporating a metallic ion within their helical backbone. Indeed, inspired by the cyclometalation reaction of phenyl$pyridine derivatives, [START_REF] Yersin | Highly Efficient OLEDs with Phosphorescent Materials[END_REF] we developed a short and efficient strategy to prepare cyclometalated helicene derivatives, named metallahelicenes, by an ortho$metalation reaction of a phenyl$pyridine bearing an extended ortho$fused polycyclic π$system (Scheme 7).

Scheme 7. General synthesis of metallahelicenes by orthometalation reaction.

A.2.1. Platinahelicenes

The ). X$ray crystallography of complex (see Scheme 9) enabled to identify it as a structural analogue of carbo [6]helicene with for example similar helicities (as defined as the dihedral angle between the two terminal rings). [START_REF] Norel | [END_REF] The stable, soluble, and neutral complexes $ were readily obtained as enantiopure samples by HPLC separations over chiral stationary phases. Later on, enantiopure cycloplatinated helicenes bearing a sulfoxide ligand, either dmso (

) or enantiopure methyl$p$tolyl$sulfoxide ( (, ) were respectively prepared by direct cycloplatination of proligands ,(, in refluxing toluene and under basic conditions. Enantiopure Pt$ [6]helicene was obtained by chiral HPLC. More interestingly, Pt$ [8]helicene ( was obtained from 1$pyridyl$ [6]helicene proligand (±)$ ( in enantiomerically and diastereomerically pure forms by using preferential crystallization of diastereomer (M,R S )$ ( over (P,R S )$ ( combined with column chromatography. Similarly, diastereomeric (P,R S ,R S )$ and (M,R S ,R S )$ consisting of bis$platina [6]helicenes were prepared from 1,3$bipridyl$ naphtalene and obtained as pure diastereomers by taking advantage of their different solubilities in different solvents. 42 Finally, by subsequently replacing the dmso or chiral sulfoxide by an acac ligand, enantiomeric M ($) and P$(+) pairs of ,(, were obtained (Scheme 9). Scheme 8. General synthesis of metallahelicenes 31a-e by orthometalation reaction. Different mono-platinahelicenes prepared using this metodology. i) K2PtCl4, ethoxyethanol, H2O, reflux, 16 hrs; ii) pentane-2,4-dione, Na2CO3, ethoxyethanol, reflux, 2 hrs. The diversity of platinahelicenes prepared with different sizes enabled us to study and compare their photophysical (UV$ vis and luminescence spectra), and chiroptical properties (ECD spectra, MR values, and CPL activity). For example, the UV$ visible spectrum of compounds displayed in Figure 8 shows several intense absorption bands below 410 nm that appeared red$shifted compared to those of its corresponding proligand due to an elongation of the π$conjugated system via the orthometalation ring closure. In addition, two weak lower$energy broad bands (> 450 nm) arising from interactions between the metal and the π$ligands were observed. 41 The same low$energy tail was present for Pt II $ [8]helicene

( and Pt 2 II $ [6]helicene
. 42 The ECD spectra of the organic 2$pyridyl$ [6]helicene ( and organometallic Pt$[6]helicene displayed similar overall shape (Figure 8) but with a blue$ shifted high$energy band for compared to (; Pt$ [8]helicene ( displayed a stronger and more red$shifted ECD spectrum compared to Pt$ [6]helicene , a well$known tendency for helicenes that can be attributed to an enlargement of the π$electron system; Pt 2 $ [6]helicene displayed a significantly different CD spectrum from ,( and (, because of cancellation effects of CD$active transitions with opposite sign rotatory strengths and similar energies, as indicated by TDDFT calculations. 42 Interactions between the platinum center and the π$ligands are responsible for strong phosphorescence at room temperature, thanks to efficient spin$orbit coupling. [START_REF] Yersin | Highly Efficient OLEDs with Phosphorescent Materials[END_REF] Indeed, platinahelicenes & ) and () are efficient deep$red phosphors, with emission maxima between 630$700 nm, quantum yields around 5% in deoxygenated solution at room temperature (Table 2) and luminescence lifetimes of 10$20 s. Interestingly, platinahelicenes ,(, displayed circularly polarized luminescence with dissymmetry factors (g lum values) as high as 10 $2 , which corresponded to one order of magnitude bigger than for usual organic helicenes. 1 The g lum values appeared positive for the P enantiomers and negative for the M, which seems to not always be the case. The platinahelicene chemistry demonstrates how powerful organometallic chemistry can be to generate new helical structures with interesting non polarized and circularly polarized luminescence properties. An additional advantage is the redox activity of the metallic ion. Indeed, the Pt II center in P could be readily oxidized to a Pt IV by reaction with iodine, thus giving new enantiopure Pt IV $ [6]helicene P with chiroptical properties that were different from P and with the luminescence switched off (Scheme 10a). 41 Complex P could be reduced back to P with zinc powder. Another important aspect in the chemistry of metallated helicenes is the use of coordination chemistry to assemble several helicene moieties within the same molecular architecture, as demonstrated in the bis$(Pt III $helicene) scaffold 41,44 ) and in the Pt II $bis$helicene 45 structure ) (Scheme 10b). It is worth noting that such assemblies of helicenes are impossible to prepare by using organic chemical processes. These organometallic assemblies displayed several interesting and innovative features. As illustrated on Scheme 11a, an isomerization process from heterochiral (M,P)$ to the more stable homochiral (P*,P*)$ occured when refluxing in toluene for several days, certainly due to high steric congestion around the Pt III $Pt III scaffold. In addition, enantiopure (P,P)$(+) and (M,M)$($)$ complexes were prepared from enantiopure samples of and revealed highly intense circular dichroism spectra and huge optical rotations 0.04)). * Such an increase was interpreted as the consequence of efficient conjugation between the two helical π$ligands through the Pt$Pt bond (σ$π conjugation). 41,44 Concerning the synthesis of ) , the C$H activation process of the second cycloplatination step combined with a similar heterochiral to homochiral dynamic isomerization globally resulted in an unprecedented diastereoselective/enantioselective process. 45 Note that Pt II $bis$helicene assemblies ) displayed the same structural features as Pt II $(ppy) 2 complexes (ppy:2$phenyl$ pyridinato) described by von Zelewsky et al., 46 in which two ppy$type are arranged in mutual cis position (trans effect, Scheme 11b), and with either a bow$shaped geometry or a /Λ stereochemistry around the Pt center (Scheme 11c).

A.2.2. Osma and irida helicenes

It can be seen from the previous paragraph that the cycloplatination of π$helical ligands leads to a rich variety of platinahelicenes with different structures, redox states, and uncommon assemblies. This synthetic strategy was applied to other metallic centers such as Ir III or Os IV , thus leading to irida [6]helicenes [START_REF] Norel | [END_REF] and ! with either two or four helicenes ligands surrounding one or two Ir centers respectively and to osmahelicene . 47 Similar organometallic helicenes bearing other metallic centers such as Ru(II) or Re(I) are currently under investigation in our group.

47

* # (

Metals are powerful templates for assembling π$conjugated ligands with coordinating heteroatoms into well$defined molecular structures. [START_REF] Lehn | Supramolecular Chemistry: Concepts and Perspectives[END_REF][START_REF] Sauvage | Transition metals in supramolecular chemistry[END_REF] This approach involves a careful design of a helical π$conjugated ligand with appropriate coordination functionalities guided by the basic concepts of coordination chemistry (trans$effect, hemilability…). It enables the construction of original chiral architectures that are difficult to achieve by regular organic chemistry. This strategy is also fruitful for the development of new catalytic systems for asymmetric synthesis and innovative molecular materials with targeted properties furnished by the type of metal and ligand chosen.

* ( % %

The most widely used ligands in asymmetric transition metal catalysis are chiral phosphanes. The first helicenic phosphane ligands 50 such as 2,15$bis(diphenylphosphino)$ hexahelicene , also named Heliphos or more often PHel (Figure 10), were prepared by Brunner et al. in 1997. 51 The same year, enantiopure samples of PHel were obtained by Reetz et al. 52 by using chiral HPLC and tested in the rhodium catalyzed asymmetric hydrogenation of di$methyl itaconic acid ester. A 39% ee was obtained in this pioneering example of asymmetric catalysis using a helicene$based complex. Note that the intramolecular P$P distance (6.48Å) obtained from the X$ ray crystallographic structure is too large for PHel to act as a ditopic chelating ligand and suggests that it rather behaved as a monodentate one. In 2000, the same enantiopure ligand was used in a palladium catalyzed kinetic resolution involving allylic substitution, with ee's up to 99% for the starting material. 53 In 2000, Katz et al. successfully used a bis [5]helicenediol ( [5]HELOL, (M,M,S)$ , Figure 10) in the asymmetric addition of diethylzinc to aromatic aldehydes with ee's up to 81 %. 54 Note that the [5]HELOL ligand mixes helical and axial chirality. Furthermore, the metal center placed in the central groove of the ligand probably helps with the efficiency of the asymmetric catalysis. A pre$transition state involving the coordination of zinc was proposed by the authors for rationalizing the approach of the aldehyde. Two years later it was shown by Yamagushi et al. that similar enantioselective addition of Et 2 Zn to aromatic aldehydes was catalyzed with moderate ee's by a macrocyclic amide bearing two helical 1,12$ dimethylbenzo[c]phenanthrene$5,8$dicarboxylates. 55 In 2003, the same group prepared phosphites displaying helical, axial, and central chirality, such as (M,M,S,1R,2S,5R)$ ", as effective ligands for the rhodium$catalyzed enantioselective hydrogenation of di$Me itaconate with ee's up to 96%. It was shown that the stereochemistry of the helicene moiety plays an important role in the asymmetric induction, and matched/mismatched phenomena were observed between helical and axial chirality. 56 In 2011, Stary et al. used chiral ligands such as (P,S)$(+)$ bearing a pendant phosphite moiety either in asymmetric Rh$catalyzed hydroformylations (moderate ee's up to 32%) or in Ir$catalyzed allylic amination reactions (high ee's up to 94%). 57 Very recently, Marinetti et al. prepared phosphahelicenes structures as efficient platforms for asymmetric gold catalysis (in cycloisomerizations of N$tethered 1,6$enynes and dienynes). 58 Fine$tuning of these phosphahelicene ligands furnished efficient catalytic systems such as (S P ,P)$endo$ displaying high activity and giving high ee's. In (S P ,P)$endo$ , the P atom is embedded within the helical structure and the gold atom points towards the helical groove (see model in Figure 10). Iridium$phosphahelicene complexes of have also been prepared and may also show good catalytic efficiency in the future. 59 Note that other gold$ catalyzed cycloisomerizations, i.e. intramolecular allene hydroarylation, were also performed recently by Hashmi, Licandro et al. using tetrathiahelicene phosphane ligands (such as in Thiaheliphos complex ) but in racemic series. 60 The same Thiaheliphos ligand was used in enantiopure form in the rhodium catalyzed hydrogenation of itaconic acid ester and 2$ acetamidoacrylate, giving final products with ee's up to 40%. 61 Finally, in all the former cases the ligands possess either P or O heteroatoms that enable coordination to the transition$metal center for enantioselective catalysis. It is however worth mentioning that helical ligands without coordinating heteroatoms, i.e. carbo [6]helicene and a thia [7]helicene have proven efficient in the autocatalytic process based on addition of diisopropylzinc to pyrimidine$5$carbaldehyde (Soai reaction). 62,63 Note that in 2007 Ben Hassine, Marinetti, et al. synthesized racemic 2$(diphenylphosphino)heptahelicene and prepared its ruthenium complex of Ru( )Cl 2 cymene. More importantly, the enantiomeric resolution of was performed by reaction with enantiopure ortho$metallated bis$[R$1$ (naphthyl)ethylamine$C 2 ,N]$di$ $chloro$dipalladium complex followed by chromatographic separation of the resulting diastereomeric complexes (P,R)$ and (M,R)$ ! (Scheme 12). This is a nice use of coordination chemistry to enantiomerically resolve a helicene bearing a coordinating unit. 64 In 2009, 3$diphenylphosphino$hexahelicene and its Ru(II) and Pd(II) complexes were prepared by Ben Hassine et al. but in racemic forms. 65 To our knowledge these complexes have not been tested in catalysis.

# ! # ## ! 6$7-# #- 32 30 , , ' & '"& 38 # , , ,- % , ,% -, ,% ,% 637- ' & 31 , , # , % , ! % , ! 2 ! 3 ' 2 ! 3 & 3
. i) bis-[R-1- (naphthyl)ethylamine-C 2 ,N]-di--chloro-dipalladium complex, acetone, r.t.; ii)
column chromatography; iii) dppe, CH2Cl2, r.t..

64

* # + , (

Coordination chemistry offers a simple way to tune the optical and electronic properties of the π$ligands since both the coordination sphere geometry and the nature of the metal$ ligand interaction can be readily modified by varying the metal center. This will produce a great impact on the properties of the molecule. However the selectivity aspects (kinetics vs. thermodynamics, stereoselectivity, ...) are major issues that need to be controlled.

B.2.1. Coordination of monodentate helicenic ligands

Compared to carbohelicenes, the thiahelicene series is easier to post$functionalize and can be decorated with groups displaying good coordinating ability, such as cyano ligands. In this context, racemic tetrathia [7]helicene nitrile derivatives were prepared by Licandro, Maiorana et al. and their Ru(II) and Fe(II) complexes were synthesized. 66 An interesting isomerization process of the Ru(II) complex was observed upon slow crystallization (Scheme 13). Such iron and ruthenium complexes were prepared for future NLO studies provided that these complexes are available in enantiopure forms. Note that their UV$vis spectra revealed metal to ligand charge transfer (MLCT) transitions in the low energy domain.

66

Azahelicene ligands (helicenes bearing one or several nitrogen atoms in their π$conjugated backbone) have been the focus of great attention since they can be readily prepared by a diversity of methods 1,[START_REF] Dumitrascu | [END_REF]11 and can be used as chiral organic catalysts [START_REF] Narcis | [END_REF] or as molecular materials in optoelectronic devices. 67,68 Among their intrinsic features are their supramolecular organization in the solid state, 68 their fluorescence and phosphorescence properties, 69 and their strong proton affinity depending on the position of the N atom within the helix. 70 In 2008, Stary et al. used aza [6]helicenes ,! (Figute 11) as N ligands for coordination, and 1:2 Ag I $ aza [6]helicene complexes such as were prepared and charaterized by X$ray crystallography. Complex exhibited a T$shaped structure with two homochiral aza [6]helicene units coordinated and the silver atom embedded within the π$electron system. Actually, the coordination environment around the silver atom was best described as a trigonal bipyramid, in which each 1$aza [6]helicene actually binds as an η 3 $N,C,C ligand, with the nitrogen atom and C=C bond occupying axial and equatorial positions, respectively. 71 The same group observed similar preferential formation of homochiral Ag + complexes in the gas phase. 72 Indeed, they prepared enantiopure deuterated 1$aza [6] ) by electrospray mass spectrometry. A pronounced preference for the formation of homochiral (P,P) and (M,M) dimers over the heterochiral (M,P) was observed. Competitive experiments with mixtures of 1$ and 2$aza [6] helicene ,! suggested a largely preferred coordination of 1$aza [6] helicene to the silver(I) cation, in agreement with stronger basicity. The distinction between homochiral and heterochiral dimers of 1$aza[n]helicenes (n = 1,7) with alkaline cations (Li + , Na + , K + ) was studied by Alkorta et al. by DFT calculations and was found greater in the case of lithium with n = 6. 73 The racemization barriers of the 1:1 complexes were also examined and appeared larger in the complexes than in the non$coordinated ligands. Very recently, the coordination of an aza [6]helicene to square planar platinum(II) revealed a new aspect of reactivity in chiral transition metal complexes. 74 Indeed, in collaboration with Mele's group, we have observed that cis$PtCl 2 (NCEt)PPh 3 reacted differently with either racemic or enantiopure 4$ aza [6]helicene giving respectively cis (racemic, ) and trans (enantiopure, ) 4$aza [6]helicene$bis$chloro$ triphenylphosphine$platinum(II) complexes (Scheme 14). This unexpected reactivity is explained through a dynamic process (crystallization$induced diastereoselective transformation). Indeed, the racemic complex cis$ readily precipitated in refluxing toluene therefore displacing the cis$ "/trans$ " equilibrium while the enantiopure series was soluble in refluxing toluene and yielded the more thermodynamically stable M$ or P$trans$ . Furthermore, X$ray crystallographic structure of racemic complex cis$ revealed the appearance of planar chirality around the square planar Pt center whose handedness was imposed by the helicene's one through efficient chiral induction (Scheme 14).

B.2.2. Coordination of extended π π π π conjugated helicenic P,N bidentate ligands

Heteroditopic 2$pyridylphosphole derivatives have been utilized as 1,4$chelating ligands towards transition metals. 75,[START_REF] Crassous | Phosphorus Chemistry: Catalysis and Material Science Applications, Series: Catalysis by Metal Complexes (CMCO)[END_REF] They possess two coordination centres with different stereo$ electronic properties ("hard" nitrogen and "soft" phosphorus centres) which, in accordance with Pearson's antisymbiotic effect (trans effect), can control the orientation of two 1,4$P,N ligands around a square planar d 8 $metal centre (Pd 2+ , Pt 2+ ), thus yielding C 2 $symmetrical complexes with optimized optical properties such as second order NLO activity. As a continuity of this work, our group has synthesized aza [4]helicene$ phosphole that acted as an efficient bidentate 1,4$P,N$ chelate ligand and yielded stable metal$bis(helicene) complexes and of respective formula [Pd( ) 2 ] 2+ and [Cu( ) 2 ] + (Scheme 15). [START_REF] Shen | [END_REF] Indeed, upon coordination to a square$planar Pd(II) and a tetrahedral Cu(I) ions, the metal centers became stereogenic, with respectively distorted square$planar or tetrahedral spiro geometry. Although aza [4]helicene$phosphole have two stereogenic elements (the helix and the P atom) that are configurationally labile due to low inversion barriers, the obtention of X$ray crystallographic structures of assemblies and allowed to examine the stereoselectivity of the Pd(II) or Cu(I) coordination of these model molecules (see Scheme 15). Among all the possible stereoisomers that can be formed, C 2 $symmetrical Pd II $bis(helicene) was obtained in the solid state as a pair of enantiomers (M,M,S P ,S P ,Λ Pd ) and (P,P,R P ,R P , Pd ) only. Likewise, the (P,M,S P ,S P ,Λ Cu )$ and (M,P,R P ,R P , Cu )$ Cu I $bis(helicene) assemblies were obtained. Note that in both cases, the simplicity of the 31 P and 1 H NMR spectra was also consistent with high stereoselectivity of the coordination process in solution. We have then prepared aza [6]helicene$phosphole with enantiopure P$helix but as a (P,R P ) and (P,S P ) epimeric mixture due to the inversion of the stereochemistry at the phosphorus atom. 78 Complexation to Pd(II) and Cu(I) yielded stable metal$ bis(helicene) complexes and . It was found that Pd(II) was more efficient than Cu(I) to stereoselectively organize two aza [6]helicene phosphole ligands around the metallic ion thanks to steric hindrance combined with trans effects and configurational lability at the phosphole's P atom. Indeed, in complex (P,P)$ , the lability enabled the P atom to adapt its configuration upon coordination in order to minimize the steric congestion induced by the two helical units, while the trans effect resulted in aligning the two P,N chelates in a cis fashion around the Pd(II) center. Overall, the P handedness of the aza [6]helicene unit was transferred to the P atom fixed at R stereochemistry which in turn imposed the configuration to the Pd center. DFT calculations further evidenced that the (P,P,R P ,R P , Pd ) diastereomer was 19.4 kcal/mol more stable than the (P,P,S P ,S P , Pd ) one (Figure 12) and that the complex having a Λ Pd configuration is not a minimum on the potential energy surface. 79 On the contrary, theoretical calculations performed on complex revealed that several diastereoisomers have similar energies (Figure 12) and consequently that the coordination to Cu(I) was not stereoselective.

Thanks to such a highly controlled stereoselective process, the chiroptical properties of the Pd II $bis(helicene) assemblies were significantly enhanced as compared to the starting ligand and to the Cu I $bis(helicene) assembly (see Figure 12). The ECD spectrum observed for was characteristic of an extended π$conjugated helical ligand, since most of the strongly ECD$active bands imply electronic transitions from molecular orbitals whose electron density is distributed all over the helicene$phosphole skeleton. In the Pd(II) complex , efficient metal$ligand electronic interaction induced MLCT type transitions responsible for the low$energy ECD$active tails (400$500 nm). This was not the case for Cu(I) complex because metal$ligand electronic interactions were much weaker and the stereoselectivity very low (vide supra). 79 In conclusion, in spite of their peculiar structures and the presence of sterically demanding azahelicene substituents, the heteroditopic P,N$ moieties of derivatives , dictate their coordination behaviour allowing a predictable coordination driven molecular engineering to be performed.

B.2.3. Coordination of multitopic helicenic ligands

We have shown in the former paragraph that phosphole$ modified azahelicenes are well designed to self$assemble onto metallic ions in a highly stereoselective way, affording original chiral architectures. Along these lines, bis(aza[4helicene)$ phosphole (Scheme 16) acting as a N,P,N$pincer with a bridging $P$donor was synthesized and its coordination to Cu(I) in the presence of dicyano$stilbene yielded a supramolecular rectangle assembly ( ") containing a total of four Cu(I), four aza [4]helicene moieties, two dicyano$stilbene bridges and two dppe ligands around the Cu(I) atoms. 80 The X$ ray crystallographic structure of " evidenced several sets of π-π stacking interactions that stabilized the supramolecular architecture in the solid sate. Note however that i) such a structure probably undergoes fast exchange processes in solution, ii) the aza [4]helicene units possess overall planar geometry. Coordination-driven synthesis of supramolecular rectangle 60 using bis-aza4]helicene-phosphole 59 80 and helicate 62 from helicand 61. 81 To go one step further, multitopic 2,6$bis(aza [6]helicene$ phosphole)$pyridine was prepared and appeared well$suited to generate structural diversity within helicate chemistry since it acted as a N,P,N,P,N$helicand upon an original coordination mode on Cu I $dimers. [START_REF] Lehn | Supramolecular Chemistry: Concepts and Perspectives[END_REF]81 The presence of the enantiopure M$ or P$helicene moieties allowed to prepare enantiopure helicates M$ and P$ , which closely assembled two helicene$capped helicands around four Cu(I) centers, and to study their chiroptical properties. Theoretical calculations evidenced the efficient chiral induction from azahelicene moieties to the Cu I $ helicate core and emphasized the presence of helicand$to$ helicand charge transfer (LLCT type) transitions that significantly impacted the ECD active bands although no MLCT was found.

# # : # " # # : # = +13120 = +910 = +1275 [ ] 23 D α [ ] 23 D φ = +23080 [ ] 23 D φ ' # & ! ' # & ! # # : # # # : # # !" [ ] 23 D α ' & ' & # : # # !" " # : # 2 3 2 $0 3 2 !" " # !" " ! 34
In 1999, phtalocyanines such as (Figure 13) fused to four non racemic [7]helicene units and bearing long chains have been prepared and studied by Katz, Persoons and collaborators. These molecules have shown to aggregate in appropriate EtOH$ CHCl 3 solvent mixtures. 82 Chiral Langmuir$Blogett films were prepared and displayed very strong second$order NLO activity. Although 2,2'$bipyridines are among the most widely used ligands in transition metal complexes, very little is known about helicenes bearing 2,2'$bi$pyridine and their coordination behavior. 83$86 Katz reported in 1999 the synthesis of [8]helicene acting as a bis$1,4$N,N'$chelating ligand (Figure 13) and its coordination to rhenium(I) and copper(I) examined. 85 Although the ECD spectra were briefly reported, the stereoselectivity issues were not examined in details. [7]helicene and displaying strong NLO activity 82 and rhenium(I) complex 64 of a [8]helicene acting as a bis-1,4-N,N'chelate ligand. 85 Finally, soluble helical conjugated ladder polymers with average molecular weight of 7000 g/mol were prepared by reaction of 1,2$phenylenediamine with enantiopure [6]helicene derivative in the presence of a metallic ion, through the well$ known salophen coordination chemistry (Figure 14a). 87,88 It was shown by molecular modelling that the Ni polymer complex bearing methoxy groups displayed a helical structure (Figure 14b) and that its extended π$conjugation resulted in a strong ECD signature at low energy (around 600 nm) corresponding to MLCT$type transitions (Figure 14c).

Conclusion

Throughout this review, we have reported many examples of helicene derivatives capped with a diversity of functional groups exhibiting efficient coordinating ability, such as cyclopentadienyl, alkynyl, vinyl, phenyl$pyridyl, cyano, phosphane, phosphite, heteroatoms, ... These helical π$ conjugated ligands can in turn be involved in simple and well$ known coordination or organometallic chemistry. Such strategy consisting of combining helicene chemistry and transition metals has many advantages. It enables to conceive uncommon helicene$based transition metal architectures. Furthermore, reacting polycyclic helical aromatic molecules with metallic ions can significantly alter their electronic density distribution and modify their properties. The carefully chosen metal thus has a great impact on the helicene properties. Firstly, it directly impacts the chiroptical properties, i.e. specific and molar rotations, and electronic circular dichroism spectra. Secondly, new properties can appear, such as non polarized and circularly polarized luminescence, NLO activity, catalytic activity, redox switching, and conductivity. Thirdly, new fundamental aspects of chirality may appear, such as the cis$trans isomerism influenced by the enantiopurity of the helicene ligand, or dynamic isomerization processes. Finally, the stereochemical outcomes of the coordination processes 89$95 are a fundamental part of the work and have to be controlled and well$understood, with the precious help of theoretical calculations. [START_REF] Autschbach | Comprehensive Chiroptical Spectroscopy Instrumentation, Methodologies, and Theoretical Simulations[END_REF] Further developments on the coordination behavior of helicene ligands at the molecular level may help to better understand other systems with higher level of complexity such as two$ dimensional chiral systems, aggregates, nanoparticles, ... All these aspects make this field of research one of constantly growing interest with several applications envisioned.

Figure 2 .

 2 Figure 2. Modification of the CD spectrum of 10a upon reduction and oxidation. Reproduced with permission from ref. 23.

Scheme 4 .

 4 Scheme 4. One-pot reaction between [Cp*IrCl2]2 and helicenes 15-17 to form the three isomeric complexes a, b and c. i) [Cp*IrCl2]2, AgBF4, CD3NO2.

Figure 4 .η 6 - 6 -

 466 Figure 4. Bimetallic η 6 -Ir complex 21 and monometallic η 6 -Ru complex 22 bearing 2,15-dimethyl-[6]helicene ligand 16.28

Figure 5 .

 5 Figure 5. a) X-ray structure of a Ag I -[7]helicene complex with one coordinated CH2Cl2 molecule. 32 b) Theoretical molecular structure of a ferrocene constructed from 10 fused cyclopentadienes. 34 Adapted with permission from ref. 32 and 34.

Scheme 5 . 36 Figure 6 .

 5366 Scheme 5. Synthesis of enantiopure mono-and bis-Ru II -vinyl-helicene complexes 24a,b by hydroruthenation of mono-and bis-ethynyl-helicene proligands 23a,b. 36

Figure 7 .

 7 Figure 7. Racemic tetratha[7]helicene-based complexes prepared by Licandro et al..

38

 38

Scheme 9 .

 9 Scheme 9. Left: synthesis of enantiopure and CPL-active phosphorescent platinahelicenes 31a,g,f. i) PtCl2(dmso)2, toluene, Na2CO3, Ar, reflux, overnight, resolution by chiral HPLC; ii) (RS,RS)-PtCl2(p-tolyl-MeSO)2, toluene, Na2CO3, Ar, reflux, overnight; iii) column chromatography and/or crystallization; iv) pentane-2,4-dione, toluene, Na2CO3, Ar, reflux, 2 hrs. X-ray crystallographic structures of 31a,f,g and 32a,f,g (one enantiomer shown). Right: linear luminescence and CPL signals of P-(+) and M-(-)-31g.[START_REF] Norel | [END_REF][41][42]

43

 43

Figure 8 . 42 !

 842 Figure 8. Comparison of the experimental UV-vis (top) and ECD spectra (bottom) of P-29f (black line), P-31f (blue line), P-31g (red line), and P-31a (green line).42

  Scheme 11. a) Isomerization of heterochiral (M,P)-34a 2 to homochiral (P,P)-34a 1 . Pt III -Pt III scaffolds; 41,44 i) toluene, reflux, 3 days. b) X-ray crystallographic structures of homochiral (P,P)-35a 1 and heterochiral (M,P)-35a 2 . 45 c) Bowlike and Λ geometries around the Pt II center in 35a 1 and 35a 2 respectively.

Figure 9 .

 9 Figure 9. X-ray crystallographic structures of homochiral (P,P,P,P)-[Ir III --Cl-(31a-H)]2 (36a) and (P,P)-Ir III -(31a-H)2 (36b). 40 Chemical structure of Os IV -[6]helicene

Figure 10 .

 10 Figure 10. Helical ligands used in transition metal asymmetric catalysis.

Scheme 12 .

 12 Scheme 12. Enantiomeric resolution of helicene-phosphane ligand 44 by preferential crystallization of diatereomeric Pd II complexes 45a,b. i) bis-[R-1-(naphthyl)ethylamine-C 2 ,N]-di--chloro-dipalladium complex, acetone, r.t.; ii)

Scheme 13 .

 13 Scheme 13. Tetrathiahelicene-nitrile complex 46 and isomerization to 47.

  helicene [7,8$D 2 ]$ and probed the chiral discrimination in Ag I $bound dimers of the type [LAgL'] + (L,L' = or [7,8$D 2 ]$

Figure 11 .

 11 Figure 11.1 and 2-Azahelicene ligands studied for coordination with AgOTf. X-ray crystallographic structure of (P*,P*) Ag I -bis-1-aza[6]helicene complex 49.71,72 Adapted with permission from ref.71.

Scheme 14 .

 14 Scheme 14. Different reactivity observed for racemic and enantiopure ligand 48c, yielding respectively cis-51 or trans-52 platinum complexes. X-ray crystallographic structure of cis-51 (one enantiomer shown) and dihedral angles used to define the M planar chirality around the Pt center.74

Scheme 15 . 79 Figure 12 .

 157912 Scheme 15. Stereoselective complexation process of aza[4]-and aza[6]helicenephospholes 53 and 56 acting as 1,4-P,N-chelate ligands to Pd(II) and Cu(I) complexes 54,57 and 55,58. Specific and molar rotations of 57,58 are measured in CH2Cl2 (C 0.01-0.02).77-79

  Scheme 16. Coordination-driven synthesis of supramolecular rectangle 60 using bis-aza4]helicene-phosphole 5980 and helicate 62 from helicand 61.81

Figure 13 .

 13 Figure13. Phtalocyanine 63 capped with[7]helicene and displaying strong NLO activity82 and rhenium(I) complex 64 of a[8]helicene acting as a bis-1,4-N,N'-

Figure 14 .

 14 Figure 14. a) Synthesis of helical conjugated ladder polymers 66. b) Model of an all helical complex with two salenophen units and three helices. 87,88 c) CD spectrum of polymer complex 66 bearing OMe groups. Adapted with permission from ref. 87.

  , †

	!"
	!# $
	&	&
		%
	'(&
		'(& ) % *
		'(& ) % *

"

# $ Scheme 1. First example of organometallic Fe(II) and Co(III) complexes bearing η

[START_REF] Stará | Science of Synthesis[END_REF]

-helicenic ligands. i) t BuLi, FeCl2; ii) CoBr2, oxidation, then NH4PF6.

15,16

$26 Figure 3. Chemical structures of metallocene complexes 11-13 bearing one

	A.1
					,
					%
					,
		" # $	+	## 0
					## 0
					'	&
					or
	two Dbf	-ligands,	24-26 and ferrocene complex 14.	27
	Finally, enantiopure ferrrocen[4]helicenequinone (pR,P)$
	showing both planar and helical chirality was recently prepared
	by Carreno, Urbano et al. through a kinetic resolution process
	using an enantioselective Diels$Alder reaction. 27 This chiral
	compound did not exhibit the typical CD signature of helicenes
	but a negative CD$active band at 621 nm was observed
	corresponding to an intramolecular charge transfer from the
	ferrocene donor to the quinone acceptor and inducing strong
	specific rotation at 589 nm ( [ ] D α = $1660, CHCl 3 , C 0.001, ee
	95%). *

.2. Transition metal complexes with η 6 helicenic ligands

	In 2012, Alvarez et al. examined the η 6 $coordination of
	iridium(III) and ruthenium(II) to hexahelicene	, 2,15$
	dimethyl$hexahelicene	and 2,15$dibromo$hexahelicene
	(Scheme 4).

' & ' & & & & &

' & ) % * " # $ ' & '"& ! ' &

& & & & :

& & &

& & & + 2 , + 2 ,-,

Acknowledgements

We thank the Ministère de l'Education Nationale, de la Recherche et de la Technologie, the Centre National de la Recherche Scientifique (CNRS), the ANR (ANR$12$BS07$ 0004$METALHEL$01 and ANR$10$BLAN$724$1$ NCPCHEM). J.C. warmly thanks Prof. Régis Réau for his scientific contribution and for longstanding fruitful discussions.

-(

a Institut des Sciences Chimiques de Rennes, UMR 6226, Campus de Beaulieu, CNRS$Université de Rennes 1, 35042 Rennes Cedex, France. E$mail: jeanne.crassous@univ$rennes1.fr † We call a [n]helicene a helicenic structure composed of n ortho$fused aromatic rings, being either benzene, cyclopentadiene, pyridine, ... The term metallahelicene is used when a metal is incorporated with an ortho$ fused π$helical backbone through a C$M σ bond.