Jean-Marc Weller
email: jean-marc.weller@enpc.fr

Frédérique Pallez
email: frederique.pallez@mines-paristech.fr

Emmanuel Coblence
email: emmanuel.coblence@isg.fr

Design Approaches in the Public Sector: Problematizations, Actors and Transformations in the French Administration

Over the past decade, French public services have introduced innovative approaches of a new kind, formally breaking with the bureaucratic engineering of the administration. These initiatives seem to be heterogeneous and diverse, but they adopt approaches sharing a similar family resemblance, inspired in a large extent by the principles of design -or "user-oriented design" -in the making of public policy. In schools, hospitals, social services or public authorities, local experimentations and research-action programs have been developed: residencies with multidisciplinary teams of professionals and stakeholders in total immersion with a public facility, prototyping tests for new innovation methods on a specific topic, ground-level actions, do-it-yourself projects, etc.

As part of a research project entirely focused to these new Forms of Public Innovation by design (FPI), the authors of this paper suggest to outline the main features of this unprecedented landscape in the French public sector. From a 200 cases database designed as a part of this research, the challenge is to provide a description of the phenomenon of emergence of these innovations carried out over the last ten years through two kinds of questions.

The first one is about temporal dynamics of such a movement and their potential meanings. Is it a sectorial trend, based on a few areas of government, particularly receptive to design methods? Or is it a global and wide wave, impacting public policies in general? The concepts of design applied to public services seem to meet an undeniable success in France. But is this rise of design approaches a fundamental tendency, revealing lasting changes in the forms of innovation in administrations, or is it just a cyclical manifestation of what evil spirits would call a "fashion effect", as plenty of management tools and managerial approaches through their life cycles, their onset, development, and inresistable decline (Abrahamson and Fairchild, 1999)? The data from the survey show, in this respect, a crucial paradox : an already possible decrease of local experiments, but in the same time an increasingly strong attractiveness of the theme.

. Actually, the FPI population from the database describe four ways of building innovation: citizen participation, data visualization, improving accessibility for public services users and reengineering decision-making process. However, these different issues seem to change over time. While the first two themes dominated the early stages, the two last ones seem to prevail today. Is this a displacement of the objects of intervention of designers, moving from a service design to that of a process design? How to interprete such an evolution?

Introduction

Over the past decade, public services have been introducing hitherto unseen innovative approaches, formally breaking with the managerial reforms that had been previously deployed: multi-week "immersion" within a territory; collective projects bringing together public servants, users, creative professions, and social science researchers; the "rapid prototyping" of new services; exhibitions mobilizing artistic processes; and the mass use of atypical media formats (blog, video, slideshow, etc.).

While the actual forms that these initiatives take on appear varied, they nonetheless pertain to techniques appearing to belong to the same family and which voluntarily place themselves under the banner of "service design". But As a part of a research project1 entirely dedicated to new Forms of Public Innovation (FPI) "by design"2 , this article presents an overview of this unprecedented landscape.

By surveying more than 200 cases in France over the past ten years (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015), within widely diverse public institutions, our intent is to provide a description of the phenomenon of emergence of these innovations "by design". To do so, and in reference to the actor-network theory, whose concepts can be used here as a guideline : i.

we first outline the general features of the changes involved, in relation to the following questions: What is the temporal dynamic of this trend? What actors mobilize these approaches? Are there sectors of administration that are more particularly receptive to them? On what fields of knowledge, apart from design science, are they based ?

ii.

we then discuss the formulation of issues and the problem framing that, from the point of view of their designers, these innovations follow. Four main types are thus identified.

General characteristics and inventory

The approaches on which this article focuses concern diverse subjects and issues, all of which present the particularity of aligning themselves with "design". As social science researchers, this intrigued us. It forced us to take a new look at each of our representations of designers' projects, thus raising the question of how the reference to design, which is widely acknowledged in the context of telephones, chairs, or tables, can play a role in public action? It is therefore this enigmatic set of interventions and actions that we thought important to explore, for the purpose of proposing a map of them. Without considering their effects, we have called these approaches "forms of public innovation" (FPI). By "forms", we intend to encompass undertakings that are necessarily heterogeneous in form, but whose creation is based on a repertoire of practical knowledge and know-how that is explicitly formulated in reference to design, albeit independently of what they are seen to mean and, therefore, without making any assumptions regarding the properties or content that supposedly characterize them. By "innovation", we mean that we are interested in projects that intend to transform a state of matters, in particular around situations that are reputed to be tricky ("wicked problems"), in such a way that they shift the focus, and in so doing highlight unnoticed aspects that are nonetheless considered to be essential a posteriori. By "public", we are referring to the fact that these experiments directly involve public institutions (territorial entities, schools, decentralized government services, the central government, hospitals, etc.).

We therefore endeavoured to assemble a sufficiently large population of FPI (n=204).

Some were intended to bring about concrete transformations, while others were for exploratory purposes, without necessarily being subject to practical implementation.

We found all of these initiatives interesting to include, due to the nature of the approaches that they proposed. To successfully complete this census, which was necessarily partial, we diversified our sources (text box below). The resulting database was organized into series of variables regarding, respectively, the identity of each FPI, its nature, its actors, and the knowledge concerned3 . It is therefore on the basis of these elements that we will describe the evolution of the phenomenon examined here (1.1.), the actors involved (1.2.), the governmental sectors concerned

(1.3.), and the practical knowledge mobilized as it appears via the classification of the professionals involved in the implementation of the project (1.4.).

Sources of the database

The results presented in this article are based on the querying of 114 Frenchlanguage websites potentially involved in the introduction of design approaches into public services. These include: the websites belonging to private agencies, which are often very small, and which are mainly or exclusively oriented towards design approaches, although based on spheres of intervention that are potentially varied (n=58); the websites of consulting firms, which generally employ a large number of staff, that use or develop innovative approaches "by design" among their methods without, however, being recognized as doing so (n=8); the websites of public services making use of the services of designers, and which establish the state of their undertakings on various levels (n=12); the websites of schools or universities offering design training (n=8); blogs by designers giving an account of their own undertakings (n=18); platforms dedicated to the online distribution of news and work carried out, in particular by designers or intermediary structures (n=5); and specialized online magazines likely to also survey these initiatives (n=5).

We identified these websites by means of two processes. The first was the result of the inventorying of design structures, carried out by multiple actors in the sector and which served as the basis for the initial identification of FPI 4 . The second was based on the surveying of websites potentially involved in the field of the study, carried out systematically with the help of the search engine google.fr. Combined, these two approaches allowed us to inventory a significant number of relevant sites, and even to cover a broad range of projects and issues. We were able to verify the data resulting from these projects, via cross-referencing to identify redundant information on the same undertakings reported by multiple websites.

Yet, given the difficulty of establishing an inventory of a fledgling field, this study can but be limited. In reality, the Internet offers only a limited and often biased view of the variety and content of design experiments in the public sphere: projects blown out of proportion for commercial and visibility purposes; websites that are not necessarily exhaustive; blogs that are rarely or poorly updated; and so on. As for other subjects of study, the challenge is nonetheless to limit arbitrariness and the necessarily partial nature of analyses by collecting a sufficiently large number of cases.

1.1. Following a marked expansion, an uncertain evolution Our examination of FPI over time revealed three main periods: that of the pioneers, which can be considered to correspond to the years up until 2008; that of expansion, which would follow it up until 2013; and that of a slowdown or even decline, which would encompass the following two years. Clearly, this chronological evolution (Figure 1) must be considered with caution, taking into account the methodological limitations mentioned above. It does nonetheless appear plausible, and is confirmed by a certain number of complementary elements. For example, the first period covers projects (n=7) which, regarding artistic approaches associated with the development 4 This survey was made possible through the exchange of information and discussions that we had under the FIP-EXPLO research programme, in particular with Stéphane Vincent (27 e Région), Olivier Hirt (ENSCI), and Jacques-François Marchandise (FING), taking into account their first-hand knowledge of this sector. Moreover, we were able to benefit from the production of publications and public reports, and specifically Manzini and Staszowski (2013), [START_REF] Cadix | Pour une politique nationale du design, Mission design, Rapport au ministre du Redressement productif et à la ministre de la Culture et de la Communication[END_REF][START_REF] Scherer | Chantiers ouverts au public, Paris, La documentation française Tonurist[END_REF]. Last of all, the inventory of FPI was completed through the consultation of a library of cases established at the 27 e Région, but which remains confidential. [START_REF] Boeuf | Design et innovation sociale[END_REF]. As for the third period, it reveals a slowdown in the phenomenon, taking into account the number of FPI surveyed (n=58). This decrease that we observed, but that still needs to be confirmed, especially because it covers only two years, also seems to be contemplated on a more general level by the actors in the sector themselves. They mention a possible "risk of running out of steam", and intend to renew their deployment strategies 5 . The subject is nevertheless of growing interest among academic communities. 5 See, for example, the case of the "extended school" animated by the NESTA, and bringing together a panel of public innovation practitioners and experts from across the world: http://www.la27eregion.fr/ischool-une-ecole-pour-remettre-de-la-reflexivite-dans-linnovationpublique/ Of particular interest in this evolution, in addition to the rise of public innovative approaches by design, is this division into three distinct phases. It specifically raises questions regarding the reconfiguration of the sector, involving public actors and designers through mechanisms that are potentially different for each of the periods mentioned. It also highlights the still fragile dimension of the phenomenon that we are seeking to describe.

FPI and their Actors

Like any innovation, each FPI is impossible to dissociate from the network of actors that it was necessary to mobilize and to involve step-by-step. Among these actors, we can highlight in particular the public institutions concerned and the professionals directly involved in the implementation of the project. Regarding the former, our first finding concerns the dominant place of territorial entities (and similar) in the management of these projects. In fact, they are involved in almost two-thirds of the projects inventoried (Table 1). Multiple explanations can be advanced. An initial explanation relates to the position of territorial entities within the landscape of public institutions in France. Their rise to power has to be linked to successive waves of decentralization, with the transfers of competence that have accompanied them and have given them a central place in the management of public facilities and services affecting the daily life of citizens -as is the case of social and health actions for departmental councils, or high schools for regional councils. To this can be added, over the past 20 years, the multiplication of inter-commune structures granting new capabilities for action at an infradepartmental level. Lastly, more general trends at play in the context of globalization are causing the recomposition of territories. Here, regions and cities are asserting themselves as key political and economic actors capable of driving or sustaining the most innovative initiatives, and are fit to play a leading role in planning, development, and regulation, to the detriment of sovereign states.

The second explanation is related to the stance of designers, who defend a contingent and contextualized vision of their action based on a specific "fieldwork"

with users that has to be directly accessed and mobilized.

Due to the combination of these preoccupations -greater capabilities for action of local governments, desire of some of them to position themselves as actors in change and design approaches based on "situated" interventions -, it is not surprising to note a large portion of territorial institutions and inter-municipal entities among the FPI identified in our corpus. We also note that with its 22 identified FPI, a large city such as Greater Lyon occupies a remarkable place in the rise of innovations making use of service design.

Furthermore, it is worth noting the very unequal distribution of FPI across the administrative territories of the country. This is true not only of regions, but also and more generally of local governments (Figure 2). Among the many hypotheses that we can put forward to explain this disparity, but which this paper is not focused on systematically testing 6 , two seem to be plausible according to qualitative inquiries carried out elsewhere. First, "prescriptive" actors, which in a recent publication [START_REF] Coblence | Acteurs intermédiaires de la mobilisation territoriale : les enseignements des démarches de prospective-action[END_REF] we called "intermediary agencies" because they are not always the direct operators of FPI, play a significant role in the promotion of these new approaches. They orchestrate relationships by animating a community composed of public actors and numerous small design firms. The map that emerges partially reflects the territorial distribution 6 We could, for example, imagine that the local governments involved share a similar sociological profile over a certain number of variables, or that the instances display identical political affiliation.

of their network. In particular, these consist of La 27 e Région, the Fondation Internet Nouvelle Génération (FING) or, more locally, the Cité du Design in Saint-Etienne.

A second hypothesis, which is not mutually exclusive with the first, relates to the progressive establishment of regional ecologies around one or more actors involved in these approaches. These "network heads" may be research and foresight teams, as in Greater Lyon, or "laboratories" integrated into public establishments or local governments which, like the Fabrique de l'Hospitalité at the Strasbourg Hospital, or the Mission Innovation at the Departmental Council of Val d'Oise, act as intermediaries in the application of design methods. Other more recent in-house public laboratories in certain local government administrations such as the regional council of the Pays de Loire or Provence Alpes Côte d'Azur, could eventually play the same role. We can also mention here the role of schools dedicated to the training of designers, albeit according to somewhat different mechanisms, in Nantes, Strasbourg, and Paris, and universities oriented towards design, such as in Nîmes, which locally build projects with public institutions and contribute to the development of these regional ecologies.

More of less receptive administrative sectors ?

The projects supported by the different FPI listed in the database apply to different sectors of activity of the public services that we have attempted to classify into broad categories. The question that led to this categorization into sectors was the following: do FPI approaches apply to all types of public services indifferently or do they have preferential sectors? In other words, can everything be "designed"? In fact, we can posit that FPI approaches, through their claim of tropism towards "users", have to be particularly adapted to public services in which the users are numerous, clearly identified, present within a restricted scope, and well-defined. From this point of view, certain sectors (health care, education) appear to correspond to these features. But what is the reality of the matter? The classification of FPI by main sector of application yields the following results (Table 2). Having taken these precautions, we can make some observations. The first is that the different sectors of activity of public services are quite unevenly represented. The FPI surveyed mainly concern urban planning, health care, territorial (regional/local) development, social affairs, the environment, culture, and education, but rarely involve sovereign public services such as justice, the police, and defence. Must this be seen as evidence of an attitude of distrust among those in positions of authority and the professionals concerned, or of their yet limited knowledge of these approaches? Reciprocally, do designers, through their personal political positions, have a more marked interest in certain sectors that are more directly related to the issue of living together and the consideration of fragile publics? Can we also consider, in accordance with the hypothesis expressed above, that there is a greater degree of compatibility between FPI approaches and the types of public services that are initially oriented towards relations with users? Lastly, can we relate these observations to the fact that urban planning, education, and health care in particular are public sectors which make use of a set of research actions, interventions, or projects based on new methodologies, and have at times done so for many years?7

At this stage in our reflection, it is clear that these elements only allow us to make assumptions and to point to issues that should be empirically explored. It is nevertheless currently likely that all of these explanations are at least partially true.

More intriguing is the importance of the FPI at work in the "administration" sector, which is the second most represented category. Note that this term encompasses all FPI focused on the transformation of workpaces, tools, specific administrative processes (as purchasing procedures, for example), or administrative "culture" in its entirety (the development of innovation "labs", for example). These "administrative" FPI have in common the fact that they are largely polarized around the internal operation or rules of a public organization, rather than around the relation of publics.

How can we explain this finding, which appears counterintuitive when compared to the of many of the advocates of these FPI or the people involved in them, who emphasize a "user" approach? Faced with this, we realize that, in the discourses of these actors, the concept of "users" does not exclusively designate the "publics" which are the recipients of public services, but also often includes the agents directly involved in delivering them (what we generally call the "front-office"), or even some of their supervisors. But, more generally, it appears that an idea is developing among some designers, according to which the quality of the relationship to the public requires a sustainable change of the administration responsible for it. For example,

this is what we read in a description of the evolution of the MindLab strategy:

"…sustainable innovation will not happen via isolated projects…The next step is to help ensure that the civil servants are practising the new ways of innovating as an integrated, natural thing…" [START_REF] Carstensen | Powering Collaborative Policy Innovation : Can Innovation Labs Help[END_REF]. Will service innovation necessarily go through a process innovation?

Knowledge applied in FPI

As noted above, we are interested in innovative approaches that make use of design.

However, many of the approaches studied also draw on other disciplines. The idea expressed by many of the promoters of these approaches is in fact that a multidisciplinary perspective must replace the excessively uniform point of view generally shared about the way to conceive or transform public services. Another more methodological argument advanced by some is that design approaches are effectively completed by social science, which can contribute its ethnographic inquiry techniques in particular.

We therefore wanted to investigate the question of the disciplines working alongside designers on the FPI identified in the database. Clearly, a great deal of caution is necessary, as indications of discipline are used as they appear in the information sources consulted, without reprocessing on our part.

One initial finding, as Table 3 below First of all, we note the large degree of representation of sociology in association with design. If we add anthropology and ethnology to it, we see that these types of association are found in almost half of all cases (46 out of 96). This seems consistent with the methodological argument mentioned at the beginning of this section, namely that the association between these three disciplines and design may relate to the need for general competencies regarding "human societies" which are indispensable to the designer working in organizations and various local authorities.

On one hand, the frequency (44 occurrences) of the association between design and the science and techniques of architecture, town planning, and engineering may be more related to the nature of the issues covered by FPI, in which spatial, building, and computing issues have been clearly identified from the beginning. It is hardly surprising, for example, that FPI employed for train station projects (FPI041) or high schools (FPI031) employ architects, that a project for the data visualization of medical information (FPI136) includes computer specialist, and that the design of new uses for an urban park (FPI204) requires the presence of a town planner. One hypothesis is therefore that, to be legitimate, the teams working with the designer must demonstrate technical abilities adapted to the nature of the problem addressed.

On the other hand, the non-negligible occurrence (20 cases) of specialties with less clear boundaries, such as management, political science, marketing, and foresight studies may lead to multiple interpretations. These rather general designations probably mask, among the individuals in question, competencies regarding the administrative procedures and organizations concerned by the FPI. Most likely, in these partners, designers are looking for "administrative technical expertise" analogous with the technical expertise previously mentioned. We furthermore have evidence of FPI in which business consultants collaborate with designers to combine complementary approaches and to ensure, as a "vehicle of change", the organizational transformation processes for which designers are often loath to take responsibility.

We also wish to point out the significant presence of disciplines skilled in visual representation techniques (18 cases out of 96). This is consistent with discourses on the importance of the material or visual presentation displayed by the promoters of FPI. There might however possibly be redundancy between their competencies and those of designers.

Problem framing, publics and territories: four types of FPI

If, as STS have shown for a long time, the success of an innovation is related less to its intrinsic properties than to the robustness of its networks, and if the soundness of the ties that characterize it involves problem framing to convince certain actors that they are affected by the "problem" to resolve and that they can find a solution to it by contributing to the implementation of the innovation in question [START_REF] Cadix | Pour une politique nationale du design, Mission design, Rapport au ministre du Redressement productif et à la ministre de la Culture et de la Communication[END_REF][START_REF] Akrich | A quoi tient le succès des innovations ?[END_REF], then FPI can be appropriately described from the point of view of the way in which their promoters "interest" the multiple actors that they wish to mobilize.

Apart from their specific methodologies -that would need to be described in situ, based on concrete cases, which is not the purpose of this article 8 -, two elements deserve to be highlighted within the database that we have compiled: the importance of the territory in the way in which the innovations in question are generally 8 For a specific example, see Abrassart, Gauthier, Proulx and Martel (2015).

understood (2.1.), and the diversity of problem framing that is tied to them, in particular from the point of view of the general aims of the approach and the way of defining its publics (2.2.).

FPI and their territories

One of the characteristics of the FPI identified is that they often turn the territory into an essential element. Whether this consists in redeveloping a subsidized housing neighbourhood to foster relations between generations and between communities (FPI160), giving an account of local uses of digital tools (FPI179), designing welcoming waiting rooms for families at a hospital (FPI085), or reflecting on the redefinition of an administrative procedure internal to a public service (FPI127), the question of places often constitutes an obligatory point of passage (Table 5). In reality, the scope contemplated by the different FPI can prove to vary greatly in terms of size: a whole valley for the FPI that consisted of coming up with an unprecedented instrument allowing for better coordination of health care professionals attending to elderly people at their homes in Haute Provence (FPI109); an entire river basin for the FPI that contributed to rethinking the interfaces responsible for preventing flood risks in the large urban centres crossed by the Loire River (FPI110); a département for the FPI that consisted of a foresight trip to the heart of the Gironde in a speciallyoutfitted bus to investigate the inhabitants from place to place (FPI050); and a hospital ward for the one that led to a new lighting device in the rooms of a specialized retirement home (FPI072).

Number of FPI FPI that make the territory an essential element of the problem framing 170

FPI with a general or national scope, without making the territory an essential element 34

Total 204

Table 5: FPI and the status of the territory This attention to the territorial aspect constitutes a key element in the problem framing carried out by the promoters of FPI. It contributes to providing their approach with a character that is most often anchored, embodied, and always situated.

Although it is philosophically readily aligned with pragmatism [START_REF] Findeli | La recherche-projet en design et la question de la question de recherche : essai de clarification conceptuelle[END_REF], this orientation still raises questions when it contradicts the local nature within which it may be tempting to enclose it. Note that, even though they are locally situated, many FPI actually claim to address issues with a general scope. For example, this is the case of the experiments carried out for possible replication purposes, such as the "residency" which took place in Cluny intended to identify concrete improvements relevant to all the Relais de Services Publics [Public Service Relays] in rural areas (FPI039) (Coblence and Pallez, 2015). It is furthermore also the case of approaches -and these are frequent -that combine the practical and situated tests and prototyping with a foresight perspective aiming to build potential scenarios involving the institution in its entirety. For example, this is the case of the initiative exploring the forms of valorizing an ancient abbey with a high heritage value via its possible uses (FPI105). Moreover, FPI that initially display a foresight orientation are not rare (18%), whether they consist in designing tomorrow's rural train station (FPI035), imagining the future of an entire département by 2033 (FPI050), or even rethinking the impact of digital technologies on the workplace on the scale of society as a whole (FPI194). Therefore, one of the characteristics of FPI lies in this tension between a constantly territorialized problem framing on the one hand and a possible ambition to take things beyond this -a tension that finds its expression in the considerations of designers themselves regarding "upscaling".

Four problem framings of innovation and the publics concerned

Beyond these general remarks, four types of problem framing appear to be able to be distinguished among the FPI collected in our corpus, each of which describes a certain territory of innovation, a definition of the publics concerned, and a precise construction of issues.

The first understands public innovation from the position of a neighbourhood, town, commune, or group of communes. It is therefore the space that is simultaneously physical, social, economic, and cultural that constitutes the subject of this problem framing, whether this consists in contemplating the planning of a housing area (FPI159), rethinking the revival of a run-down city centre (FPI187), or promoting the identity of area recently brought into the spotlight (FPI046). The scope contemplated by the different projects can prove to vary greatly: the bank of a waterway for the project that consisted in consulting with inhabitants to contemplate modifications to the Saône (FPI010); a tramway for the project that attempted to understand the mobility of the inhabitants of Stains (FPI010); a neighbourhood for collecting the testimonials of the inhabitants of an outlying area undergoing renovation (FPI089);

and an entire département for the project based on a foresight mission to the heart of the Gironde to question residents place by place, using a specially-outfitted bus (FPI050). If we take into consideration that the general issue relating to design techniques pertains to the formatting of reality via artefacts destined to make action possible [START_REF] Norman | Les artefacts cognitifs[END_REF], these FPI express a key focus: shaping the expression of publics from the position of a given territory so that their experiences can take on a comprehensible form. Innovations, which at times integrate a social science inquiry approach or proceed more intuitively by producing information artistically, specifically concern the formats devised to communicate these experiences: maps, travelling exhibitions, video clips, etc. They describe a participationist ideal that is potentially associated with political issues pertaining to democratic life [START_REF] Walker | Rising Participation and Declining Democracy[END_REF][START_REF] Politix | Dispositifs participatifs[END_REF][START_REF] Espace Et Territoires | Le nouvel esprit de la démocratie. Actualité de la démocratie participative[END_REF], and that shares a "family likeness" with similar initiatives that are already found in urban matters [START_REF] Arab | Expérimenter l'intervention artistique en urbanisme[END_REF]Deviste and Ouvrard, 2015). There is nevertheless is a nuance: what appears to be important is not only allowing the residents of a city or neighbourhood to participate, but also making this participation known in such a way that it is able to capture publics whose concern is deemed to be strategic (passersby, administrative authorities, etc.). This problem framing of the territory, through the question of space and participation, is behind more than 40% of the FPI collected in our corpus and is therefore of prime importance.

A second way of conceiving of innovation encourages the examination of public action from the point of view of its facilities. Whether this consists in reflecting on the uses of a future travelling multimedia library intended for rural communes in Auvergne faced with significant changes (FPI037), rethinking the reception area of a geriatric hospital in Strasbourg for patients suffering from cognitive disorders (FPI001), proposing original sign posting at the high school in Givors in collaboration with stakeholders (FPI145), or designing a new space for handicapped people in Val d'Oise destined to facilitate their lives (FPI102), it is through the way in which the public is received and the relationship with users that the territory is problematized.

Knowledge of administrative trajectories, the experiences of users and, more broadly, the use of places often take place through phases of immersion, in which designers are in contact with the public and professionals. This results in the production of unusual artefacts, given that the purpose is to equip the new users with new information or action devices (sign posts, digital interfaces, documentary media, etc.)

intended to increase their ability to appropriate spaces. These spaces may moreover be targeted for redevelopment. Therefore, in this case, the territory is mainly understood through spaces of reception, and public action is problematized through the issue of accessibility. This conception is by no means negligible: it comes in second place among the innovations collected in our study, and involves almost 30% of FPI.

A third way of deploying design approaches within administration consists in focusing on its organization. At times these approaches involve the work spaces or the equipment of agents, such as: the "offices of the future" that the Regional Council of the Pays de Loire is making an effort to think up as a part of a foresight exercise (FPI124); the "mobile offices" provided to the professionals at the Parc régional de Millevaches in Limousin to allow them to hold their meetings while travelling (FPI174); or the work tools of the agents at departmental entities of the Protection Judiciaire de la Jeunesse in Seine-Saint Denis (child protection services) (FPI177).

These may also concern the regulatory procedures whose reconfiguration they encourage, such as the regulations regarding public procurement and the tendering process that delimit the activity of territorial entities (FPI127) or the management of European funds (FPI125). Lastly, they encourage the rethinking of decision-making processes in the strict sense, by providing actors with new tools to manage a high school (FPI112) or to offer ground-breaking digital interfaces to help in strategic decision-making for the army (FPI137). This is thus often a matter of solving the problem of coordination between actors, whether for a school, a local government, a sector of economic activity declared to be strategic, or a battlefield. The territory put to the test by FPI appears to be that of organization, considered from the position of the diversity of professionals, as well as regulations, procedures, or hierarchies. Even though we did not initially expect to encounter this way of conceiving of design approaches, it occupies third place in our corpus and accounts for almost 20% of all the projects inventoried.

Finally, a fourth way of problematizing public action is through approaches conceiving of the public as a general entity, without specifically designating or problematizing any particular territory. In collaboration with government ministers or the Etalab, which is responsible for the open public data portal, this is the case of a number of digital innovations proposing: tools for visualizing data on prostate cancer (FPI36); a digital dictionary of Egyptology (FPI138); or cultural production offering an unprecedented compilation of elements (FPI054). It is furthermore also the case of:

training and meeting projects, such as the invitation sent by La 27 e Région to a small group of public officials from different fields to reflect on the work of the elected official (FPI199); the production of use scenarios regarding the reduction in the energy divide as part of research overseen by la Cité du Design (FPI099); the stage design of a temporary exhibition on food (FPI152); or the production of reports intended to clarify public decisions regarding sustainable development (FPI011). This understanding of the territory and of the public nevertheless seems to correspond to a minority, and involves less than 15% of all FPI examined.

We have just described four ways of conceiving of public innovation by design. It is worthwhile to consider these orientation trends, without the problem framings that they describe necessarily being mutually exclusive of one another. Furthermore, certain FPI appear to combine the features of many of them: creating a waste sorting and recovery centre for a community of rural communes in Limousin pertains both to the issue of the use and management of waste infringing on a specific territory, and to the creation of public facilities for local governments (FPI166); the rearrangement of the workspaces of a maternity ward at the Strasbourg CHU simultaneously addresses the issues of public facilities for women giving birth that the innovation intends to set up at the centre, and challenges regarding the organization of professionals' work (FPI002) (Table 6, Figure 3). would call "just a fad"? How can we not think of the multitude of management tools and managerial approaches -quality circles, total quality control, the "six sigma" method, etc. -whose life cycles have been described by research, including their beginning, their peak, and then their decline (Abrahamson and Fairchild, 1999)? Is it not possible that the inventory of FPI in our database itself follows such a trajectory, by revealing, following a growth phase, a certain decline in the number of experiments currently underway? While the answer remains open, we note that, contrary to the management tools just mentioned, service design approaches do not align themselves solely with one hitherto unseen methodology. They originate from a professional environment capable of giving original substance to the phenomenon that we are examining here, and for some their promoters advocate a veritable political vision of the transformation of public action.

The second element with which we wish to conclude concerns the quality of the phenomenon observed. While it cannot be denied that there exist design approaches within public services, the issues that are inspired by them nonetheless take on evolving forms. Among the four ways of conceiving of innovation that we have identified, the FPI that are created based on the issues of space and participation are in clear decline after having experienced the most growth. On the other hand, FPI mobilizing design from the point of view of organizational issues internal to the government appear to be experiencing constant growth (Figure 4). Is this a case of the shift of the objects of designers' interventions, transitioning from service design to process design? However, while it is possible to put the services provided by a government or its organization to the test of design methods, are there limits that make it more difficult to deploy the approaches proposed at other levels, such as public policies? Can everything be "designed"?

Bibliographic references

Abrahamson , E. and Fairchild, G., (1999)

Figure 1 :

 1 Figure 1 : Chronological evolution of FPI (2006-2015). Data source : FIP-Explo database

  Figure 2: Distribution of FPI within local governments, source: FIP-Explo Database

  indicates, is that only around half of the approaches inventoried (96 out of 194 approaches surveyed) actually call upon other disciplines as a complement to design. This challenges the claim of multidisciplinarity mentioned above. That being said, by looking at the nature of the FPI pertaining to the work of the designer alone, we can posit that these are often onetime interventions (most likely with limited financing), such as the facilitation of meetings or seminars, at which the designer essentially has the function of facilitating and producing media intended for collective creativity.

(

  *) The data exceeds the 204 FPI in the corpus because a minority of them simultaneously correspond to multiple problem framings.

Figure 3 :

 3 Figure 3: FPI and their problem framing

Figure 4 :

 4 Figure 4: Chronological evolution of the problem framing of FPI (2006-2015), source: FIP-Explo Database

  of public spaces or participatory approaches inviting the inhabitants of a neighbourhood to rethink certain facilities, brought together designers to work with town planners, plastic artists, architects, or social sciences researchers for the first time. The major feat lies not only in these unprecedented combinations; it is also

	contained in the novel production of a discourse of legitimization by design, the
	methodologies of which appeared inspiring. The second period corresponded to
	strong growth of the phenomenon, when the number of FPI observed constantly
	increased over five years (n=139). This expansion, based on the entry in force of
	designers into projects, very generally corresponds to the structuring of a
	professional milieu that is clearly visible elsewhere as well: the entry onto the scene
	of a number of actors playing a strategic role in the steering of projects, such as La
	27 e Région in 2008 or La Cité du Design in 2010; the establishment of international
	networks of similar experiences such as the DESIS (Design for Social Innovation and
	Sustainability) network created 2009; and the more active role played by design
	schools and universities (Le

-Social, cultural and security public services 18

		Number	Total	%
	A.-Central government and similar		25
	Ministries	21
	National authorities and agencies	04		10 %
	B.-Territorial entities and similar		149
	Regional councils	56
	Departmental councils	38		59 %
	Communes, cities, inter-municipal associations	53
	Public development establishments	02
	C.-Public hospital services		20
	Hospitals	13		8%
	Retirement homes	07
	D.-Public research and training services		31
	Schools	21
	Universities	08		12 %
	CEA [atomic and alternative energy commission]	02
	E.Social Security funds	02
	Pôle Emploi [French employment agency]	01
	DRAC [Regional cultural affairs department]	04
	Emergency housing centres	02		7 %
	Social centres	01
	Museums	04
	OPAC [Public development and construction bureaus]	01
	Regional nature parks	02
	Paris fire brigade	01
	F.-Public companies		09
	SNCF [French national railway company]	02
	EDF [French national electricity company]	03		4 %
	La Poste [French national postal service]	04
	Total	252 (*)	252 (*)	100 %
	Table 1: FPI and their public actors
	(*) The total exceeds the 204 FPI because each one may apply to multiple public actors.

Table 2 :

 2

Public sectors of activity involved in FPI, source: FIP-Explo Database Clearly, we must not grant too much importance to the details of the numbers indicated, which are largely dependent on the chosen nomenclature and the definition of the categories. For example, "urban planning" FPI appear to be the large majority, but this category encompasses all FPI involving the transformation and development of the public space, which can explain such a result. In reality, this intentionally very broad definition encompasses relatively varied actions: the development of train stations, green spaces, urban spaces in relation to disabilities, and so on.

Table 3 :

 3 Frequency of multidisciplinary in FPI, source: FIP-Explo Database

	Disciplines associated with design	Number Total
	Social sciences and humanities	75
	Sociology	35
	Ethnology-anthropology	11
	Management, economics, political science and similar	20
	Other social sciences and humanities (psychology, philosophy, etc.)	09
	Science and techniques of architecture, urban planning, and	44
	engineering
	Architecture and similar	17
	Urban planning and territorial development	04
	Engineering sciences	23
	Arts and artistic techniques	26
	Visual, plastic, photo, and video arts	21
	Dramatic arts: dance, theatre, stage design	05
	Sciences and techniques of education, mediation, and	07
	communication
	TOTAL	152

Out of the 96 observed cases of multi-disciplinarity, we have attempted to provide an initial view of the types of association between the discipline and design, by grouping into disciplines (which are necessarily debatable) (Table

4)

Table 4 :

 4 Association of other disciplines with design, source: FIP-Explo Database

Table 6 :

 6 FPI and their problem framing

This Research Project FIP-EXPLO (ANR-13-SOIN-0003) was funded by the French National Research Agency (ANR).

We simply refer to this as FPI in the remainder of the text, to remain consistent with the acronym chosen at the beginning of the research.

More specifically, to investigate these four main categories of variables, we attempted to identify different items: regarding the identity of the FPI, we were able to provide the title, the scope of action, the place, and the date of the project. Regarding its nature, we included the public sector concerned, the type of action carried out, and the intended goal of the approach. Regarding the public actors involved, we included the institutions or actors concerned, and noted the possible presence of an intermediary structure, as well as the people involved among external stakeholders. Regarding knowledge, we established the list of disciplines displayed for each project when we were able to do so, based on the information available to us.

For example, artistic approaches at schools, hospitals, or local development, are part of a long history


Xóchitl López-Lozano

G Plascencia-Villa

G Calero

R L Whetten

H.-Ch Weissker
email: weissker@cinam.univ-mrs.fr

Cinam § Etsf

Is the largest aqueous gold cluster a superatom complex? Electronic structure & optical response of the structurally

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Monolayer-protected gold clusters have been commercially available since many years ("Pep-tideGold" 2 ), and they are used in a multitude of biological and medical investigations over the past decade which all require aqueous-phase compatibility; applications include bioconjugation chemistry, [START_REF] Ackerson | Synthesis and Bioconjugation of 2 and 3 nm-Diameter Gold Nanoparticles[END_REF] protein tagging, 2 biomolecule labeling, [START_REF] Ackerson | In Cryo-EM Part A Sample Preparation and Data Collection[END_REF] inhibition of HIV fusion, [START_REF] Bowman | Inhibition of HIV Fusion with Multivalent Gold Nanoparticles[END_REF] as well as growth inhibition of bacteria. [START_REF] Bresee | Growth Inhibition of Staphylococcus aureus by Mixed Monolayer Gold Nanoparticles[END_REF] But their approved use is severely inhibited by a lack of precise knowledge of their structure, composition, and related fundamental properties. Herein, we present a comprehen-sive study of the electronic and optical properties of the novel water-soluble gold cluster Au 146 (pMBA) 57 , the structure of which has been recently determined at sub-atomic resolution by Vergara et al. 1 The stability and chemical nature of many metal clusters has been found to follow the super-atom model, [START_REF] Khanna | Assembling crystals from clusters[END_REF] in which the delocalized states (derived from the N s electrons in noble metals, where N is the number of noble metal atoms) belong to distinct values of angular momentum and follow an Aufbauprinzip similar to that found for the spherical jellium model. [START_REF] Ekardt | Work function of small metal particles: Self-consistent spherical jelliumbackground model[END_REF] In medium-sized gold clusters, the n * delocalized orbitals derive mainly from atomic 6s orbitals. The Aufbau rule is This observation was generalized as "super-atom complex model" (SAC model) [START_REF] Walter | A unified view of ligand-protected gold clusters as superatom complexes[END_REF][START_REF] Wyrwas | The colours of nanometric gold[END_REF] to describe monolayer-protected clusters of roughly globular shape. It assumes that stabilizing ligands may either withdraw electrons or localize electrons into covalent bonds. Assuming the withdrawal of one electron for each of the M pseudohalide ligands and noting that each of the N gold atoms provides one 6s electron, one obtains the requirement that n * = N -M -z be equal to one of the magic numbers listed above for an electronically closed superatom complex, where z is the overall charge. [START_REF] Walter | A unified view of ligand-protected gold clusters as superatom complexes[END_REF] If electronic shell structure is an important factor in the stability of the compound, there should be a clear gap after the shell closure, which implies a deep minimum in the electronic density of states. [START_REF] Walter | A unified view of ligand-protected gold clusters as superatom complexes[END_REF] Projection of the Kohn-Sham orbitals onto spherical harmonics allows for the decomposition of the electronic density of states, [START_REF] Walter | A unified view of ligand-protected gold clusters as superatom complexes[END_REF][START_REF] Yoon | Size-Dependent Structural Evolution and Chemical Reactivity of Gold Clusters[END_REF] clearly showing the SAC character of many clusters.

The number of clusters that have been synthesized, purified, and studied has increased immensely over the last few years. 12 Among the monolayer-covered Au clusters, the size range of approximately 140 to 150 gold atoms is of great interest, with the particularly stable, ubiquitous structure Au 144 (SR) 60 playing a special role for multiple reasons:

(i) Its size is such that the localized surface-plasmon resonance (LSPR) is not yet visible, although an incipient LSPR has been discussed. [START_REF] Malola | Birth of the Localized Surface Plasmon Resonance in Monolayer-Protected Gold Nanoclusters[END_REF][START_REF] Qian | Atomically precise gold nanocrystal molecules with surface plasmon resonance[END_REF] (ii) The cluster has been shown in 2014 to exhibit a multitude of discrete peaks in the absorption spectra which reflect the discrete electronic structure. 15 (iii) Various groups have synthesized and studied the compound, with different thiolate ligand rest groups, demonstrating a high degree of reproducibility (see Ref. 16 for a collection).

(iv) Different Au 144 -based alloy clusters have been studied both experimentally and theoretically. In particular, the general effect of alloying with silver was studied, [START_REF] Kumara | AuAg) 144 (SR) 60 alloy nanomolecules[END_REF][START_REF] Malola | TDDFT Analysis of Optical Properties of Thiol Monolayer-Protected Gold and Intermetallic Silver-Gold Au144(SR)60 and Au84Ag60(SR)60 Clusters[END_REF][START_REF] Barcaro | Comment on[END_REF][START_REF] López-Lozano | Effect of Alloying on the Optical Properties of Ag/Au Nanoparticles[END_REF] as well as the interesting case of adding copper which seems to produce a plasmon-like resonance, [START_REF] Dharmaratne | Au 144-x Cu x (SC 6 H 13 ) 60 nanomolecules: effect of Cu incorporation on composition and plasmon-like peak emergence in optical spectra[END_REF][START_REF] Bhattarai | ESI-MS Identification of Abundant Copper-Gold Clusters Exhibiting High Plasmonic Character[END_REF] the origins of which remain, however, unclear. [START_REF] Sinha-Roy | In Search of the Quantum-Electronic Origin of Color Change: Elucidation of the Subtle Effects of Alloying with Copper on ≈ 1.8 nm Gold Nanoclusters[END_REF] (v) Moreover, the size of 144 gold atoms is where fcc-based (i.e., bulk-like or similar) structures start to dominate, [START_REF] Negishi | A Critical Size for Emergence of Nonbulk Electronic and Geometric Structures in Dodecanethiolate-Protected Au Clusters[END_REF] whereas for smaller clusters molecule-like structures prevail.

Specifically for the size of 144 gold atoms and pMBA ligands, polymorphism has recently been inferred: a truncated octahedron structure may coexist with the well-known icosahedral structure. [START_REF] Jensen | Polymorphism in magic-sized Au144(SR)60 clusters[END_REF] (vi) Finally, it has been shown that the electronic structure around the HOMO-LUMO gap of Au 144 (SR) 60 corresponds to super-atom-like states. [START_REF] Lopez-Acevedo | Structure and Bonding in the Ubiquitous Icosahedral Metallic Gold Cluster Au 144 (SR) 60[END_REF] The new monolayer-protected gold cluster Au 146 (pMBA) 57 , the structure of which has been recently determined by Vergara et al., 1 is the largest aqueous gold cluster ever structurally determined and likewise the smallest cluster with a stacking fault. The core presents a twinned truncated octahedron, while additional peripheral gold atoms follow a C 2 rotational symmetry. With the usual electron counting rules as mentioned above, 9 a charge state of 3-(three additional electrons) leads to a number of SAC electrons of 146 -57 -(-3) = 92, which would correspond to a SAC shell closing. This raises the question if such a shell closing could explain the stability of the cluster compound.

In the present manuscript, we use density-functional theory (DFT) calculations to show that despite the proximity of the magic SAC number of 92 electrons, the Au 146 (pMBA) 57 cluster does not derive its sstability from super-atom complex character. After a description of the technical details, we discuss briefly the types of bonds and the bond lengths in the relaxed structure. Subsequently, we analyze the electronic structure and the optical response of the cluster and show that the nature of a superatom complex is not realized.

Technical details

We start from the experimental structure of Au 146 (pMBA) 57 determined as reported by Vergara et al. 1 In order to obtain a tractable size for the ab initio calculations, we have removed the restgroup R of all the p-MBA ligands, leaving only the carbon atoms directly bound to the sulfur atoms in place. Subsequently, the structure was saturated by hydrogen atoms (resulting in R = CH 3 methyl groups) in such a way that one of the hydrogen atoms pointed to the midpoint of the line connecting the two adjacent Au atoms (i.e., the plane defined by S-C-H intersecting this line at its midpoint). For comparison, we have also studied an isoelectronic-substitution model where each complete ligand molecule (pMBA) is replaced by one Cl atom.

The structure was then relaxed using the VASP code 27-29 using density-functional theory (DFT) with the projector-augmented wave method (PAW) [START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmentedwave method[END_REF] and employing the LDA exchange-correlation functional and, for comparison, the GGA functional PBE, 30 until all forces were smaller than 0.06 eV/ Å. A charge state of 3-(three additional electrons) was used to comply with the expected electronic shell closing at 2350 electrons according to the SAC model. Relaxation was slow, it appears clear that the total energy surface is composed of many shallow local minima (in particular, sensitive to the orientation of the methyl-group ligands). The chlorine-substituted model relaxed much faster to very small forces (smaller than 0.001 eV/ Å). The energy difference between the initial and the relaxed structure is about 17 eV for the relaxation using the LDA functional.

The optical absorption spectra are calculated by TDDFT using the real-space code octopus 31,32 with the time-evolution formalism [START_REF] Yabana | Time-dependent local-density approximation in real time[END_REF] and the PBE exchange-correlation potential [START_REF] Perdew | Generalized Gradient Approximation made simple[END_REF] for coherence with previous studies.

Results and Discussion

In Fig. 1 The distribution of interatomic distances, g(d), is shown in Fig. 2 where we compare the values found for the experimental structure as is with the LDA-relaxed structure and, for comparison, with the structure relaxed using the PBE GGA functional.

Clearly, the Au-Au distances are very well reproduced with LDA, which holds not only for the nearest-neighbor distances but also for the Au-Au distances of more distant Au atoms. By contrast, relaxation using the GGA functional PBE overestimates the bond lengths significantly. This is a direct confirmation of the commonly known fact that LDA yields good interatomic distances for gold, which is ex post facto a justification of using it in the present calculations. However, the preference of the LDA functional over PBE is certainly less well justified for the Au-S bonds.

Unlike the nearest-neighbor Au-Au bonds, the Au-S bond lengths show a bi-modal distribution already in the experimental coordinates, where, however, this double-peak structure is rather diffuse. These peaks get much narrower following the relaxation, indicating a slight symmetrization of the structure compared to the "noisy" data from the (average of multiple) diffraction experiments. The thin arrows indicate the average (weight) value of the peaks, using the same color as the curves. It is interesting to note that in spite of the differences between the LDA-relaxed and the experimentally determined Au-S bonds, their averages as indicated by the thicker arrows in Fig. 2 are almost identical, which serves as a further justification for the use of LDA in the relaxation.

In order to understand the origin of this bimodal distribution, we turn to the colored representation in the inset of the lower panel of Fig. 2. We color in red the S atoms which have two bonds shorter than 2.330 Å. (This is the value of the minimum separating the two peaks.) It turns out that these are exactly the four S sites that bridge two peripheral Au sites, as colored in dark green in Fig. 1. By contrast, the S atoms which have two bonds that are longer than 2.330 Å, rendered in blue in Fig. 2, turn out to connect two core Au sites (cf., white in Fig. 1). All the others (yellow) belong to "simple bridging thiolates" with one bond longer and one bond shorter than 2.330 Å. Inspection shows that this is similar to the situation found for the Au 144 (SCH 3 ) 60 cluster where in the so-called "staple motifs" the two collinear S-Au-S bonds are shorter than the Au-S bonds connecting to the core. 16 We compare the unrelaxed structure from experiment as is (thick blue and black) with the structure relaxed using the LDA functional and in the 3-charge state. For comparison, the result obtained using PBE-GGA is also shown (dashed green). The thin arrows indicate the average (weight) value of the peaks, using the same color as the curves. The first peak of the experiment is centered at 2.268 Å, the second at 2.416 Å. The narrower peaks of the LDA-relaxed structure are centered at 2.297 Å and 2.360˙Å. Interestingly, the average of all Au-S bonds (thick arrows) have almost the same distance: 2.327 Å for the experiment, and 2.334 Å after relaxation (LDA). By comparison, the PBE relaxation led consistently to larger values.

The inset in the lower panel shows the LDA-relaxed cluster including the methyl groups.

To highlight the spatial distribution of the Au-S bond lengths, the S atoms are colored blue for those with two S-Au bonds longer than 2.330 Å. These are the sites that connect to two core-Au sites, shown in white in Fig. 1. Colored red are those with two S-Au bonds shorter than 2.330 Å (bridging two peripheral sites, dark green in Fig. 1. (The minimum separating the two peaks of the distribution of Au-S bonds is at 2.330 Å for the LDA relaxed structure.)

The yellow ones have both one bond longer and one shorter than 2.330 Å. This corresponds to the situation in Au 144 (SCH 3 ) 60 where in the "staple motifs" the two collinear S-Au-S bonds are shorter than the S-Au bonds connecting to the core. [START_REF] Weissker | Optical Spectra of the Special Au144 Gold-Cluster Compounds: Sensitivity to Structure & Symmetry[END_REF] All curves were obtained by convolution with a Gaussian of σ = 0.01 Å.

In conclusion of this part, we have a rather good justification for the use of the LDA functional in the calculation, and the character of the geometric features of the ligand layer is in agreement with previously obtained results of the Au 144 cluster.

In Fig. 3 we show the results of the electronic structure calculations of Au 146 (SCH 3 ) -3 57 . In the upper panel, we show the full density of states and the individual electronic energies. As usual, one sees the clear Au 5d band and additional peaks originating from the ligands. The region around the HOMO-LUMO gap is enlarged in the inset, with isosurface representations of the frontier orbitals shown. The zero of the energy axis has been set to the HOMO energy.

Comparing the electronic energies of the relaxed cluster in Fig. 3 with those shown for comparison for the as is experimental structure, one observes the effect that was to be expected from the findings of Fig. 2 which shows a symmetrization, i.e., a narrowing of the distribution of the Au-S bonds. While the eigenenergies of the unrelaxed structure are more or less equally distributed, with no discernible differences, neither degeneracies nor an appreciable gap, the gap increases significantly under the relaxation, reaching the value of 0.22 eV. Moreover, the cumulative density of states shows an inflection point, corresponding to a minimum in the density of states as it is characteristic for a SAC shell closure and indicative of "electronic stability". [START_REF] Walter | A unified view of ligand-protected gold clusters as superatom complexes[END_REF] Nonetheless, this gap remains rather small, even in view of the possibility that the LDA underestimates the gap compared to the true value. Thus no clear conclusion about any SAC character can be drawn from the gap value.

For a clearer conclusion concerning the SAC character, the angular-momentum-projected density of states is shown in the second panel of Fig. 3, again choosing the HOMO energy as origin of the energy scale. It becomes clear here that despite the small gap that might have been indicative of a SAC shell closure, the electronic states are mixtures of many different angular-momentum components. In particular, the strong P contribution (green) would not be consistent with the Aufbau rule expected in case of a SAC shell closing at 92 electrons.

Upon visual inspection of the wavefunctions (Fig. S2 of the ESI) we conjecture that maybe )) The inset shows a zoom of the region around the gap for the relaxed structure (blue crosses) and the as-is experimental structure (green circles). In addition, the wavefunctions of the nondegenerate HOMO and LUMO states are shown (iso value of 0.001 Å-3 .) Below, we show the angular-momentum-projected DOS of Au 146 (SCH 3 ) -3 57 . Clearly, in spite of the small gap at the potential shell closing at 92 SAC electrons, the electronic states do not show any clear SAC character, as they are by and large mixtures of different angular-momentum components. This contrasts strongly with the case of the fully symmetric Au 144 (SCH 3 ) -8 60 cluster, shown for comparison, the states of which exhibit clear SAC character. (The high charge state -8 was chosen to obtain a number of SAC electrons of 92; the structure was from the neutral calculation.) Note that the result is slightly modified compared to the projected DOS of Ref. 26 because the fully symmetrized structure of Ref. 39 has been used in the present calculation. The angular-momentum components are as indicated in the legend, while the grey area reports the full, integrated DOS. Note that the DOS of Au 144 (SCH 3 ) 60 is more strongly peaked than that of Au 146 (SCH 3 ) -3 57 due to the much higher symmetry-related degeneracy. All energies are Kohn-Sham energies from the LDA calculation; the DOS is convoluted with a gaussian of σ = 0.025 eV. The zero of all energy axes was set to the HOMO energy.

a modified ellipsoidal SAC model would be better adapted to describe the cluster. In Fig. S2 of the ESI we show the frontier orbitals in different representations for illustration, along with the geometry of the R=CH 3 model used in the calculation.

To further confirm these findings, we compare with the case of the fully I h -symmetric Au 144 (SCH 3 ) 60 cluster 15,[START_REF] Weissker | Optical Spectra of the Special Au144 Gold-Cluster Compounds: Sensitivity to Structure & Symmetry[END_REF][START_REF] Bahena | STEM Electron Diffraction and High-Resolution Images Used in the Determination of the Crystal Structure of the Au 144 (SR) 60 Cluster[END_REF] in the lower panel of Fig. 3. (The high charge 8-was chosen to obtain a SAC electron count of 92, corresponding to a possible shell closure. The structure was that of the neutral calculation. [START_REF] Bahena | STEM Electron Diffraction and High-Resolution Images Used in the Determination of the Crystal Structure of the Au 144 (SR) 60 Cluster[END_REF] ) The difference between the two systems is striking: most of the Au 144 states exhibit rather pure SAC character with distinct angular-momenta, even though the condition of a shell closing at 92 SAC electrons is not fulfilled. (The HOMO-LUMO gap is actually very small; the SAC gap is at HOMO+1.) Second, the DOS is more peaked in this case, indicating a higher degree of degeneracy due to the high symmetry.

In Fig. 4, we report the calculated absorption spectra for light polarized along the Cartesian directions alongside the absorption averaged over all directions that would be measured in a solution-phase experiment where the orientation of the clusters is random. As to be expected in view of the symmetry, the absorption of the cluster is not isotropic. However, the differences between the directions are relatively small. The average absorption of Au 146 (SCH 3 ) 57 shows comparably little structure, in particular by comparison with the spectrum of the Au 144 (SCH 3 ) 60 cluster which is isotropic due to the high symmetry, and which has been reported before. 15,[START_REF] Weissker | Optical Spectra of the Special Au144 Gold-Cluster Compounds: Sensitivity to Structure & Symmetry[END_REF] The reasons for this remarkable difference are two-fold: first, the average over the different directions has a smoothing effect.

Second, the I h symmetry of Au 144 (SCH 3 ) 60 leads to a high degree of degeneracy in the electronic states, which is in turn visible in the spectra. By comparison, as mentioned above, Au 146 (SCH 3 ) 57 shows little symmetry-related degeneracy; its DOS is less peaked than that of the icosahedral Au 144 cluster, which translates into smoother spectra. These findings mean that the optical spectra measured in solution will not easily find individual spectral structures that calculations could be compared with. We hope that these 57 . The black line shows the average (trace of the full absorption cross-section tensor), while the red, green, and blue lines show the absorption for light polarized along x, y, and z, respectively. Clearly, the system is not isotropic. However, its spectra show comparably little structure compared with the spectrum of the Au 144 (SCH 3 ) 60 cluster which is shown for comparison (Green dashed line, shifted for visibility). The latter system is isotropic due to its high symmetry (I h ). Moreover, this high symmetry leads to higher degeneracy of electronic states, which in turn results in clear, discrete structures in the spectra. The electronic states of Au 146 (SCH 3 ) -3 57 , by contrast, show little degeneracy (cf., Fig. 3) and the resulting optical response spectrum is rather smooth. (The spectra have been calculated using the PBE functional in order to be consistent with earlier calculations; a comparison with LDA spectra is shown in the ESI.) results motivate the measurement of optical absorption on pure Au 146 (pMBA) 57 crystals in order to obtain spectra for well-defined directions.

Conclusions

We have studied the electronic structure and the optical properties of the novel monolayerprotected gold cluster Au 146 (pMBA) 57 , the structure of which has been recently determined by Vergara et al. 1 It is the largest aqueous gold cluster ever structurally determined and likewise the smallest cluster with a stacking fault.

The density-functional theory calculations were carried out for the charge state 3-(three additional electrons), motivated by the fact that this charge results in a number of 92 SAC electrons for which a major shell closing is expected in case the cluster conforms with the SAC model. The ligand rest groups were replaced by methyl groups, CH 3 .

Relaxation with the LDA functional resulted in close agreement with the experimental Au-Au distances. The relaxed structure kept all the connectivity of the original coordinates from the experiment, whereas much of the irregularity of the interatomic distances was removed, enhancing the C 2 symmetry feature.

Study of the angular-momentum-projected density of states allows us to draw the following central conclusion of the present study: while there is a small gap of the order of 0.2 eV, the electronic states do not even approximately exhibit SAC character. The strong P-type component of the states close to the HOMO is likewise inconsistant with the Aufbauprinzip which would expect even L values to dominate. Thus one cannot attribute the stability of the Au 146 (SR) 57 compound to a superatomic shell closing, despite the proximity of the magic number of 92 SAC electrons.

Finally, we have shown that relatively weak individual structures are found in the absorption spectra. We hope that these results can motivate experimental measurements of the absorption spectra on crystallized samples.

  Is the largest aqueous gold cluster a superatom complex? Electronic structure & optical response of the structurally determined Au 146 ( p -MBA) 57 Xóchitl López-Lozano, G. Plascencia-Villa, G. Calero, R. Whetten, Hans-Christian Weissker To cite this version: Xóchitl López-Lozano, G. Plascencia-Villa, G. Calero, R. Whetten, Hans-Christian Weissker. Is the largest aqueous gold cluster a superatom complex? Electronic structure & optical response of the structurally determined Au 146 ( p -MBA) 57. Nanoscale, 2017, 9 (47), pp.18629 -18634. 10.1039/c7nr04764a. hal-01720302

  Figures reported herein.

  The results of the time-evolution formalism are equivalent to those obtained using the transition-based Casida formalism.[START_REF] Casida | Recent Advances in Density Functional Methods[END_REF][START_REF] Casida | Recent Developments and Applications of Modern Density Functional Theory[END_REF] A comparison of the time-evolution results with a transition-based calculation is shown in the Supplementary Material of Ref. 15 for the thiolate-ligand covered Au 38 cluster. For a bare Au cluster, a similar comparison is shown in the supplementary material of Ref.38. The good agreement shows likewise that the technical parameters of our calculations are well controlled.The electronic energies shown herein are from the VASP calculation. The plotted wave functions are from an octopus calculation. In order to obtain the angular-momentumprojected density of states (PDOS), we use the (Kohn-Sham LDA) wavefunctions from the octopus ground state calculation and project them onto spherical harmonics according to the prescription of reference 9 used for instance in Ref.26. Details are given in the ESI.

Figure 1 :

 1 Figure 1: Geometry of the Au 146 (SR) 57 cluster compound with characteristic sites highlighted. Shown are the gold sites colored as described in the following, and the S atoms of the ligands. A complete figure of Au 146 (SCH 3 ) 57 is shown below in Fig. 2 and in Fig. S2 of the ESI. The cluster holds C 2 symmetry (the vertical y-axis corresponds to the two-fold rotation axis). Consequently, 4 of the possible 6 views suffice to present the cluster fully. "Top" and "base" views are parallel to this two-fold axis. Color scheme for the 146 Au-sites: No Au-S bond -dark red (59); single Au-S 'surface' sites (60); red (20+2), to complete the twinned truncated-octahedron 81-site core; pink (14), magenta (2), purple (2), also on FCC lattice (99) orange (10+10), completes sum to 119. (A rendition of this is seen in the ESI.) Apart from this core, there are 27 peripheral gold sites shown in yellow (small) in S-Au-S collinear bonds.Color scheme for 57 S-sites: 7 sites bridging two core-Au-sites -white; 4 sites bridging two peripheral-Au-sites -dark green; 38 + 8 = 46 sites bridging surface and core siteslime-green.

  we show the structure of the Au 146 (SR) 57 cluster compound with different sites colorcoded. All gold sites and the S sites of the ligands are shown. The cluster is approximately globular and exhibits C 2 symmetry. (The top view looks down along the two-fold rotation axis.) It's core consists of a twinned truncated octahedron, which is surrounded by an ordered layer of peripheral gold atoms and p-MBA ligands.

Figure 2 :

 2 Figure 2: Interatomic distances: We show the distribution g(d) of Au-Au and Au-S interatomic distances over a wider range (lower panel), with the upper panel showing a blow-up of the region of Au-Au and Au-S bonds.We compare the unrelaxed structure from experiment as is (thick blue and black) with the structure relaxed using the LDA functional and in the 3-charge state. For comparison, the result obtained using PBE-GGA is also shown (dashed green). The thin arrows indicate the average (weight) value of the peaks, using the same color as the curves. The first peak of the experiment is centered at 2.268 Å, the second at 2.416 Å. The narrower peaks of the LDA-relaxed structure are centered at 2.297 Å and 2.360˙Å. Interestingly, the average of all Au-S bonds (thick arrows) have almost the same distance: 2.327 Å for the experiment, and 2.334 Å after relaxation (LDA). By comparison, the PBE relaxation led consistently to larger values. The inset in the lower panel shows the LDA-relaxed cluster including the methyl groups. To highlight the spatial distribution of the Au-S bond lengths, the S atoms are colored blue for those with two S-Au bonds longer than 2.330 Å. These are the sites that connect to two core-Au sites, shown in white in Fig.1. Colored red are those with two S-Au bonds shorter than 2.330 Å (bridging two peripheral sites, dark green in Fig.1. (The minimum separating the two peaks of the distribution of Au-S bonds is at 2.330 Å for the LDA relaxed structure.) The yellow ones have both one bond longer and one shorter than 2.330 Å. This corresponds to the situation in Au 144 (SCH 3 ) 60 where in the "staple motifs" the two collinear S-Au-S bonds are shorter than the S-Au bonds connecting to the core.[START_REF] Weissker | Optical Spectra of the Special Au144 Gold-Cluster Compounds: Sensitivity to Structure & Symmetry[END_REF] All curves were obtained by convolution with a Gaussian of σ = 0.01 Å.

Figure 3 :

 3 Figure 3: Electronic structure of Au 146 (SCH 3 ) -357 . In the upper panel, we show the electronic density of states (red) as well as the individual energies (blue crosses) as a function of their state number. (The HOMO state corresponds to state number 1175 (2-fold degenerate for spin.)) The inset shows a zoom of the region around the gap for the relaxed structure (blue crosses) and the as-is experimental structure (green circles). In addition, the wavefunctions of the nondegenerate HOMO and LUMO states are shown (iso value of 0.001 Å-3 .) Below, we show the angular-momentum-projected DOS of Au 146 (SCH 3 ) -3 57 . Clearly, in spite of the small gap at the potential shell closing at 92 SAC electrons, the electronic states do not show any clear SAC character, as they are by and large mixtures of different angular-momentum components. This contrasts strongly with the case of the fully symmetric Au 144 (SCH 3 ) -8 60 cluster, shown for comparison, the states of which exhibit clear SAC character. (The high charge state -8 was chosen to obtain a number of SAC electrons of 92; the structure was from the neutral calculation.) Note that the result is slightly modified compared to the projected DOS of Ref. 26 because the fully symmetrized structure of Ref. 39 has been used in the present calculation. The angular-momentum components are as indicated in the legend, while the grey area reports the full, integrated DOS. Note that the DOS of Au 144 (SCH 3 ) 60 is more strongly peaked than that of Au 146 (SCH 3 ) -3 57 due to the much higher symmetry-related degeneracy. All energies are Kohn-Sham energies from the LDA calculation; the DOS is convoluted with a gaussian of σ = 0.025 eV. The zero of all energy axes was set to the HOMO energy.

Figure 4 :

 4 Figure 4: Optical absorption spectrum of Au 146 (SCH 3 ) -357 . The black line shows the average (trace of the full absorption cross-section tensor), while the red, green, and blue lines show the absorption for light polarized along x, y, and z, respectively. Clearly, the system is not isotropic. However, its spectra show comparably little structure compared with the spectrum of the Au 144 (SCH 3 ) 60 cluster which is shown for comparison (Green dashed line, shifted for visibility). The latter system is isotropic due to its high symmetry (I h ). Moreover, this high symmetry leads to higher degeneracy of electronic states, which in turn results in clear, discrete structures in the spectra. The electronic states of Au 146 (SCH 3 ) -3 57 , by contrast, show little degeneracy (cf., Fig.3) and the resulting optical response spectrum is rather smooth. (The spectra have been calculated using the PBE functional in order to be consistent with earlier calculations; a comparison with LDA spectra is shown in the ESI.)

  9 |1S 2 |1P 6 |1D 10 |2S 2 1F 14 |2P 6 1G 18 |2D 10 3S 2 1H 22 |..., leading to shell closures at n

* = 2, 8, 18, 34, 58, 92, 138... which explain particular stability when the electron count matches one of these "magic numbers."

Acknowledgments

Enlightening discussions with Andres Saul and Ignacio Garzón are gratefully acknowledged. X.L.L. acknowledge previous funding from NSF-DMR-1103730 and NSF-PREM DMR-0934218.

RLW acknowledges the support of the Welch Foundation under grant AX-1857. HCW acknowledges support from the French National Research Agency (Agence Nationale de Recherche, ANR) in the frame of the project "FIT SPRINGS", ANR-14-CE08-0009. This work has used HPC resources from GENCI-IDRIS (Grant 096829) and from the Laboratory of Computational Nanotechnology and UTSA Research Computing Support Group through the HPC clusters Antares3 and SHAMU, respectively, as well as the Texas Advanced Computing Center (TACC) at the University of Texas at Austin.