Professor Didier Bigo

Professor ad personam Jean Monnet

Queen Elspeth Guild

Dr Elif Kuskonmaz

Obedience in times of COVID-19 pandemics: A renewed governmentality of unease?

This article transects and articulates different disciplines and lines of thought in order to understand the redefinitions of the boundaries of political power in times of COVID-19, and the practices which may outlive the potential normalization of the crisis when an efficient vaccine is discovered. We claim that the COVID-19 pandemic is an original form of governmentality by unease articulating three dimensions. First, the basic reaction of modern states when faced with uncertainty to apply national-territorial logics of controls. Second, bureaucracies consider the virus along the frame of a danger to security and organize public health emergencies according to the rules of the game of national security, creating tensions between internal security, public health and the economy because policy makers may be unsure about the priorities and may have privilege border controls. Third, resistance against the chosen national policies show that people are not led by a politics of fear and-or protection, but rather their own concerns about themselves with a peer-to-peer surveillance based on the denunciation of potentially contaminated persons as one key element of their compliance. Contact tracing technologies and strategies of border controls are key elements to analyze. We do so in different contexts: UK, European Union and Turkey.

Obedience in times of COVID-19 pandemics: A renewed governmentality of unease?

This article transects and articulates different disciplines and lines of thought in order to understand what the redefinitions of the boundaries of political power in times of COVID-19 are, and what the practices which may outlive the potential normalization of the crisis are, even after vaccines are discovered and being distributed widely. While referring to the habitus inspired by Bourdieu and paying specific attention to legal practices, it reinforces an articulation that is often missing in strictly Foucauldian approaches between a reflection in terms of governmentality and an analysis of practices of bureaucratic fields. At the core of the discussion on the impact of COVID-19 on freedom, security and democracy lies the question of the type of politics that most states have pursued to generate compliance. A possible type of politics might be that of obedience and resistance, which involves the introduction of emergency public health policies that while being different from each other in certain aspects, have been driven more by nationalistic agendas than by a common analysis of the pandemic itself. Based on this politics of obedience and resistance, we claim that the governments from differing parts of the political spectrum under examination here (EU countries, the UK, and Turkey) have tried to convince their populations that pandemic emergency measures are for their own good, by acting upon their unease. It is neither a politics of protection led by care, nor a politics of fear and terror implying coercion, nudging and developing an illiberal regime. Rather, it is an original form of governmentality by unease [START_REF] Bigo | Security and immigration: Toward a critique of the governmentality of unease[END_REF]) that creates illiberal practices inside liberal regimes while operating on the basis of personal choices, bureaucratic fights and territorialized forms of modern state sovereignty. Even in Turkey, this form of governmentality respects formal representative democracy. But the fundamental freedoms and basic principle of the rule of law are subverted by the development of horizontalized suspicion that fosters the use of technologies of surveillance and digital predictive analytics. We may not be sleepwalking into an Orwellian society. Nevertheless, a liquid type of surveillance, i.e. a peer-to-peer -DIY surveillance to quote Zygmunt Bauman [START_REF] Bauman | Liquid surveillance: A conversation[END_REF] -is propagated in the name of protection of the self and the others. Its logic is to organize people into clusters which distribute them as more or less "suspect", but never fully sane. This thus brings about the connection with the governmentality of unease that is articulated upon the concerns of the individuals themselves and their relations to the place they have in this society of individuals, which makes it different from the state coercion [START_REF] Elias | Society of individuals[END_REF]. This is not something new that has only become apparent with the COVID-19 pandemic. It has already been experimented with counterterrorism and migration deterrence practices. But with the recent COVID-19 measures, it has reached a larger scale and is enacted and translated into health.

Media debates have unfolded by opposing both the national public health response to COVID-19, which has involved strict restrictions on movement to limit the spread of the virus and its death toll, and the slowdown of the economic activity, which threatens the livelihoods of economically vulnerable households and may generate a general major crisis. The discourse of a balance between protecting the health, on the one hand, and risking an economic recession, on the other, has been based on the argument that the protection of individuals has to be balanced against the protection of the nation. The idea is effectively that the virus' impact on the vulnerable is terrible but has to be weighted against the global economic competitiveness of a country and the importance of being among the first to escape the crisis characterized by the cessation or diminution of some essential activities. This politics of protection with its two faces (one as a sanctuary and the other as a tutelage) has already been discussed, and as Huysmans et al discussed (2006), a logic of sacrifice and utilitarianism can use the term of protection to discriminate against some groups of people. This discussion indicates that a language of protection is not always a form of humanitarianism because it can be a form of cynicism. Unfortunately, despite this general criticisms towards it, some scholars have observed that several governments have adopted this framing of a politics of protection to oppose the individual interests against the state and societal interests [START_REF] Wagner | Pandemica Panoptica: Biopolitical Management of Viral Spread in the Age of COVID-19[END_REF].

Another type of politics also transpires from government messages in the media that play with individuals' existential fear of death in order to make them obey coercive measures which appear as absolute necessities. Inspired by the idea of Giorgio [START_REF] Agamben | Homo Sacer: Sovereign Power and Bare Life[END_REF] of "homo sacer", the contemporary power of most regimes relies on a permanent exception -or in a more subtle version they enact what Corey [START_REF] Robin | Fear: The history of a political idea[END_REF][START_REF] Arcarazo | Transnational diffusion or different models? Regional approaches to migration governance in the European Union and Mercosur[END_REF] has called a politics of fear -involving a certain cynicism and a biopolitical vision of the people to be led like a herd, but embracing the individuals instead of reducing them to "bare life".

Using the very same terminologies as each other, many governments have used legal mechanisms by declaring a state of emergency or a state of exception, but, de facto, very different logics and technologies of coercion, surveillance, and persuasion, have been at work in applying these measures effectively [START_REF] Bigo | Ni État de droit, ni État d'exception. L'état d'urgence comme dispositif spécifique ? Introduction[END_REF]. Therefore, an analysis in terms of the politics of fear does not exhaust the understanding of the situation. If governments and commentators have tried to justify their own specific choices, as opposed to the ones of their neighbours, by a type of propaganda that is rarely seen outside of a war context, they were not clearly successful. Nowhere has a consensus around government emerged through propaganda and nudging. On the contrary, across Europe, as well as other parts of the world, popular opinion is divided. Parts of the population reject the policy of their own government, asking for the policies of neighbouring countries to be adopted instead. Dissent exists on the details of policies. Therefore, though the politics of fear approach highlights certain truths, as our case studies show, its view of the general frame of governmentality is not adequate to understand the concrete forms of "governmentality" at work and their relation to obedience and compliance of divided groups of populations. This is why we propose an analysis in terms of a "governmentality by unease" [START_REF] Bigo | Security and immigration: Toward a critique of the governmentality of unease[END_REF]. This particular terminology suggests a less coercive and intimidating perspective than the one of a politics of fear organized by the state (hence the rejection of the term) and privileges an analysis of a transversal "dispositif" based on three specific interconnected modalities or dimensions. The first dimension is related to the ways of seeing and reacting that Western states have in terms of emergency management by enacting nationalist and territorial logics of control. The second dimension relates to the conflicting ways of seeing the pandemic that each bureaucracy has, and the tendency to consider the virus through the frame of a danger to security. This has led to the organization of sanitary emergencies under the rules of the game of national security, thus creating tensions between national security, public health and the economy. Professionals of politics, unsure about their priorities, have the tendency to privilege borders controls and confinement. The third dimension is related to the resistance against the preferred national policies and the scale of some protests which show that they are not "subjectivized" by fear. Nevertheless, people are torn between their own personal concerns to stay safe, to avoid being seen as suspicious, and a desire or support for forms of peer-to-peer surveillance based on the denunciation of the suspected contaminated persons (which may include themselves potentially). Technologies like contact-tracing applications are therefore at the core of the discussion, even when they are not efficient. Controls at the national borders, local lockdowns, and wearing a mask are equally manifestations. They may stay with us. Against the background of these dimensions, the first part of this article investigates their rationale and why the situation of COVID-19 in terms of obedience and resistance is not so exceptional. The second part of the article develops these elements in more detail through the practices of digital contact tracing applications and thus digital surveillance implemented by the Turkish and the UK governments based on the different modalities of governmentality by unease and the modalities of obedience through which they try to frame their discourses and respective practices. This is a key test for determining the existence of such a general form of governmentality and its diverse modalities. This also opens interrogations on the boundaries of liberal and illiberal regimes and how far democratic practices are respected. How far are privacy and freedoms affected by the crisis? Is it a temporary or a more permanent trend? In the third part of this article, we explore in even more detail the impact on democratic practices of the discourses and practices of governmental policies regarding the Schengen logics of managing movement of persons in Europe, as we consider that it is one of the most structural changes brought about by (and extending beyond) the COVID-19 period.

I)

Governmentality of unease: seeing COVID-19 like a state, like a bureaucrat, like someone suspected of being infected.

A) COVID-19: Seeing like a state, invisible networks and the territorial trap.

The COVID-19 pandemic has taken world bureaucracies by surprise, be they international or national. This was the case in China as well as in the World Health Organisation (WHO) as was evident from the first signals given inside the organization. Previous pandemics of smaller scope, despite the views of medical authorities, have played in favour of the politicians' view that it was easy for the developed countries to manage pandemics and that the dangers were confined to poor countries, especially in Asia and Africa. For example, most Western governments already knew in December 2019 or January 2020 that the spread of the virus and the danger of asymptomatic transmission created an original situation for this pandemic. However, they did not react, before the stealth of the virus was publicly demonstrated, not only in far-flung China, but at the core of Western Europe. Surprise turned into a form of state of panic of decision-makers, which then turned into a panic of the "state", and, by default, a panic of imaginative solutions that resulted in falling back into the most traditional practices: lockdown, management by territorial and administrative zones irrespective of social density and virus propagation, the reintroduction of border controls at the national frontiers and regional or local ones, even in areas of free movement like the Schengen area of the European Union.

Why did we have such a "spontaneous" fallback reaction? James Scott's book: Seeing like a state: How certain schemes to improve the human condition have failed (1998) provides an important point of departure for answering the question. It allows us to understand the focus on territoriality, sovereignty, nationalism and national security that so many states have embarked on, despite various alternative policy answers to the virus. To implement these nationalist policies, they used security measures designed to control by stopping and detaining people in certain places. But, in so doing, they fell into what John Agnew (2017) has called a "territorial trap" in which geography and administrative logics are the first reaction of modern states in front of the unknown. Seeing like a state is therefore very often seeing like a defence-security manager. It is like a "second nature", a collective doxa engrained into the habitus of the policy makers. Governments, administrations, and other actors of globalization routinely and independently of the specificities of any particular catestrophe frame their way of thinking of space and scale through territory and not networked approaches. They therefore had great difficulties in understanding a networked logic like the spread of COVID-19.

The specificity of COVID-19 as a disease, whose asymptomatic phase is very long, has exacerbated the uncertainty about the kind of policies available, by adding a temporal dimension to the incapacity to understand non-territorial scales.

Some governments (Taiwan, South Korea or Germany during the first wave) had the capacity not to choose between territoriality approaches and traceability of individuals in networks because they had highly operational health infrastructures and could "absorb" the rise of sick people in their hospitals. However, the other governments were obliged to choose, by default, territorial confinement to limit the spread of the virus. Decades-long neoliberal pressures to reduce costs had impeded their ability to trace the networks of individuals and treat people in their own hospitals. This incapacity of the "welfare" state to deliver what was expected by citizens pushed many governments, irrespectively of their political regimes, to use border controls and quarantine-based territorial measures. COVID-19 was treated like the plague or even leprosy, even this meant keeping in the same territory people who were sick (unhealthy) and those who were not sick (healthy) but were suspected nevertheless of having been in contact with the "virus carrier" and have not yet developed symptoms [START_REF] Vigarello | Le sain et le malsain : santé et mieux-être depuis le Moyen Âge[END_REF]. Modern medicine from at least the cholera epidemics has been against this view of "contamination". But fear, uncertainty, and division about the nature of the virus created this regression to the habitus of 19 th century medicine, giving at least a sort of certainty that imprisoning people in a certain space and limiting social interactions was the less bad solution.

If some considered herd immunity an alternative, they were a minority among medical experts. Public health authorities controlling the management of hospitals (more than doctors and epidemiologists) claimed to be the sole competent authority (truth speakers), as they were the only ones who understood the shortterm effects of pandemics and the necessity to act immediately. In the division inside the medical profession itself, the ones in charge of infrastructure joined the ministries of national security in the name of emergency. Both groups insisted that an absolute territorial lockdown, i.e., a no-risk policy, was required. The syndrome of seeing like a state, i.e., to deploy a geopolitics of territory, blocked the possibility of imagining different policies and those few proposing diverging policies were not heard or rejected. This, often, led governments to miss key elements in their "geographies of knowledge" [START_REF] Agnew | Know-where: Geographies of knowledge of world politics[END_REF][START_REF] Agnew | Globalization and sovereignty: Beyond the territorial trap[END_REF].

B) Bureaucratic fights into the field of professionals of security based on a logic of suspicion

The second dimension to consider is the analytical necessity to deconstruct the homogeneity of state discourses at the governmental levels and their rhetoric of "balances". Territorial states do not "act" as a unified actor, even if international geopolitical scholarship continue to think so. States have to be understood as a field in which political and bureaucratic actors fight for power, sometimes with the support of the private sector [START_REF] Bourdieu | Sur l'État[END_REF]. It is critical to analyze the contradictory policies that exist in each country as well as the fact that struggles and alliances are often organized along sectorial lines and transnational interests (Hibou and Béatrice 2015;[START_REF] Dezalay | The Import and Export of Law and Legal Institutions: international strategies in national palace wars[END_REF]Yves 2001, Bigo 2020). Medicine is not organized as a global and unified field of knowledge. Disputes as well as material and national interests exist within it. But the field has quite a strong autonomy about what is at stake. With a pandemic of such a scale, doctors entered into the field of the traditional professionals of security when they claimed in the name of science and emergency grounds the right to design and decide about national security. This did not last long. Very quickly they were confronted by traditional actors who considered that, if this was a state of emergency, doctors could only be advisors not decision makers.

In several countries, lockdowns and/or curfews have been decided by the actors of the "defence and intelligence community", albeit sometimes with the support of the top of public health officials, but frequently against the advice of epidemiologists and local practitioners. Medical staff working in hospitals have often been left out from the pandemic decision making and sometimes the support of economic interests have been linked with the freedom of circulation to reinforce decisions framed by national security interests different from health.

This relationship between the defence and intelligence community and public health officials has certainly been slightly different from country to country, but it has nevertheless often existed and has had transnational links. One extreme example of the alliance in favour of lockdown, in a liberal regime, is the case of France where the choice of the administrative setting of the decision-making mechanism was crucial to get a view in favour of national security logics. The Defence and National Security Council (CDSN) is chaired by the Head of State and is composed of the Prime Minister, the Chief of Staff, the heads of intelligence services, the ministers for the armed forces, the interior, the economy and foreign affairs. All decisions are covered by secrecy. The Minister for Health is invited to attend but he had only one vote. France is not the only country to do so. The leaders of Turkey and many other countries declared that we are at war against the virus, even if some countries like Sweden or the UK were more reluctant with this line of thought and continued to require the full cabinet to vote for the different organizational measures.

All in all, despite some differences, the same logic of subordination of medicine to defence is preeminent, and the left hand of the state sees its vision of protection of individuals as subordinate to the vision of a danger for national security. Therefore, the inner fight of state bureaucracies between a territorial defence logic following the administrative organization of the state and a more local, networked sanitary logic has not only been national, but also it has been replicated locally through engaging different forms of resistance against the central government, and transnationally, with the help of international organizations like the WHO when they challenged the views of strong state politicians (the US with Donald Trump, Brazil with Jair Bolsonaro, but also Sweden with Stefan Lofven). The notion of a transnational field of power opposing professional guilds in security matters may be useful to avoid a methodological nationalism and a vision of IR as a series of national state policies [START_REF] Bigo | Sociology of transnational guilds[END_REF]2020). COVID-19 management has been articulated by transnational dynamics locally reproducing different forms of governmentality by unease.

C: Potential suspect of contamination, liquid surveillance and forms of active obedience. Governing the self?

The third dimension to analyze is the forms of obedience to power that are sought by the different governments and often contradicted by the self-steering apparatus(es) of individuals to use the terminology of Norbert Elias [START_REF] Elias | Society of individuals[END_REF].

The lived experience of being potentially infected and a danger for others is crucial for the unease created by the pandemic. It is not just a question of influence, of nudging, and success or failure of an information strategy, or a conduct of conduct of others. Rather, it is related to a conduct of conduct of the self, to a habitus forged by previous events and dynamics concerning fear and concerns (like unemployment, war, terrorism or fear of migration) and how they interplay in the present, and come to affect individuals differently depending on factors such as age, class and race. This point of articulation on the body and soul of each individual, with their social trajectories, creates the conditions of possibility to generate active obedience or not. It is the process of a governmentality of the self in society that organizes the conduct of people's conduct, and not (only) a propaganda machine, which is sometimes counter-productive and generates resistances [START_REF] Foucault | The Government of Self and Others[END_REF]. So, if almost nobody is really terrorized or in a state of panic and fear because of COVID-19, to the point that some people just negate its existence, everybody is nevertheless actively thinking about themselves and their families when the idea of death is transformed into an experience which has touched friends or neighbours. This reflexivity on this experience of the proximity of death and sickness contradicts general policies of management, especially when they are applied on territorial bases creating artificial distinctions between regions, cities and neighbours, and mixing the categories of the healthy and the ill into the one in which everyone must be suspected of contamination. The inner politics of vulnerability of the self and of uncertainty on an existential scale, has been played out to reinforce the institutional discourse of care and protection, but it has not been effective via the different state narratives. It has permeated the experience through the expected resilience of individuals and a discourse involving an ethic of self-responsibility and care for others and oneself. Each individual has simultaneously thought and been asked to feel responsible and to participate voluntarily in the measures of protection, which has generated a form of peer-topeer or self-surveillance different from acceptance to coercive policing. This is what Zygmunt Bauman and David Lyon have called a "liquid surveillance" in opposition to a "solid surveillance" carried out by coercive and intelligence institutions [START_REF] Bauman | Liquid surveillance: A conversation[END_REF]. Liquid surveillance is not a less intensive surveillance than institutional surveillance. On the contrary, it is more permeable, more invisible, but very effective because of its horizontality and its appearance as acting for the common good. The way the digital applications for contact tracing have been justified is clearly a case of this logic, in which beliefs in medical discourses have been used to justify established information interests into the public health realm in order to collect in mass personal data and to allow the use of predictive algorithms whilst letting people believe that their privacy is nevertheless respected. Meanwhile, people are urged not to be selfish and to share their data to save themselves and the others [START_REF] Doyle | The role of IS in the covid-19 pandemic: A liquid-modern perspective[END_REF]. People have also been pushed to reflect on their desires and to suggest they stay at home, and do not travel abroad. In this framework, the case of the digital contact tracing application and its justification is not anecdotal. It says a lot about the form of governmentality at work. This is what we will develop now to show the complexity of the different situations as they are among the elements which may stay with us, after the end of pandemic.

II) Contact tracing and digital surveillance in Turkey and the UK. What consequences for our future?

Digital surveillance is not a new phenomenon, but with the COVID-19 pandemic its use has triumphed because the digitization of contact tracing has been the common denominator of most COVID-19 related policies [START_REF] Woodham | COVID-19 Digital Rights Tracker[END_REF]. The very same technology has been introduced in a variety of forms (e.g., centralized collection versus decentralized collection; Bluetooth-based tracing versus GPS tracing). But the main rationale of digital contact tracing is, in all cases, to repurpose people's smartphones as devices to trace their physical movements and interactions with others for public health ends. Its introduction thus is based on the assumption that digital technologies, in general, and smartphones, in particular, have been integrated into the everyday lives of most people in developed countries and some developing countries. This assumption underpins why we will consider digital contact tracing applications when we explore COVID-19 governmentality of unease. We will briefly explore two exemplary uses of mobile contact tracing applications as they are implemented by Turkish and British bureaucracies (the second bureaucracy being supposedly more liberal than the former), to explore different forms taken by a governmentality by unease.

At first glance, digital contact tracing seems like an antidote to state policies managing the pandemic inside a grid of territorial management of the kind that we outlined in the introduction. They are based on network thinking and may appear as new geographies of knowledge. This is why these applications have been presented as a way to avoid or leave widespread lockdowns that have caused economic, social, and physiological problems for the public. They were presented as the 'magical' technology that would rapidly help people distinguish the healthy from the sick and even detect the suspects without destroying their privacy by using pseudonymization. The applications would also enable governments to collaborate on Big Data analytics to find common solutions to the pandemic. This digital intervention nevertheless still confines public to a territorial grid by way of targeting their movement at the individual level since its prominent feature is to alert its user to self-isolate (until the isolation period is passed or in some cases until the user's test turns negative). This self-isolation as such may be considered as a policy articulated on the freedom and reflexivity of the individual, but, de facto, it depends on the way the self-isolation is declaratory, or is controlled, and by whom (e.g., peer to peer verification or centralized control by health authority and/or police).

This assumed 'magic' of technology is not without controversy. A key issue here is the way this form of digital intervention normalizes techno-solutionism with dataveillance and the ratchet effect it creates for the future, given that the distributors of these platforms may have interests that extend beyond epidemiology, whether these be commercial or general public health [START_REF] Tréguer | The State and Digital Surveillance in Times of the COVID-19 Pandemic[END_REF]). This possible 'brokerage' of data raises a range of legal problems. Needless to say, the initial plan of introducing the applications comes with its figurative baggage of legal issues and a brief look at the issues may shed light on how governments may have shaped their policies on digital applications to enhance greater participation by the public.

In essence, the applications involve activities (e.g., collection and use personal information about users of the applications from their movements to health status) that interfere with individuals' right to privacy and data protection [START_REF] Sacco | Digital contact tracing for the COVID-19 epidemic: a business and human rights perspective[END_REF][START_REF] Zwitter | Big data, privacy and COVID-19 -learning from humanitarian expertise in data protection[END_REF]. This interference does not amount to a human rights violation if certain legal principles are followed: do public authorities ensure that the limits to the right have a legal basis in national law and if so, is that limitation necessary and proportionate to protecting public health? At a regulatory level, data protection legislation, which aims to safeguard, among others, the right to privacy, provides a number of principles with which data processing activities must comply. Among them is the lawfulness principle, according which a legal basis must be satisfied for personal data processing. A key legal justification for digital applications has been the furtherance of public interest in the area of public health in addition to users' consent, albeit with reservations on the appropriateness of the latter (European Commission 2020).

We can certainly see that legal norms on protecting privacy and personal data allow governments to implement digital contact tracing subject to the above conditions. These norms form the legal constraints of a regime that subscribes to liberal principles of fundamental rights protection. A selection of the incentives for the wider public adoption of the contact tracing application during the pandemic ('mandatory' versus 'voluntary' solutions) however brings about its own legal issues. For example, a voluntary application does not automatically mean that there is a legally valid consent obtained from its users, which must be freely given, specific, and informed. However, a power imbalance such as government vis-a-vis individuals in the case of the applications may raise doubt on its validity. Without valid consent, the use and collection of personal data through a voluntary application may be based on another legal basis. Mandatory use of digital applications on the other hand would directly negate consent as an option for a legal basis. Aside from legal questions on adherence to data protection legislation, making digital contact tracing applications obligatory would call into question the obligations and responsibilities of a state that subscribes to social policy and welfare state. This is because, from a more juridical stance, that type of legal mandate would put a financial burden on people. A state-imposed burden would be legal if it is provided by law and subject to the proportionality principle. Therefore, it needs to be the state itself, instead of its citizens, that would need to bear this type of burden.

Because of the problematic aspects of mandatory digital applications, many countries have opted for a 'voluntary' solution (O'Neill et al 2020) and the majority of European countries (e.g., with the exception of Poland) as well as the EU institutions, such as the European Commission, supported by the European Data Protection Board, have favoured a voluntary solution (European Commission 2020; EDPB 2020). Nevertheless, a dilemma emerges here because one of the issues on the effectiveness of the application is that it must be used by a considerable proportion of the population [START_REF] Ferretti | Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing[END_REF]. Managing the pandemic with this digital intervention, therefore, has been procured through creating conditions for the public to agree with self-surveillance and, as we argue here, these boundaries redefine its 'voluntary' nature. How is a practical logic of responsibility is implemented upon the public? What does a 'voluntary' acceptance of the contact tracing applications mean?

An extreme example here is the digital application implemented by the Turkish Government, Hayat Eve Sığar (HES) ('Life Fits Home'), which became operational in April 2020 (Turkish Ministry of Health 2020). This application collects a range of personal information about its users from national identity information to location data and to health status. It was originally set up to monitor people who had tested positive for COVID-19, who may have interacted with someone who had tested positive, or who were subject to confinement rules (e.g., there were restrictions in place for people aged over 65 and younger than 20). If someone needs self-isolate left home, he/she receives a warning message. If he/she does not comply with the self-isolation rules, his/her information is shared with the police, who may subsequently impose administrative fines or start criminal investigations for refusing to comply with precautions relating to epidemics. As of writing moment, no law has been adopted to legally require people to use the application, despite the statements by officials to the contrary. Thus, from a legal standpoint, the use of the application is voluntary, but the reflexive reactions of the government have started to create a de facto mandatory regime for the application (the devil is in the detail). Effectively, it has become mandatory for Turkish citizens to present a code called a HES code, which is obtainable through the application, before they undertake intercity travel by bus or plane [START_REF] Bianet | Turkey to Use App to Track Intercity Travels, Test International Passengers for COVID-19[END_REF]. As the COVID-19 cases continued to surge in September 2020, this de facto mandatory regime has been expanded. For example, a new rule was introduced that required people to present the code when entering public institution buildings and buildings where people may be crowded such as post offices, notaries, and banks (Turkish Ministry of Health 2020).

As this de facto regime surfaced, an undertone of national duty streamlined the discourse among the ministerial offices in Turkish government, which even in normal conditions do not present an overt friction at governmental levels. Playing with the unease of the population and the balancing between risk of death by the COVID-19 and risk of death by poverty and hunger, an almost pandemic consensus has been created inside the national media throwing a cloak over actions whose constitutionality would otherwise be questioned (Turkish Medical Association 2020). Evidently, those rules limit people's fundamental rights such as the right to privacy and freedom of movement and a limitation as such can be legal only if it is based on law according to Article 13 of the Turkish Constitution. That said, each rule was imposed gradually across the provinces by provincial Public Health boards presided by provincial governors based on circulars from the Ministry of Interior. Because a ministerial circular does not have force of law to legislate the limitation of fundamental rights, a legal issue on the constitutionality of these measures exists. But this is a legal issue which the Ministry apparently is not occupied with nor has it faced any opposition. While this top-down national duty undertone presented a form of homogeneity in state discourse, it became the role of the Ministry of Health to justify that its actions had been constraint by liberal values. The Ministry of Health (through the Directorate of Communications of the Presidency) emphasized that its data collection, part of which is the application, follows Turkish data protection law. In a way, this communication aimed at legitimizing its practice by showing how it constraints itself with national law (Presidency of Turkey Directorate of Communications 2020). Coercion and deterrence against the ones not using the contact tracing application have never been used directly, but they have been on the imagination of people and some elements of politics of fear are embedded into the more general governmentality of unease.

In governments that claim to be liberal regimes, however, contact tracing applications have been presented immediately as a democratic option when compared to the Turkish counterpart. Nevertheless, the discourse around the implementation of the applications comparably refigures the logic of voluntariness through attaching, instead of threats, benefits to their use. To support this idea, we can make tentative observations on how digital contact tracing has unfolded in the UK. The first attempt to implement an application in England and Wales came in May 2020 with the trial conducted on the Isle of Wight. Concerns over the compatibility of the trial with data protection legislation emerged, however, not least because it used a centralized server overseen by the National Health Service to send alerts to its users about potential risk of contagion (UK Joint Committee on Human Rights 2020). Soon it turned out that the trial had been unsuccessful, which led to a second attempt at developing an application, which this time relied on a framework developed by Google and Apple. This second version of the application made its debut in late September 2020. Instead of being collected in a central database as it was adopted in the first version, the second version uses Bluetoothbased proximity tracing and has a decentralized model whereby matches through this proximity tracing are kept on users' phones.

Considering that two different versions were rolled out in a period of five months, the use of contact tracing application in the UK -like the rest of the world -must be regarded as experimental. But one of its features resonates with the reconfigured logic of voluntariness that attaches benefits and advantages to the use of the application (e.g., checking in venues, a narrative of less invasive and more accurate determination of risk of contagion). Since the introduction of the second application in mid-2020, the hospitality sector, such as restaurants and pubs, and other places where people may congregate, such as places of worship, have been required to record the contact details of their customers to support the NHS Test and Trace program. In England, these places must display an NHS QR barcode whereby their visitors can scan and check-in to the premises. Information about the venues where they have checked-in will be stored in users' devices for a period of 21 days.

But what about customers who do not wish to download the application or that who do not have the means to have a smartphone that supports the application? Venues -in theory at least -can still collect information in more traditional ways because there is no legal requirement for the public to use the application. Clearly, this is different from how the public is coerced into using the voluntary application in Turkey since no alternative options are presented to those members of the public who do not or cannot use the application for one reason or another. However, the discourse created around its use in venues seems to be targeted towards convincing people to 'trust' the UK government and choose a more convenient 'invasive' option. The 'option' in terms of privacy transforms into a decision between the bad and the worse, which generates unease and by default obedience, because the government presents the decision to download the application as an individual rational choice based primarily on ethics of responsibility and a fair balance between privacy and care for others.

Overall, the digital contact tracing applications are a telling example, in terms of practice, of the use of a governmentality of unease we have outlined in the introduction. That said, the examples of their implementation by the Turkish and UK government generate different situations. These two examples of digital tracing applications reveal how the governmentality of unease may work differently depending on the historical context and the extent to which state bureaucracies subscribe to liberal principles (or enforce them in practice). At first, the digital intervention in Turkey came in the form of a 'voluntary' option, but there was a shift change to de facto mandatory regime (the constitutionality of which is contentious) as the threat of coercion has been imposed on the population. In the UK, however, the similar level of coercion does not exist (presumably due to the greater adherence to the liberal values), but the reconfiguration of voluntary nature of the digital intervention was nevertheless occurred. Despite these differences and the fact that each digital intervention is framed by the different "rapport de forces" between institutions, they converge on how public health and traditional security on both sides join to create incentives for digitization and surveillance of everyday lives based on the premise of citizens' civic duty to protect themselves and others.

To enable greater complicity -if not coercion -for their participation, certain aspects of everyday life are framed towards digital applications, shaping people's interaction and creating boundaries for non-compliance such as boundaries for some members of the public when they want to access their consumer rights and to public services. As we see in the UK government's strategy, a form of compliance is encouraged based on the subjectification of an autonomous and reflexive individual, which, in fact, is more driven by the herd logic of social networks and nudge management based on the so-called positive reinforcement and indirect suggestions to influence the behaviour of groups or individuals than a selfreflexivity [START_REF] Thaler | Nudge: Improving decisions about health, wealth, and happiness[END_REF]). How far this management relates to a governmentality of unease or to a politics of fear depends on the appreciation of the degree of coherence given by the researcher to the dominant discourses and the homogeneity of the group of spoke persons. If it is seen as too homogeneous or only as an effect without specific will to a depoliticized vision of governmentality, it may easily enhance a plot theory against the "Machiavellian rich others, or the fat guys" [START_REF] Birnbaum | Genèse du populisme: le peuple et les gros[END_REF].

II) Governmentality of unease at work in management of the freedom of movement in the Schengen area during COVID-19. What is left of freedom?

As regards the way states envisage their spatial policies and their territorial sovereignty, and the way they seek to anticipate the next move of the pandemic with digital applications, two preoccupations have been visible. The first is the local surveillance of the suspected unhealthy and their association with foreigners. The second is the reintroduction of national border controls inside Schengen.

The first preoccupation of surveillance of lockdown rules in local areas is a classical spatial strategy of population control based on a territorial grid that Michel Foucault (1991) associated with disciplinarisation. This strategy has been accompanied by heavy-handed policing in many areas with fines for those failing to comply with the rules. The effect of fining people (disproportionately Black individuals) also entails the entry of their data in local and national databases, which can then be checked by many state (and in some cases non-state) authorities. The stigmatization goes far beyond the local fine itself and reaches into the mechanisms of transnational surveillance of people, putting at risk the full political economy of freedom of movement and democratic exchange of opinions. Nevertheless, it is difficult to judge in practice what forms of governmentality of unease are embedded in the COVID-19 measures on movement of persons, and what is the part of a governmental coercion into it. What is at stake seems less directly sovereignty than controlling flows, less directly an exercise of political will than a form of governmentality linked with the conditions of travel in an area like Schengen. Liberal regimes continue, but they do not shy away from illiberal practices.

There are of course many multinational regimes of free movement of persons around the world of which the European Union's Schengen area is only one (Aracanzo and Geddes 2014). However, the Schengen area of border control free movement of persons across 26 European states is among the most developed.

It is also unique in that its legal framework is designed around the prohibition of border control checks at intra-Schengen borders rather than the creation of a right to cross those same borders for individuals. In effect, the Schengen system attacks the border control institution -outlawing the positioning of border guards on intra-Schengen borders (though it allows border controls to be reinforced at extra-Schengen borders, some which has in fact happened [START_REF] Groenendijk | In search of Europe's borders[END_REF]).

Because of this specificity of the Schengen area, we will focus on the COVID-19 measures taken there from the perspective of the three articulated dimensions, we have developed in the introduction.

In particular, the Schengen Area COVID-19 reactions reveal the extent of the role of the Agnew's territorial trap in the framing of the sanitary exceptions to free travel and the fact that decisions were taken initially by interior and security ministries with only advice from the Public Health authorities, advice they did not really follow. In the border control free regimes, of which Schengen is an example, tendencies of interior ministries to perceive the re-introduction of border controls as a measure of safety were exacerbated [START_REF] Guild | Internal border controls in the Schengen area. Is Schengen crisisproof?[END_REF]. Some states, like Poland [START_REF] Cervinkova | Citizenship after COVID-19: thoughts from Poland[END_REF] and Hungary [START_REF] Drinóczi | COVID-19 in Hungary and Poland: Extraordinary situation and illiberal constitutionalism[END_REF], 'closed' their borders altogether using the COVID-19 pandemic as a mechanism to reinforce nativist discourses about dangers being external in the form of outside the borders.

The European Commission pleaded with the Schengen states to keep their borders open for a range of persons on the grounds of the states' own needs for key workers -e.g. healthcare professionals -the needs of individuals to travel to their own states, and so on (European Commission COM 2020, p 115). The Schengen external borders were frequently the place of quite extreme interior ministry controls, at least in discourse if not in practice. As the Commission noted there was a dramatic slowdown in air-traffic; according to the Commission, by 31 March 2020 the overall reduction was 86.1% compared to a year earlier (European Commission COM 2020: p148), With ferry, coach and rail transport following suit. But many states were very slow in requiring passengers who continued to travel to provide increased personal information, no doubt relying on existing passenger name record requirements and increased interoperability capacities with other state databases [START_REF] Fahey | Law and governance as checks and balances in transatlantic security: Rights, redress, and remedies in EU-US passenger name records and the terrorist finance tracking program[END_REF][START_REF] Bigo | The interoperability controversy or how to fail successfully: lessons from Europe[END_REF].

Justifying the necessity and proportionality of extreme lockdown measures became increasingly difficult for some states [START_REF] Lebret | COVID-19 pandemic and derogation to human rights[END_REF]. In Schengen states that did not follow the Poland/Hungary approach of designating the national border (albeit a Schengen border) as the place where sorting safe people from unsafe ones would take place, most Schengen states allowed a greater role for health ministries (as opposed to their interior counterparts) in determining strategies. In such countries, the pandemic risk was accepted as a medical emergency. Often this was given greater specificity to the pandemic strategies -it was an emergency for national health systems which often were unprepared for the challenges which the pandemic brought as a result of substantial funding cuts over the preceding decade [START_REF] Johnson | Potential scenarios for the progression of a COVID-19 epidemic in the European Union and the European Economic Area[END_REF]. Health ministries, which had rarely been engaged with issues of border control or state sovereignty preoccupations, were obviously relevant institutions for this public health approach. For these authorities, the challenges were between atavistic containment reflexes and reinforcement and improvement of medical capacities. However, European health ministries have a long history of struggling with the tensions between patients' entitlement to privacy and surveillance on public health grounds. The new COVID-19 approach of many Schengen states was to change their measures from ones which block people from travelling to ones which dissuade people from travelling on account of the consequences.

Quarantine measures where anyone, citizen or foreigner, who enters a state must spend a specified period of time (usually between 10 and 14 days) in self-imposed isolation became the preferred mechanism of dissuasion of movement. Of course, the first question about the quarantine measures has been the necessity of imposing them where testing is already in place. In other words, where travellers have been tested either on departure or arrival and proven not to have the virus, how can quarantine rules be considered proportionate and necessary? Courts of course tend to move slowly, but it is likely that, in due course, they will need to determine this question.

As an inherent part of isolation, international travellers are required to complete, usually online, a questionnaire providing extensive personal information. This includes information about themselves and their families, but also about where they will be staying, who they will be visiting and how long they will be on the territory, as well asmobile telephone numbers, sometimes not only of the passenger but also of the place where he/she will be quarantined. The purpose of this collection of personal data is ostensibly to allow state authorities to trace individuals in the event of an increase in infection rates. However, as with many of the COVID-19 measures, requirements regarding access, use, and destruction of this personal data are less evident. The nebulous but life-threatening definition of the threat is accompanied by a lack of clarity and definition of individual's privacy rights. The possibility of using interoperable tools to track passengers for reasons other than the spread of COVID-19 is ever-present.

Quarantine measures, therefore, permit two types of management of travel within Schengen. The first is closer to conduct of conduct: creating a reluctance among people to travel and, thus, to change their conduct to avoid quarantine rules. The second is the creation of new opportunities for state surveillance through the justification of policing quarantine rules and, for this purpose, accessing personal data on passengers from multiple sources and for indeterminate lengths of time. These measures have long-lasting impacts on both the way people respond to coercion based on dissuasion in financial and temporal terms, as well as the obligation to provide state authorities with substantial amounts of personal data.

This framing of speed and travel as an essential element of freedom [START_REF] Bigo | Freedom and speed in enlarged borderzones[END_REF]) is challenged by these quarantine measures, which 'punish' the traveller for seeking to exercise this 'freedom' in the name of both the protection of the traveller and of the public generally. Traditionally, the justification for the state's acquisition of personal data has been to prevent serious crime and terrorism threats [START_REF] Kuskonmaz | EU exclusive jurisdiction on surveillance related to terrorism and serious transnational crime, case review on opinion 1/15 of the CJEU[END_REF]. The new ground, public health, provides opportunities for a wide variety to actors to enter the data collection sphere where their actions face less public resistance at the moment because of the variable success of the politics of fear project which has accompanied state measures to fight the pandemic.

Conclusions

At the outset, we discussed what could be the most appropriate framework to analyze the compliance of the population regarding states' responses to the COVID-19 pandemic. We rejected the ostensive dilemma of the politics of protection -in which a trade-off between health and economy is presumed. Instead, we have sought to identify three dimensions by which a governmentality of unease has emerged as a general frame, despite the variations on so-called answers to the pandemic.

First, in the different countries we examined, diverse governments have been prisoners of the territorial trap identified as a way of seeing like a modern Western state, including Turkey. The state responses have reproduced the administrative territorial logic and the national borders to secure their national territory as the solution against the virus, instead of following a network mapping and a coordinated strategy. Despite claims of the European Commission to do so, the EU Council has dismissed this approach and has even put at risk the basic principles of free movement of persons in Schengen by re-instating internal border controls to please populist claims of national preferences and indifference to others.

Secondly, public health bureaucracies have had enormous difficulties in deciding anything on their own and have been obliged to lobby the other traditional security agencies to have a chance at least to be heard by the highest authorities (president or prime ministers). The politics of lockdown with many variations and specificities in different states, have been primarily decided by defense and interior ministries. This resulted in the healthy and the infectious being locked down together and the rethinking of borders from state borders to borders of people's homes and all permutations being included in the measures. However, the shift from state borders to household borders in terms of lockdowns or self-isolation (sometimes combined and asked through contact-tracing applications) also revealed an internal shift from seeing like an interior ministry (e.g., foreigners are the source of infection) to seeing like a public health official (e.g., contagion requires contact among people) when the latter privilege surveillance and confinement. This has been the reason of the simultaneous development of contact tracing applications which under the argument of technology were de facto a form of political negotiation around national security and international collaboration. This transnational factor did not lead to coherent international answers based on the same appreciation of the pandemic development. Rather, it has resulted in chaotic nationalist responses, depending on politics as usual between the political partis and of the weight of defense and security settings (about emergency and secrecy rules) in the decision-making process. Therefore, the policies at stake have been the result of the struggles inside the field of the professionals of security between the heirs of traditional security and the pretenders coming from public health, to use Bourdieu's terminology. If the UK had allowed more permeable boundaries of the field of security, letting the voice of medical staff treating patients in hospitals to be heard, it has been less the cases in Turkey and France where secrecy of decisions has been privileged. The EU Commission has called for transparency but has not delivered it about the commercial agreements with the pharmaceutical firms, except one due to the disputed with the firm. This will stay with us for long and may create even more defiance than before on the democratic process of deliberation.

Thirdly, and even more importantly the development of a logic of suspicion about the potential sick individuals inside the population and their so-called lack of responsibility has been based on reciprocal individual anxieties and has helped to justify forms of liquid surveillance (including their digital technologies). Key to the acceptability of the surveillance measures has been convincing individuals that they are voluntarily taking part in the schemes. The articulation of heterogeneous concerns and their focus on the risk of death with peer-to-peer surveillance have enacted forms of compliance. This has shaped the face of obedience in COVID-19 measures under which the active engagement of individuals in their own surveillance has been key.


Anissa Amar

Aziz Elkechai

Jean-François Halet
email: jean-francois.halet@univ-rennes1.fr

Frédéric Paul
email: frederic.paul@univ-rennes1.fr

Abdou Boucekkine
email: abdou.boucekkine@univ-rennes1.fr

Two-photon absorption of dipolar and quadrupolar oligothiophene-cored chromophore derivatives containing terminal dimesitylboryl moieties: a theoretical (DFT) structure-property investigation

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

During the last decades, numerous dimesitylboryl (BMes2) derivatives have been synthesized and studied for their remarkable photophysical properties by Todd B. Marder and coworkers, [1][2][3][4][5][6] especially for the non-linear optical (NLO) responses often observed for multipolar derivatives of this kind. Interestingly, high two-photon absorption (2PA) crosssections have been reported for several series of quadrupolar derivatives. Among the latter chromophores those constituted by a thiophene oligomer acting as a conjugated bridge spanning two terminal dimesitylboryl terminal groups turned out to be quite promising nonlinear absorbers for various applications for which high two-photon absorption (2PA) cross-sections are usually needed, such as photodynamic therapy, data-storage and optical limitation. [7][8][9][10] The NLO properties of the latter compounds are mainly due to the BMes2 moiety that acts as a strong -electron acceptor thanks to the vacant boron pz orbital, the latter being sterically protected by the bulky mesityl groups tethered to the boron atom, insuring its chemical stability. Given that these derivatives were also fluorescent, exhibiting usually fluorescence quantum yield above 20%, 4 applications in fluorescence bio-imaging were also envisionable after proper functionalization to solubilize these derivatives in water.

Accordingly, Todd B. Marder and coworkers recently investigated a series of new watersoluble dimesitylboryl analogues of these compounds bearing four NMe3 + groups attached to the terminal BMes2 moieties. 5,6 Interestingly, these charged compounds exhibit very high 2PA cross-sections, much higher than the ones obtained for the analogous neutral systems previously studied as well as stronger fluorescence quantum yields in organic solvents.

Remarkably, these derivatives are also fluorescent in water and a good photochemical stability in the water solvent was stated for some of them, allowing their use for bio-imaging purposes. The best bi-photonic absorbers among this series, namely 2TM-NMe3 + and 5M-NMe3 + (Scheme 1), are the subject of this study. 1 ACCEPTED MANUSCRIPT -CLEAN COPY Scheme 1 2TM-X and 5M-X series of compounds (X = H, NH2, CN, NMe3 + ). 5,6 We have theoretically investigated their 2PA properties trying to understand and rationalize the structural origin of their large NLO responses. Here, we report and discuss results obtained via density functional theory (DFT) and time-dependent (TD) DFT computations on these cationic species and on analogous neutral dimesitylboryl-based quadrupolar systems for comparison, replacing the four NMe3 + terminal groups in 2TM-NMe3 + and 5M-NMe3 + by hydrogen atoms (2TM-H and 5M-H), cyanide groups (2TM-CN and 5M-CN) as well as amino groups (2TM-NH2). To calibrate our calculations, we start our study considering vinyl (nV, n = 2-5) and alkyne (nT, n = 2-5) related systems previously studied and their dipolar derivatives 2VD, 4VD, 2TD and 4TD (Scheme 2). 4 These investigations were performed at the DFT level, the computation of the 2PA spectra being carried out using the damped cubic response theory of Jensen and coworkers 11 implemented in the ADF program package. [START_REF]ADF Amsterdam Density Functional; Scientific Computing & Modelling[END_REF] The SAOP Model Potential [START_REF] Schipper | [END_REF] was used for the 2PA calculations with a DZP basis set, considering the various molecules in the gas phase.

Standard PBE0/6-31G(d) computations 14 were also carried out using the Gaussian16 program, [START_REF] Frisch | Gaussian 16[END_REF] in particular for the geometry optimizations in solution (acetonitrile) that cannot be performed with the SAOP model (see ESI).

B S S B H N N H O O X X X X B S S B X X X X 5M-X (X = H, CN, NMe 3 + ) 2TM-X (X = H, CN, NMe 3 + )
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Results and Discussion

In order to check the reliability of the computational method that we employed, the onephoton absorption (OPA) and 2PA properties of derivatives nV (n = 2-5), for which experimental and theoretical data were reported 4 were computed as well as those of the corresponding dipolar sub-systems 2VD and 4VD (Scheme 2). For comparison, 2PA

properties of the analogous series nT (n = 2-5) and the corresponding dipolar sub-systems 2TD and 4TD (Scheme 2) were also computed to evaluate the effect of triple bonds replacing double bonds in these chromophores. The main results as well as the available experimental data are reported in Table 1, and the simulated 2PA spectra shown in Figure 1. For these quadrupolar systems the excited S2 state is generally one-photon forbidden (or at least approximately forbidden in the case of slight symmetry distortions) and two-photon allowed, as expected for quadrupolar chromophores (Scheme 3). 10,16 The 2PA energy corresponds therefore to the half of the OPA excitation energy to the S2 state. This 2PA-allowed excitation corresponds generally to a HOMO → LUMO+1 transition. Comparing the computed OPA energies to the experimental values (Table 1), it appears clearly that the SAOP model largely underestimates the HOMO-LUMO gaps. This is not surprising since the SAOP model potential is not based on a hybrid functional but rather on the generalized gradient approximation (GGA) corrected for its asymptotic behavior. Thus, when these gaps are compared to gaps computed at the PBE0/6-31G(d) levels using the same PBE0 optimized geometry, they also appear smaller (Table S1, ESI). This drawback of the SAOP calculations generates in turn a dramatic overestimation of the 2PA cross-sections. We have already quoted this in previous 2PA calculations using the SAOP method with octupolar derivatives. 17 However, it is worth observing that in spite of this overestimated prediction, a very good linear regression coefficient (R 2 = 0.998) is found for the correlation between the SAOP-computed and experimental values found for the 2PA cross-sections measured in solution (Figure 2). This result gives in turn confidence regarding the reliability of the 2PA trends given by the SAOP model. It is worth noting that the dipolar counterparts of the nV and nT compounds, namely 2VD, 4VD (Table 1 and Figure S1, ESI) exhibit practically no 2PA, as well as the 2TD and 4TD species. This indicates that the quadrupolar NLO responses of the nV and nT compounds are not directly related to the dipolar one by an additive process. This is not surprising for mainly two reasons. Firstly, comparison of related dipoles and quadrupoles based on essential molecular orbital models reveals than one order of magnitude can often be stated between their respective two-photon cross-sections in favor of the quadrupoles. 16 Secondly, half-molecules such as 2VD and 2TD might not constitute proper dipolar equivalents of their respective quadrupolar parents 2V and 2T since the donor group (2thienyl) has been halved compared to that present in 2V or 2T (5-(2,2'-bithiophene)). In this respect, 4VD and 4TD are certainly more representative dipolar equivalents of 2V and 2T

and, accordingly with expectations, when the 2PA cross-sections of these molecules are compared, roughly one order of magnitude (or less) improvement in cross-section is observed when going from the dipole to the corresponding quadrupole. Comparing the nV and nT series of compounds, it appears that the NLO response of the latter is higher than the former. Moreover, a very good linear correlation (R 2 = 0.997) is found between the 2PA cross-sections of the two series of compounds (Figure S2, ESI). At

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first sight, this result seemed surprising to us, since the HOMO-LUMO gaps (Table S1, ESI)

for the nT compounds (except 2T) are computed to be slightly higher than those of their nV counterparts. However, a closer look at the three-state (or essential state) model for the quadrupolar derivatives reveals that if such a simple approximation presently holds, the maximum 2PA cross-section value ( 2PA )max is given by eq. 1, where C is a constant term, ga and ge, the transition moments from the GS toward the OPA-forbidden state (e) and the OPA- allowed state (a), respectively,  ge is a line-broadening factor for the former transition and Eeg and Eag are the respective energies of these states from the GS. 16

  2PA )max = C.(ga) 2 (ae) 2 /[ge(2Ega-Ege)] 2 (1)
Thus, considering that the C.(ga) 2 (ae) 2 /eg product is roughly constant for a series of homologous compounds,  2PA could be inversely proportional to (2Ega-Ege) 2 . Actually, this seems to be the case, since when Eeg is considered to be twice the energy determined for the 2PA transition by the SAOP calculation (Scheme 3) and Eag to the energy for the OPA transition toward the allowed OPA state (Table 1), the (2Ega-Ege) 2 term can be calculated for each quadrupolar compound. A very good linear correlation is found between these terms and the calculated ( 2PA )max values for the nV (R 2 = 0.98) and nT (R 2 = 0.93) series (see ESI).

That being said, the (2Ega-Ege) 2 term for corresponding nV and nT compounds is not always larger for nV. In other words, it does not originate from a more efficient detuning, since the (2Ega-Ege) 2 terms are not systematically lower in the nT series. Actually, these terms are quite close for corresponding compounds of each series. Possibly, the difference in ( 2PA )max originates from the (ga) 2 (ae) 2 product which must be larger in the nT series, explaining the larger cross-sections values found for nT derivatives and the correlation reported in Figure 2.

To attempt shedding some light on this hypothesis, frontier MOs (FMOs) of nV and nT were examined (Figures 3 and4, and Table S1, ESI). Incidentally, it is worth noting here that the FMO diagrams computed using SAOP/DZP and PBE0/3-31G(d) are similar (see Figure S3, ESI for 2V for instance) allowing the use of the latter MOs for our discussion, as well as the SAOP ones. As exemplified below for 2V than for 2T, it was stated that the HOMO energy is always higher for nV than for nT (-9.47 eV vs. -9.63 eV for n = 2), whereas the LUMO and LUMO+1 of nT are lower in energy than those of nV (-7.85 vs. -7.68 eV for the LUMOs for n = 2). These observations indicate that the electron-donating ability of the conjugated bridge is higher in the nV series, while its electron-accepting ability is higher in the nT series. This results in red-shifted transition energies from GS to the first allowed one-

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photon state (a in Scheme 3) for the nV derivatives. However, larger transition moments between the GS (g) and a excited states (ga) are stated for the nT series making the (ga) 2 (ae) 2 product larger for these compounds (if the second transition moment between the two first excited states (ae) is considered as being roughly constant), in line with the increased 2PA cross-section stated for these compounds. With these results in mind, let us consider now the 2TM-X and 5M-X series of compounds (Scheme 1). The main computed results are given in Table 2. In this table, the experimental data for 2TM-NMe3 + are also given for comparison. The simulated 2PA spectra of 2TM-X (X = H, CN, NH2) are displayed in Figure S4 (ESI). The frontier MO diagrams of all compounds are shown in Figures 5 (2TM-NMe3 + ) and 6 (5M-NMe3 + ) and Figure S5 (2TM-X; X = H, CN, NH2). The excited state reached by the two-photon absorption is identified by its energy that must be twice the 2PA one. Identification of the one-photon forbidden states to which 2PA takes place reveals that the energy of these excited states with very weak oscillator strengths corresponds quite well to twice the computed 2PA energies (Table 2). For all compounds the low energy absorption corresponds to a HOMO to LUMO+1 transition, i.e., the S2 excited state, except for 2TM-NH2 for which the excited state is S4. The MO diagrams of the 2TM-X series of compounds shown in Figure 5 (X = NMe3 + )

and Figure S6 (X = H, CN, NH2, ESI) indicate that the LUMO and LUMO+1 energies are lower when more electron-attracting groups are attached to the phenyl rings tethered to the terminal BMes2 groups, reminding that the latter MO is strongly involved in the one-photon forbidden/two-photon-allowed electronic transition toward the S2 state. In more detail, we can ACCEPTED MANUSCRIPT -CLEAN COPY state that in line with eq. 1, there is a good linear correlation with the (2Ega-Ege) -2 term (R 2 = 0.97) for all compounds except for 2TM-NH2. When the data of the latter is incorporated, the correlation coefficient drops (R 2 = 0.63), in line with the fact that eq. 1 is certainly no more valid for this compound. This reveals that more than three states are needed to describe the 2PA behavior of this compound, in line with the occurrence of several low-lying excited states close in energy. Thus, it appears that for all 2TM-X derivatives, except 2TM-NH2, the electron transfer from the central electron-donating bridge to the substituted BMes2 moieties (excitation to the S2 or S4 states) is determining for the 2PA and, without any surprise, it is larger with the strongest electron-withdrawing group. From Table 2, it can be seen that the computed cross-sections follow the order 2TM-H < 2TM-CN < 2TM-NMe3 + consistent with the (2Ega-Ege) -2 ordering, which also roughly follows the reverse HOMO-LUMO gap trend.

The differences of the electron densities between the state S2 and the ground state S0 (Figure S6, ESI) show a variation of the dipole moment that follows the same ordering, suggesting also some positive influence on the 2PA magnitude via the HOMO-LUMO transition moments (e.g., ga in eq. 1). We note also a slight variation of the oscillator strength along this series of compounds reflecting similar changes in the transition moment ga. In line with the observed correlation cited above, such a change is certainly balanced by a reverse change in ae for each of these compounds, except 2TM-NH2, leading to a nearly constant numerator in eq. 1. Thus, the increased CT character leading to a lower HOMO-LUMO gap for 2TM-NMe3 + can nicely explain the significantly better 2PA response observed for this compound.

In contrast, for 2TM-NH2, the presence of the strongly electron-releasing amino substituents which significantly perturb the FMO ordering, results in a more complex situation and additional excited states become determining for the 2PA response, explaining the deviation of the 2PA cross-section of that compound from correlations based on a three-state model.

This compound exhibits nevertheless also a high 2PA cross-section that might now be correlated with the high electron-donating ability of the conjugated bridge and the change in the nature of the first two-photon-allowed excited state of this compound.

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For 5M-X compounds (X = H, CN, NMe3 + ), opposite statements can be made compared to their 2TM-X analogues. Though a very similar ordering is found for their first FMOs and excited states, and a good linear correlation between the 2PA of these compounds and the (2Ega-Ege) -2 term can be evidenced (R 2 = 0.99), this time, the slope of this correlation is opposite to expectations and the computed cross-sections follow the order 5M-H > 5M-CN > 5M-NMe3 + which is roughly opposite to the decrease of the HOMO-LUMO gap for these compounds, questioning the adequacy of a three-state model (eq. 1) to describe their 2PA

properties. Obviously, the much larger changes in the transition moment to the first OPAallowed state (ga) dominate the evolution of 2PA, contrary to what was observed for 2TM-X (X = H, CN, NMe3 + ) series.

Comparatively to 4V (Table 1), 2TM-H, that contains the same number of aromatic rings in the conjugated bridge, differs by the values of the 2PA cross-sections as well as by the 2PA energy. Indeed, the  2PA value is equal to 9086 GM for 4V but only to 2967 for 2TM-H. In the latter compound phenyl rings have replaced the alkyne units (see Schemes 1 and 2). Thus, the latter exhibits a longer conjugated bridge. This result is consistent with the smaller HOMO-LUMO gap of 4V with respect to that of 2TM-H (1.57 vs. 2.03 eV, respectively; SAOP/DZP calculation, Table S1, ESI) and with the better planarity of the manifold in the former. This result is also consistent with the better electron-attracting ability within the 4V species that is reflected by its lower LUMO energy comparatively to the 2TM-H ones.

Finally, two peaks appear in the simulated 2PA spectra of 2TM-NMe3 + and 5M-NMe3 + (Figure 7, left). In particular, it is worth noting that the 2PA peaks at higher energies have much larger cross-sections than the peaks at lower energies. The high-energy peaks correspond to transitions to higher excited states, i.e., S20 for 2TM-NMe3 + and S6 for 5M-NMe3 + and, by definition, they cannot be modeled by a three-state model (eq. 1). The corresponding transitions are given in Table 2 and the involved MO is depicted in Figure S7 (ESI). Note that these excitations might have quite close transition moments since the peak found for 5M-NMe3 + is slightly broader than that computed for 2TM-NMe3 + (Figure 7). As it can be seen upon comparison of the peaks at lower energy, the maximum cross-section is higher for 2TM-NMe3 + while the reverse is observed for the peak at energy. The ionic systems exhibit 2PA cross-sections higher than the neutral ones. Solvation effects should be more important for such cationic species. The counterions, four triflate anions here for 2TM-NMe3 + , certainly play a role, especially in the solid state where they are supposed to be located closer to the NMe3 + groups of the tetra-cationic molecule than in solution. The structures of the optimized geometries of the isolated cationic 2TM-NMe3 + and of the neutral 2TM-NMe3[OTf]4 molecules are given in Figure S8 (ESI). When considering the surrounding triflate (OTf -) counter-ion, its main effect is a drastic reduction of the maximum 2PA cross-section, as can be seen in Figure 7 (right). This is probably due to their negative charge, which likely reduces the attracting ability of the substituted BMes2 moieties.

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Normalizing the NLO response of a given molecule by the effective number of π electrons (Neff) constitutes a simple and practical way to correct its NLO response for the size of its π manifold. 18,19 When this is done for our computed 2PA cross-sections (Table 2), the most efficient systems according to the resulting figures (Table S3, ESI) are 2T followed by 5M-H. Based on these figures of merit it appears that, contrarily to a common belief, the ethynyl-bridged mesityl boranes derivatives 2T should be better two-photon absorbers that their ethenyl bridged homologues 2V, which is not so surprising given the constancy of Neff between nT and nV analogues. Then, the performance of the new 5M-X systems as twophoton absorbers over the known 2TM-X is clearly pointed out. Overall, these results confirm also further the interest of using the new water-soluble 2TM-NMe3 + and 5M-NMe3 + quadrupoles for bioimaging studies. compounds that were studied. The 2PA of these compounds seems to be mainly dependent on the energy gap between the GS and the two first excited states. Its evolution can be qualitatively modeled by a three-state model, explaining the huge impact of the underestimation of the actual energy gaps of these molecules by the SAOP method on the magnitude of the calculated cross-sections, while remaining qualitatively correct.

Results have also indicated that replacing the terminal ethynyl double bonds in the nV species by alkynyl triple bonds in the 2T-5T compounds leads to an increase of the 2PA cross-sections. The tetracationic compounds 2TM-NMe3 + and 5M-NMe3 + that contain one NMe3 + groups attached to the phenyl rings of the BMes2 moieties were shown experimentally to present very high 2PA cross-sections. This is confirmed by our computations that also show two 2PA peaks at different wavelengths, the low energy one corresponding to the absorption to the S2 excited state, whereas the second one to higher excited states. Neutral 2TM-X and 5M-X systems, where CN groups replace NMe3 + groups, should exhibit lower 2PA cross-sections than the ionic 2TM-NMe3 + and 5M-NMe3 + counterparts. For these compounds, the adequacy of the three-state model to qualitatively predict the 2PA properties is more questionable, especially for the 5M-X series (X = H, CN, NMe3 + ). Due to their lower solubility in polar solvents, these compounds should be far less interesting for two-photon bio-imaging purposes.

Scheme 3

 3 Scheme 3The three first states of quadrupolar chromophores and transition energies.

Fig. 1

 1 Fig. 1 Simulated 2PA spectra (2PA cross-sections vs. frequencies) of the nV (n = 2-5) and nT (n = 2-5) series of compounds.

Fig. 2

 2 Fig.2Linear regression between experimental (in acetonitrile solvent) and theoretical 2PA cross-sections (in gas phase) of the nV (n=2-5) series of compounds.

y = 9 . 6 R²

 96 735 x -5167.

Fig. 3 Fig. 4

 34 Fig. 3 Frontier MO diagram of 2V. Contour values: ±0.03 au.

Fig. 5

 5 Fig. 5 Frontier MO diagram of 2TM-NMe3 + . Contour values: ±0.03 au.

Fig. 6

 6 Fig. 6 Frontier MO diagrams of 5M-NMe3 + . Contour values: ±0.03 au.

Fig. 7

 7 Fig. 7 Comparison of the simulated 2PA spectra of 2TM-NMe3 + and 5M-NMe3 + (left) and 2TM-NMe3 + and 2TM-NMe3 + [OTf -]4 (right).

  a series of quadrupolar dimesitylboryl (BMes2) derivatives containing different conjugated thiophene oligomers spanning terminal BMes2 moieties have been investigated theoretically. Interestingly, SAOP/DZP DFT calculations gave correct trends regarding the cross-section variation with the length of the thiophene oligomer in the 2V-5V series of compounds. Results confirmed that the excited state reached by the two-photon absorption is the S2 state corresponding to the HOMO→LUMO+1 transition for all

Table 1

 1 Experimental and SAOP/DZP calculated OPA (S1 state) and 2PA  (eV) absorption energies and  2PA (GM) cross-sections of the nV and nT series of compounds.

		Experimental a			Calculated
	Cmpd	(eV)			(eV)
				 2PA (GM)			 2PA (GM)
		OPA	2PA		OPA	2PA
	2V	2.73	1.63	780	2.17	1.20	2556
	2VD				2.69	1.46	72
	3V	2.63	1.61	1170	2.03	1.10	5938
	4V	2.55	1.50	1450	1.88	1.00	9086
	4VD				2.51	1.46	663
	5V	2.54	1.61	1930	1.77	0.96	13637
	2T				2.20	1.20	3857
	2TD				2.77	1.45	78
	3T				2.04	1.12	8845
	4T				1.90	1.05	12255
	4TD				2.58	1.40	369
	5T				1.78	0.95	17912

a Ref.

4.

Table 2

 2 Experimental and SAOP/DZP calculated OPA and 2PA  (eV) absorption energies and  2PA (GM) cross-sections of the 2TM-X and 5M-X series of compounds.

		Experimental	Calculated
	Cmpd	 (eV)		 (eV)
		OPA 2PA	 2PA	OPA	2PA	 2PA
				(GM)	 (f) transition a		(GM)
	2TM-H				S1: 2.19 (0.690): H→L	1.15	2967
					S2: 2.30 (0.002): H→L+1
	2TM-NH2				S1: 2.26 (0.986): H →L	1.20	4919
					S4: 2.40 (0.001): H → L+1
	2TM-CN				S1: 1.86 (0.500): H→L	0.98	4365
					S2: 1.94 (0.001):H→L+1
					S1: 1.44 (0.563): H→L
	2TM-NMe3 +	2.89	1.55	693	S2: 1.53 (0.0004): H→L+1	0.78	6269
			1.42	140	S20: 3.04 (0.003):	1.50	134620
					H→LUMO+10
	5M-H				S1: 1.86(1.298): H→L	1.02	9423
					S2: 2.06(0.000): H→L+1
	5M-CN				S1: 1.55(0.817):H→L	0.82	9096
					S2: 1.63(0.0001):H→L+1
					S1: 1.05 (0.418): H→L	0.55	7482
	5M-NMe3 +				S2: 1.12 (0.005): H→L+1
						1.07	112052
					S6: 2.11 (0.000): H-1 →L

a Oscillator strength (f) and major transition (H = HOMO; L = LUMO).

Acknowledgements

The financial support of ANR (Isogate Project) is acknowledged as well as GENCI-IDRIS and GENCI-CINES for computing time allocation (Grant 2019-2020-080649).

Conflicts of interest

There are no conflicts to declare.