Roberto Galbiati
email: roberto.galbiati@sciencepo.fr

Emeric Henry
email: emeric.henry@sciencepo.fr

Nicolas Jacquemet
email: nicolas.jacquemet@univ-paris1.fr

Max Lobeck
email: max.lobeck@psemail.eu

Hensel, Jachimowicz, Haushofer, Ivchenko, Caria Witte

Fiorin Roth Reutskaja

Götz Kraft-Todd Gómez

Petherick, Phillips Hale Webster

How Laws Affect the Perception of Norms: Empirical Evidence from the Lockdown *

Keywords: JEL Classification: K1, I12, I18 laws, norms, expressive function, misperception, COVID-19

Laws not only affect behavior due to changes in material payoffs, but they may also change the perception individuals have of social norms, either by shifting them directly or by providing information on these norms. Using detailed daily survey data and exploiting the introduction of lockdown measures in the UK in the context of the COVID-19 health crisis, we provide causal evidence that the law drastically changed the perception of the norms regarding social distancing behaviors. We show that this effect of laws on perceived norms is mostly driven by an informational channel and that the intervention made perceptions of social norms converge to the actual prevalent norm.

Introduction

Individual behavior is affected both by material incentives, in particular those codified in laws, and by social sanctions or rewards, embodied in norms of behavior. The interactions between laws and norms is of growing interest both in law and in economics. [START_REF] Benabou | Laws and Norms[END_REF] propose a theoretical framework that formalizes two types of interactions. First, laws, by changing material payoffs, affect the norm of behavior understood as an equilibrium object: if fewer people take the condemned actions, the social stigma attached to these actions increases. Second, laws, when there is an underlying uncertainty on the prevailing social norm, provide information on societal values. Both these mechanisms imply a shift in the perceived social norm as the result of the implementation of a law; because the norm did actually change in the first case, and through an informational channel in the second case. Taking into account such interactions between laws and norms is key to understand why policies designed to foster cooperation fail or succeed (see [START_REF] Bowles | Policies Designed for Self-Interested Citizens May Undermine "The Moral Sentiments": Evidence from Economic Experiments[END_REF]Bowles and Polania-Reyes, 2012, for recent surveys).

In this paper, we take advantage of the lockdown measures introduced to face the Covid-19 pandemic and of rich survey data, gathered by [START_REF] Fetzer | Perceptions of an Insufficient Government Response at the Onset of the COVID-19 Pandemic are Associated with Lower Mental Well-Being[END_REF] worldwide, to provide causal evidence that laws affect the perception of norms, and disentangle the mechanisms behind the change. Our setting allows us to observe the effects of the law not only on perceived social norms (i.e., ones' beliefs about what others consider appropriate) but also on personal norms (i.e., ones' belief about what is an appropriate behavior). This allows us to build a measure of social norms that we can compare to perceived social norms. We focus on the case of Boris Johnson's announcement of a nation-wide lockdown in the UK in the evening on March 23 2020. This setting has several key features that we can exploit to investigate the causal effect of laws on perceptions of the social norm. First, the implementation of this law came as a relative surprise. Indeed it represented a sharp change in the UK government's strategy that has previously signaled strong reserves regarding total lockdowns. Second, the law was far reaching, including several different policies, such as lockdown and store closures, that had been typically more gradually implemented in other countries.

The law had an immediate impact on mobility, reducing for instance trips to parks by 30% within days. We provide evidence that this strong effect on behavior is supported by changes in perceptions of the social norm. To that end, we examine how the law affected individual's beliefs of whether other people believe social-distancing measures are important. We test the causal effect of the lockdown announcement on the perception of social norms by comparing daily responses of individuals that were interviewed before March 23 2020 in the UK with those that were interviewed after March 23 2020 in the UK. Trends in the perception of the social norm are controlled for by looking at the beliefs on the same days for respondents living in a set of control countries. The event study analysis coupled with a difference-in-differences estimation strategy show that the lockdown announcement significantly increased the likelihood that individuals believe that their compatriots view positively staying at home, closing stores, and not participating in social gatherings. The effect is very sizable, representing for instance a 15 percentage points increase in the belief that other people think that stay at home measures should be followed. We show that these results are robust to various identification strategies.

In the second part of the paper, we distinguish the two mechanisms proposed in [START_REF] Benabou | Laws and Norms[END_REF] that can explain the shift in the perception of social norms. We study the impact of the law on personal norms, i.e., one's own normative view about social distancing measures. First, we show that, before the law was passed, there was a large gap between the social norm (measured as the weighted average personal norm) and the average perception of the social norm, a gap we call misperception. Second, performing the same event study exercise as on the perceived social norm, we show that misperceptions sharply drop after the implementation of the policy. This mostly reflects the fact that personal norms did not themselves shift much. Overall, this suggests that the law mostly acted to provide information on the prevalent social norm, and helped to correct misperceptions about it.

This paper relates to different strands of literature. First it contributes to a literature at the intersection of law and economics, that presents conceptual and theoretical mechanisms through which legal interventions interact with existing social norms. [START_REF] Mcadams | An attitudinal theory of expressive law[END_REF] is the first study to argue that, when people seek social approval, laws may provide information about prevailing social values. [START_REF] Acemoglu | Social Norms and the Enforcement of Laws[END_REF] study a context where the effectiveness of laws depends on their coherence with social norms that drive social stigma for illegal behavior. [START_REF] Huck | Trust, Treason, and Trials: An Example of How the Evolution of Preferences Can Be Driven by Legal Institutions[END_REF] and [START_REF] Bohnet | More Order with Less Law: On Contract Enforcement, Trust, and Crowding[END_REF] take a different approach by studying the effects of laws on social norms in the context of evolutionary preferences adaptation. These papers look at the short and long-run effects of legal rules and point out that they can have long-run effects on behavior because they affect the evolution of preferences. As previously mentioned, in [START_REF] Benabou | Laws and Norms[END_REF] social norms directly affect the utility of individuals who care about their social image. Laws can, in this context, shift norms since certain behaviors become more rare, and thus more socially frowned upon, but can also bring information on the prevailing norm. Our work provides evidence consistent with the informational channel.

An experimental and empirical literature has examined how laws affect personal norms. A first wave of studies (e.g., [START_REF] Mcadams | Coordinating in the Shadow of the Law: Two Contextualized Tests of the Focal Point Theory of Legal Compliance[END_REF], in a lab coordination game setting, [START_REF] Galbiati | Obligations and cooperative behaviour in public good games[END_REF][START_REF] Tyran | Achieving compliance when legal sanctions are non-deterrent[END_REF]Galbiati et al., 2018, in the context of social dilemmas and[START_REF] Funk | Is There An Expressive Function of Law? An Empirical Analysis of Voting Laws with Symbolic Fines[END_REF], in the field) finds that laws affect behavior beyond changing monetary incentives. Most of these studies argue that the findings are consistent with the fact that laws shift personal norms. A second wave of studies provides direct evidence of this effect of laws. [START_REF] Aksoy | Do laws shape attitudes? Evidence from same-sex relationship recognition policies in Europe[END_REF] show that the legal recognition of same sex unions is associated with a significant improvement in personal norms towards sexual minorities. Using a vignettes experiment, [START_REF] Lane | Law and norms: Empirical evidence[END_REF] show that laws exert an effect on whether people perceive certain behaviors as socially appropriate or not. On the other hand, very few papers examine how laws affect the perception of social norms, with the exception of [START_REF] Tankard | The Effect of a Supreme Court Decision Regarding Gay Marriage on Social Norms and Personal Attitudes[END_REF] and [START_REF] Casoria | Perceived Social Norm and Behavior Quickly Adjusted to Legal Changes During the COVID-19 Pandemic in France[END_REF], which compare perceived social norms before and after the intervention in a single country.

Our work takes a comprehensive approach that goes beyond the scope of the aforementioned literature, since we study the impact of the law on the combination of personal and perceived norms and in particular study the impact on misperceptions. This enables us to disentangle the mechanisms proposed by [START_REF] Benabou | Laws and Norms[END_REF].

Finally, our study also contributes to an emerging literature studying change in social norms in response to information provision. Bursztyn et al. (2020b) show that, in Saudi Arabia, individuals misperceive the level of social support of women working outside home and provide experimental evidence that correcting beliefs about others increases married men's willingness to help their wives search for jobs. In a study focusing on the effect of information on the change of xenophobic social norms, Bursztyn et al. (2020a) show that providing information about the constitutionality of a Muslims' bans from public office affects people beliefs about the popularity of the policy. Our analysis shows that the introduction of new laws constitutes a different channel to provide information that corrects misperceptions about the prevailing social norms.

Data

Our data come from a large online survey gathered by Fetzer et al. (2020, henceforth FWH). The survey collects data on individual attitudes and beliefs concerning Covid-19 measures. The survey was launched on March 20 and we use responses up to March 30, resulting in over 99, 000 respondents from up to 58 countries. 1 The data contains daily information on respondents' beliefs about four distinct social distancing measures: social gatherings, avoiding handshakes, closing stores and implementing a general curfew. For each of these measures, respondents are asked about their perception of the social norm, specifically whether they believe other individuals in their countries think that these measures should be adopted (see the Online Appendix, Section A, for detailed information about the variables and their definition). We complement this information with external daily country-level data on coronavirus cases and deaths in the respondent's country provided by the John's Hopkins University [START_REF] Dong | An interactive web-based dashboard to track COVID-19 in real time[END_REF]. Boris Johnson's March 23 announcement of a full and immediate lockdown in the UK is our main source of identification. 2 The lockdown prohibited citizens to leave their home except for one form of exercise per day, medical visits, shopping basic necessities, and traveling to and from work if work from home is not possible. It also banned gatherings of more than 2 people and ordered non-essential shops to close. Importantly, this decision marked a stark change in the government's approach to contain the epidemic. Indeed, as late as March 22 the prime minister recommended that individuals stay two meters apart when interacting outdoors, noting that he "want[s] people to be able to go to the parks and open spaces and to enjoy themselves -it is crucial for health and mental and physical wellbeing" (office U.K. [START_REF] Government | Prime˜ministeroffice . Prime Minister's statement on coronavirus (COVID-19): 22[END_REF]. The government in fact initially suggested that they would aim at achieving herd immunity. The measures also marked a change Note. These figures plot the day-fixed effects of a specification that regresses a measure of mobility on days as well as Covid deaths and confirmed cases. The outcome variable is mobility data provided by Google. It characterizes in percent how many individuals spend time in (a) recreational areas, (b) parks, (c) transit, and (d) stores and pharmacy relative to a baseline. This baseline is the average number of visit on the same weekday between January 3rd and February 6th. A negative value thus means that there are fewer people at a given place than in the baseline period. The unit of observation is percent and the coefficients have to be interpreted as percentage points.

in policy relative to other countries that did not implement any further restrictions (e.g., Sweden) or that have already implemented such measures on a large scale (e.g., France, see [START_REF] Hale | Oxford covid-19 government response tracker[END_REF]. It turned out however that the enforcement was not as stringent as in other countries. Over a period of 3 months following the lockdown, less than 16, 000 fines for violation were issued (compared to more than a million in France), whereas the fine of 60 pounds was lower than in many other countries (135 Euros in France). The police force had been instructed to favor discussion and education over sanctions. Nevertheless the law had a strong impact on the behavior of the Note. The figure reports the share of countries in the control group where the corresponding policy was enforced on each day provided on the x-axis.

population. Using Google mobility data and regressing different measures of mobility, controlling for the state of the pandemic in each country, we show in Figure 1 that all types of movements were significantly reduced after March 23rd in the UK, in particular those for recreational purposes. 3For example, the lockdown reduced time spent in parks by 29 percentage points compared to the average time spent in parks on the same weekday between January 3rd and February 6th. Note that this is the pure effect of the lockdown, controlling for behavioral changes before the lockdown.

In what follows we will examine whether this large impact of the law on mobility is correlated with changes in the perception of the social norm. 4 To that end, we exploit the lag in the implementation of similar policies in other countries. This policy information comes from the Oxford COVID-19 Government Response Tracker that tracks social distancing policies on the country level by day [START_REF] Hale | Oxford covid-19 government response tracker[END_REF]. Figure 2 displays the timeline of the implementation of the following policies: school closing, workplace closing, cancellation of public events, stay at home requirements, closure of public transportation, restrictions on internal movements and restrictions on international travel.5 Figure 2 shows that, even though there was gradual adoption of more stringent policies around the world, there is no discontinuity around March 23rd, the date of the UK lockdown. This will be the basis of our estimation strategy, as described below. 3 Results

The causal effect of the law on perceived social norms

Figure 3 provides descriptive support for our main result. For each of the four policy measures (forbid social gatherings, no handshake, close stores and introduce a curfew), we report the dayfixed effects for the regressions of the perceived social norm in the UK and in control group countries. We control for differences in observed heterogeneity by including country, age (measured in bins of 5 years), gender, education, and income-fixed effects, as well as a measure of household composition. For all four social distancing measures the pre-trends are similar prior to the announcement by Boris Johnson. However there is a sharp discontinuity in the trend for the UK after March 23rd.

We statistically test for these effects by running difference-in-difference (DiD) regressions on the perceived social norm for each of the four policies, measured at the individual level, i, on each day d. We generalize the approach as compared to the usual linear model by introducing day and country fixed-effects (which allow for a non-linear effect of the post-treatment and the treatment-group dummy variables) and estimate the following model (bold letters denote column vectors):6

y id = α + βP ost d × U K i + Country i γ + Day d φ + x id κ + u id , ∀i, d (1)
The control variables in the x vector notably include (current and lagged) measures of countrydate variations in Covid deaths and confirmed cases. We also include country-age-gender, countryeducation, income quintile, and day fixed-effects as well as a control for the household composition. Last, we account for individual correlation in unobserved heterogeneity both over time within countries and between individuals within countries by clustering the standard errors at the country-gender level. 7The results of DiD estimates are provided in the first row of Table 1, where we perform the estimation both on the whole set of countries available in the sample (panel A) and on the more homogeneous subset of Western and Northern European countries (panel B; the list is provided in the Online Appendix, Table A). The lockdown announcement has a strong positive effect on the perceived social norm, for all of the different social distancing measures (note that their unit is the same). The effect is strongest for the implementation of a general curfew and the closure of stores. It is weaker for social gatherings and positive, small, and for the most part insignificant for the no handshake policy. The effect is similar in magnitude if we only compare the UK respondents to respondents from other North-Western countries (panel B).

Robustness analysis

Our identification strategy relies on the sudden and unexpected change in law that happened in the UK, to measure the causal effect of this change on the perception of norms. It is thus conditional on the assumption that (i) the announcement is the only reason why norms change in the UK; (ii) countries in the control group provide a counterfactual and did not experience similar shocks affecting the norms. We consider below several alternative identification strategies, aimed at assessing the robustness of our results to the relaxation of these assumptions. The main results are presented in the Online Appendix, Section E.1.

We address the first concern in two ways. First, as explained in Section 2, our main source of identification is the discontinuity in the government's policies in the UK on March 23. As an alternative to the difference-in-difference estimates on the whole sample period, we narrow the analysis to the neighborhood of the discontinuity and focus solely on data observed on March 22 and March 24. The results confirm that the March 23 announcement is the main source of variations in norms observed in our main specification. It could still be the case, however, that the results are driven by other events that happened in the UK on that same day. To address this concern, we exploit changes in the timing of the introduction of lockdowns in all countries over the time period of interest (lockdowns were introduced in 49 out of the 172 countries represented in our sample), by regressing perceived social norms on country fixed effects, day fixed effects and an indicator variable measuring whether a lockdown is in place. The results on pooled data show that the introduction of a lockdown is correlated with a significant and large increase in perceived social norms. While these results are useful to confirm that the change observed in the UK is unlikely to be due to simultaneity with unrelated events, it is worth stressing that the UK provides a unique experience of a sudden and unanticipated lockdown, hence achieving a more convincing and more conservative identification of its effect.

The second concern is that our estimates could capture the announcement of similar policies in the countries in the control group. Figure 2 indeed shows that some policy variation does occur in the control group during the sample period -although the trend is very flat around the discontinuity. To wash-out these variations from the estimated effect, we run the differencein-difference estimation in (1) on the control group made only of countries in which no policy variation happens between March 20 and March 30. This exercise leads to very similar estimates in terms both of magnitude and statistical significance. To further investigate this issue, our last robustness checks relies on variations in the composition of the control group used to generate the estimates provided in Table 1. We replicate the estimation based on the same control group, but from which we remove each country one at a time (the results are provided in the Online Appendix, Section E.2). All estimated coefficients are statistically indistinguishable from the baseline coefficient (first line in the figure). This shows that our results are not driven by the dynamics in one particular country.

The gap between perceived and actual norm

The results in the previous section clearly show that the law had a strong effect on individual perceptions of the social norm. We now examine the mechanism that could lie behind this effect. [START_REF] Benabou | Laws and Norms[END_REF] suggest two main channels: first, the law, by changing material payoffs of the socially desired action, also affects the norm of behavior resulting from equilibrium behavior. In particular, if individuals start adopting the prescribed action because of sanctions imposed by laws, those who still do not take this action will signal their extreme attitudes and carry worse stigma. Here, the law thus directly affects the social norm. A second channel is that the law may bring information on the social norm, even if the norm itself remains unchanged.

These two explanations notably differ regarding whether the social norm actually changes. We build a measure of actual social norms thanks to an additional variable in the survey asking respondents about their personal norm, i.e. whether they think people should comply with the policy (the variables are described in the Online Appendix, Section A). If the information about the prevalent social norm was perfect, the average over the entire population of the personal norms should be equal to the average perception of the social norm. We thus build a measure of the actual social norm based on the average personal norm. To account for the fact that the sample is not representative of the entire population, we compute the weighted average of this variable at the country level separately before and after March 23, where the weights rescale the data to make our sample representative of the gender-age-income-household size composition of the population at the country level.

Using this measure, we first show that there was an initial gap between the actual social norm and the average perception of the social norm in the UK, a gap we call misperceptions. Section F in the Online Appendix presents misperceptions before March 23 in the left panel and after in the right panel. The left panel clearly shows that before the lockdown, misperceptions were very high, in other words, the perceptions of the social norm were significantly below the norm itself for most dimensions, except for handshake where the discrepancy was much lower. The right panel shows that after March 23, this misperception sharply drops. This evolution observed in the raw data is confirmed in Figure 4 where we replicate Figure 3 but on the misperception measure.

As shown in Table 1 (second row in each subpanel), these results all are statistically significant based on DiD estimates from linear models similar to (1) in which the misperception is used as a dependent variable. This effect on misperceptions, that echoes the effect on the perceived social norms, is essentially driven by the fact that personal norms themselves do not change (see the Online Appendix, Section G). We also ascertain that the effect is not driven by the use of weights thanks to a replication on weighted data of the DiD estimation of the effect on perceived social norms (see the Online Appendix, Section H). This set of results suggests that the most plausible channel is that the law changed the perceptions of the social norm without actually changing the norm itself. In fact, for handshakes, the dimension where misperceptions was initially the lowest, the law had virtually no effect on the perceptions of the social norm.8

Remarks and Conclusions

In this paper, we use the announcement of a sudden lockdown in the UK to provide causal evidence that laws affect the perception of social norms in the population. We also show that the most plausible mechanism is an informational channel rather than a direct change in the social norms. The UK context had several features that favoured this informational channel. First, the population was initially pessimistic about the prevalent norm, as indicated by the large misperception gap before March 23rd, leaving room for new information to affect beliefs. Second, as described in Section 2, the enforcement of the law was weaker than in other countries, decreasing the potential for a direct impact on social norms themselves. In this context, our results show that the law provides information, resulting in a large change in the perceptions of social norms.

Our study thus sheds new light on the mechanisms explaining why and under what circumstances laws are effective, and contributes to a better understanding of how perceptions about prevailing social norms are formed.

As a conclusion, it is worth discussing to what extent the particular context we study differs compared to other environments where laws may affect social norms and their perception. An important difference relates to the timing of the implementation of the new legal rule and to the procedure of its adoption. Laws are usually debated in parliaments and subject to public discussion (this is for instance the case of the introduction of same-sex marriage), while the UK lockdown was a sudden decision of the government. This specific setting has clear advantages in terms of identification since it relies on a sudden change. Moreover, even though the policy is not publicly debated, it still provides information about the underlying norm. Indeed, in a democracy, accountability constrains politicians to take into account voters' preferences. Thus British citizens, who are aware of this accountability mechanism, receive a clear message regarding the perception the government has of the general support in the population for this measure.

A.2 Verbatim of Boris Johnson's March 23 announcement

According to UK government official communication, the speech reads as follows (https://www.gov. uk/government/speeches/pm-address-to-the-nation-on-coronavirus-23-march-2020, text emphasized by us):

Good Evening, The coronavirus is the biggest threat this country has faced for decades -and this country is not alone. All over the world we are seeing the devastating impact of this invisible killer. And so tonight I want to update you on the latest steps we are taking to fight the disease and what you can do to help.

And I want to begin by reminding you why the UK has been taking the approach that we have. Without a huge national effort to halt the growth of this virus, there will come a moment when no health service in the world could possibly cope; because there won't be enough ventilators, enough intensive care beds, enough doctors and nurses.

And as we have seen elsewhere, in other countries that also have fantastic health care systems, that is the moment of real danger.

To put it simply, if too many people become seriously unwell at one time, the NHS will be unable to handle it -meaning more people are likely to die, not just from Coronavirus but from other illnesses as well.

So it's vital to slow the spread of the disease.

Because that is the way we reduce the number of people needing hospital treatment at any one time, so we can protect the NHS's ability to cope -and save more lives.

And that's why we have been asking people to stay at home during this pandemic.

And though huge numbers are complying -and I thank you all -the time has now come for us all to do more.

From this evening I must give the British people a very simple instruction -you must stay at home.

Because the critical thing we must do is stop the disease spreading between households.

That is why people will only be allowed to leave their home for the following very limited purposes:

• shopping for basic necessities, as infrequently as possible

• one form of exercise a day -for example a run, walk, or cycle -alone or with members of your household;

• any medical need, to provide care or to help a vulnerable person; and travelling to and from work, but only where this is absolutely necessary and cannot be done from home.

That's all -these are the only reasons you should leave your home. You should not be meeting friends. If your friends ask you to meet, you should say No. You should not be meeting family members who do not live in your home. You should not be going shopping except for essentials like food and medicine -and you should do this as little as you can. And use food delivery services where you can.

If you don't follow the rules the police will have the powers to enforce them, including through fines and dispersing gatherings.

To ensure compliance with the Government's instruction to stay at home, we will immediately:

• close all shops selling non-essential goods, including clothing and electronic stores and other premises including libraries, playgrounds and outdoor gyms, and places of worship;

• we will stop all gatherings of more than two people in public -excluding people you live with;

• and we'll stop all social events, including weddings, baptisms and other ceremonies, but excluding funerals.

Parks will remain open for exercise but gatherings will be dispersed.

No Prime Minister wants to enact measures like this. I know the damage that this disruption is doing and will do to people's lives, to their businesses and to their jobs.

And that's why we have produced a huge and unprecedented programme of support both for workers and for business.

And I can assure you that we will keep these restrictions under constant review. We will look again in three weeks, and relax them if the evidence shows we are able to.

But at present there are just no easy options. The way ahead is hard, and it is still true that many lives will sadly be lost.

And yet it is also true that there is a clear way through.

Day by day we are strengthening our amazing NHS with 7500 former clinicians now coming back to the service.

With the time you buy -by simply staying at home -we are increasing our stocks of equipment. We are accelerating our search for treatments. We are pioneering work on a vaccine. And we are buying millions of testing kits that will enable us to turn the tide on this invisible killer. I want to thank everyone who is working flat out to beat the virus.

Everyone from the supermarket staff to the transport workers to the carers to the nurses and doctors on the frontline.

But in this fight we can be in no doubt that each and every one of us is directly enlisted. Each and every one of us is now obliged to join together.

To halt the spread of this disease.

To protect our NHS and to save many many thousands of lives. And I know that as they have in the past so many times. The people of this country will rise to that challenge. And we will come through it stronger than ever. We will beat the coronavirus and we will beat it together. And therefore I urge you at this moment of national emergency to stay at home, protect our NHS and save lives.

Thank you.

B Effect of March 23 lockdown measures on movements in the UK

The Table below reports the results of the Difference-in-Difference estimation (Post × UK variable) of the March 23 lockdown decision in the UK on mobility data collected from Google's community mobility reports. Each outcome variable is the change in spending time at a given place relative to the median value of the same weekday in the January 3-February 6 period. The specification controls for COVID-19 statistics (lagged and current confirmed cases and deaths) as well as a non-linear effect of the group and Post variable through day-and country fixed-effects.

Retail

C Correlation between self-reported mobility and norms

The survey contains information on whether respondents intend to leave their home in the course of the next five days and for what motives. Table C reports the results from an OLS regression of these mobility variables on the personal norm about a curfew and the perceived social norm to support a curfew. We build the variables used as dependent variables in Table C from two series of the survey questions: the first asks "Do you need to leave your home in the next 5 days? " [yes = 1; no =0]. The second is phrased "What are the reasons for you to leave your home (check all that apply)? "; among all possible answers, we focus on: [Friends] ("Meeting friends or relatives"); [Tired] ("Getting tired of being inside of the house"); [Bored] ("Getting bored "); [Work] ("Going to work "); [Freedom] ("Exercising my freedom"). The results support the existence a relation between mobility behavior and both the personal norms and the perception of social norms: respondents who believe that others support a curfew are less likely to state that they plan to leave their home in the coming days.

E Results from the robustness analysis E.1 Regression results

The Table below reports the Difference-in-Difference estimates from the robustness analysis described in Section 3.1.1. The full results are available from the authors upon request.

E.2 Step deletion of countries from the control group

The figure below reports the point estimates along with 95% confidence intervals resulting from the difference-in-difference estimation in (1) performed on control groups resulting from the step deletion of each country one after the other. The countries iso-code are defined in Table A. G Time-pattern of personal norms in the UK and the control group

For each of the four policy measures, the figure below reports the day-fixed effects from individual personal norms in the UK and in control group countries, controlling for country-, age-, gender-, education-, and income-fixed effects, as as well as a measure of household composition. The results from difference-indifference estimates of the effect of March 23 announcement on individual personal norms, available from the authors upon request, confirm that the announcement has a non-significant effect regarding both handshaking and social gatherings, and a small but statistically significant effect regarding stores closure and a total curfew.

(a) Social gatherings

I Heterogeneity in the UK response to the lockdown

The tables below provide the results from separate regressions in which we allow the DiD estimate in (1) to interact with observed individual covariates (Table H) and subjective variables (Table I). For each set of regressions, we report the coefficient of the corresponding variable, the resulting DiD estimate (Post × UK variable) as well as the interaction. The subjective variables come from the "Perceptions of government/public response and efficacy" part of the survey, and are measured as: For each variable, we generate dummy variables equal to 1 if the individual's response is above the midpoint of the Likert scale, and 0 if it is below.

Figure

  Figure 1: Mobility patterns in the UK (a) Recreation

Figure 2 :

 2 Figure 2: Timeline of policies implementation in the control group

Figure 3 :

 3 Figure 3: Time pattern of perceived social norms in the UK and the control group (a) Gatherings

Figure 4 :

 4 Figure 4: Time pattern of misperceptions in the UK and the control group (a) Gatherings

F

  Before-After comparison of misperceptions in the UKThe figure below displays the discrepancy between the norm and the individual perception of the norm in the UK before and after March 23. The horizontal line in the middle of the box characterizes the median. The upper (lower) ends of the box characterizes the 75th (25th) percentile. The upper (lower) ends of the vertical lines are the upper (lower) adjacent values. Points above (below) are outliers.

•

  perceivedeffectivnes: What do you think: How effective are social distancing measures (e.g., through a general curfew) to slow down the spread of the coronavirus? [5-point scale; 1 = Not at all effective; 2 = Not effective; 3 = Neither effective nor ineffective; 4 = Effective; 5 = Very effective] • govtrust: How much do you trust your country's government to take care of its citizens? [5-point scale; 1 = Strongly distrust; 2 = Somewhat distrust; 3 = Neither trust nor distrust; 4 = Somewhat trust; 5 = Strongly trust] • govfact: How factually truthful do you think your country's government has been about the coronavirus outbreak? [5-point scale; 1 = Very untruthful; 2 = Somewhat untruthful; 3 = Neither truthful nor untruthful; 4 = Somewhat truthful; 5 = Very truthful]

Table 1 :

 1 DiD estimates of the effect of the UK lockdown

		Gatherings Handshake	Stores	Curfew	N	Clusters
			A. Full sample
	Perceived norm	7.370***	3.133**	12.907*** 13.950*** 94,544	155
		(1.287)	(1.158)	(1.386)	(1.311)
	Misperceptions	-6.182***	-0.278	-6.037***	-3.910*	91,182	137
		(1.518)	(1.499)	(1.649)	(1.630)
		B. Western and Northern Europe
	Perceived norm	7.825***	4.262***	14.284*** 14.405*** 37,745	38
		(1.429)	(1.185)	(1.913)	(1.764)
	Misperceptions	-7.622***	-1.699	-6.773*	-4.269*	37,745	38
		(2.020)	(1.153)	(2.979)	(1.958)

Note. This table presents the difference-in-difference estimates (Post × UK variable) from regressions of perceived social norms (first row in each panel) and misperceptions (second row) on country-age-gender, country-education, income quintile, and day fixed-effects as well as controls for household composition and COVID-19 statistics (lagged and current confirmed cases and deaths). The sample uses all countries and respondents that answered between March 20 and 30. The second line only uses countries for which we have enough responses to compute a misperception variable. Standard errors are clustered at the country-gender level. Significance levels: * 5%, * * 1%, * * * 0.1%.

Table A :

 A Distribution of responses across countries

		iso-code	N	%		iso-code	N	%
	Brazil	BR	11, 230 11.27	Vietnam	VN	634	0.64
	United Kingdom	GB	11, 151 11.19	Slovakia	SK	609	0.61
	United States	US	11, 060 11.10	Latvia	LV	601	0.60
	Germany	DE	82, 77	8.31	Belgium	BE	551	0.55
	Sweden	SE	57, 46	5.77	Dominican Republic	DO	546	0.55
	Switzerland	CH	4, 152	4.17	Portugal	PT	542	0.54
	Russia	RU	3, 364	3.38	Chile	CL	522	0.52
	Mexico	MX	3, 240	3.25	Malaysia	MY	512	0.51
	Turkey	TR	2, 784	2.79	Denmark	DK	504	0.51
	Canada	CA	2, 709	2.72	Albania	AL	468	0.47
	France	FR	2, 632	2.64	South Africa	ZA	468	0.47
	Belarus	BY	2, 621	2.63	Israel	IL	403	0.40
	Spain	ES	2, 211	2.22	Singapore	SG	395	0.40
	Italy	IT	1, 794	1.80	Poland	PL	377	0.38
	Colombia	CO	1, 633	1.64	Morocco	MA	351	0.35
	Indonesia	ID	1, 541	1.55	Kenya	KE	340	0.34
	Ukraine	UA	1, 440	1.45	China	CN	333	0.33
	Netherlands	NL	1, 346	1.35	New Zealand	NZ	330	0.33
	Austria	AT	1, 042	1.05	Bulgaria	BG	313	0.31
	Peru	PE	1, 015	1.02	Greece	GR	310	0.31
	India	IN	935	0.94	Thailand	TH	303	0.30
	Qatar	QA	860	0.86	Ecuador	EC	299	0.30
	Argentina	AR	858	0.86	Norway	NO	292	0.29
	Australia	AU	852	0.86	South Korea	KR	275	0.28
	Romania	RO	791	0.79	Japan	JP	274	0.28
	Finland	FI	756	0.76	Czechia	CZ	256	0.26
	Philippines	PH	731	0.73	Uruguay	UY	240	0.24
	Ireland	IE	695	0.70	Hungary	HU	232	0.23
	Venezuela	VE	655	0.66	Nigeria	NG	212	0.21
					Total		99, 613 100.00

Note. Countries in bold letters are part of the Northern and Western European countries sub-sample.

Table B :

 B Respondents' covariates

		Control	UK	Overall
	Women	56.6%	50.4%	55.9%
	Years of Education	16.20	17.26	16.33
		(4.815)	(3.713)	(4.711)
	Age	38.22	43.54	38.85
		(12.84)	(12.89)	(12.96)
	Single	45.1%	33.0%	43.7%
	Number of Household Members	2.863	2.664	2.839%
		(1.591)	(1.356)	(1.566)
	First income quintile	8.60%	10.68%	10.43%
	Second income quintile	6.51%	6.66%	6.64%
	Third income quintile	4.90%	7.18%	6.91%
	Fourth income quintile	12.13%	12.56%	12.51%
	Fourth income quintile	67.86%	62.92%	63.50%
	Confirmed COV-19 cases p.c.	0.206	0.0978	0.193%
		(0.290)	(0.0409)	(0.275)
	Lag confirmed COV-19 cases p.c.	0.0259	0.0141	0.0245%
		(0.0339)	(0.00676)	(0.0322)
	Confirmed COV-19 deaths p.c.	0.00591	0.00553	0.00587%
		(0.0169)	(0.00410)	(0.0159)
	Lag Confirmed COV-19 cases p.c. 0.00106	0.000985 0.00105%
		(0.00244) (0.000863) (0.00231)

Table C :

 C Relation between self-reported behavior and both personal and perceived social norms Note. Standard errors are clustered on the country-gender level (N = 99, 613; 170 clusters). The perceived social norm explanatory variable is the original variable from the survey but divided by 100 to make it comparable with the social norm. Significance levels: * 5%, * * 1%, * * * 0.1%.

		Leaves Home Friends	Bored	Tired	Work	Freedom
	Perceived social norms (Curfew)	-0.058	-0.056*** -0.023*** -0.048*** -0.048***	-0.008
		(0.037)	(0.014)	(0.005)	(0.011)	(0.011)	(0.006)
	Personal norms (Curfew)	-0.167***	-0.059*** -0.054*** -0.101*** -0.101*** -0.034***
		(0.015)	(0.007)	(0.006)	(0.005)	(0.005)	(0.005)
	Constant	0.743***	0.118*** 0.089*** 0.184*** 0.184***	0.048***
		(0.032)	(0.015)	(0.008)	(0.011)	(0.011)	(0.008)

D Full results from Table

1

Table D :

 D DiD estimates of the effect of the UK lockdown on perceived social norms Note. Standard errors are clustered at the country-gender level. Significance levels: * 5%, * * 1%, * * * 0.1%.

		Gatherings Handshake	Stores	Curfew
	A. Full sample (N = 94, 544; 155 clusters)
	Post x UK	7.370***	3.133**	12.907*** 13.950***
		(1.287)	(1.158)	(1.386)	(1.311)
	Lagged confirmed COV-19 cases p.c.	-0.090	-7.487	-4.801	-9.290
		(13.873)	(10.020)	(14.224)	(14.560)
	Lagged confirmed COV-19 deaths p.c.	-253.572	-24.141	216.299	298.979
		(261.672)	(262.240)	(275.434) (361.588)
	Confirmed COV-19 cases p.c.	-7.885***	-7.108***	-6.045	-8.313
		(1.676)	(1.233)	(3.455)	(4.608)
	Confirmed COV-19 deaths p.c.	59.200***	24.718	-30.181	-31.590
		(15.496)	(20.375)	(25.644)	(28.736)
	Household size	0.189***	0.109	0.292***	0.481***
		(0.055)	(0.063)	(0.059)	(0.064)
	Constant	68.304***	76.253***	58.690*** 48.829***
		(0.346)	(0.316)	(0.654)	(0.855)
	B. Western and Northern Europe (N = 37, 745; 38 clusters)
	Post x UK	7.825***	4.262***	14.284*** 14.405***
		(1.429)	(1.185)	(1.913)	(1.764)
	Lagged confirmed COV-19 cases p.c.	-1.267	-4.035	-17.841	-34.271*
		(18.043)	(11.962)	(16.923)	(16.785)
	Lagged confirmed COV-19 deaths p.c.	-362.520	-281.885	455.944	1179.429
		(490.437)	(446.046)	(421.836) (587.650)
	Confirmed COV-19 cases p.c.	-6.500***	-3.496*	-0.432	-7.228
		(1.608)	(1.454)	(5.654)	(5.974)
	Confirmed COV-19 deaths p.c.	117.739	42.186	18.662	-99.899
		(62.331)	(53.258)	(68.630)	(108.627)
	Household size	0.145**	0.209***	0.189**	0.468***
		(0.046)	(0.051)	(0.056)	(0.084)
	Constant	72.534***	83.664***	61.210*** 51.851***
		(0.859)	(0.599)	(2.076)	(2.243)

Table E :

 E DiD estimates of the effect of the UK lockdown on misperceptions Note. Standard errors are clustered at the country-gender level. Significance levels: * 5%, * * 1%, * * * 0.1%.

		Gatherings Handshake	Stores	Curfew
	A. Full sample (N = 91, 182; 137 clusters)
	Post x UK	-6.182***	-0.278	-6.037***	-3.910*
		(1.518)	(1.499)	(1.649)	(1.630)
	Lagged confirmed COV-19 cases p.c.	7.022	13.025	16.393	51.882*
		(14.491)	(10.938)	(14.992)	(22.504)
	Lagged confirmed COV-19 deaths p.c.	344.059	115.689	115.465	-595.692
		(333.648)	(248.481)	(355.525) (303.982)
	Confirmed COV-19 cases p.c.	7.849***	7.387	-0.077	-1.014
		(1.923)	(4.296)	(4.429)	(6.441)
	Confirmed COV-19 deaths p.c.	-87.380***	28.834	-75.645	20.271
		(18.264)	(26.188)	(49.525)	(45.952)
	Household size	-0.175**	-0.127	-0.252*** -0.453***
		(0.057)	(0.064)	(0.060)	(0.069)
	B. Western and Northern Europe (N = 37, 745; 38 clusters)
	Post x UK	-7.622***	-1.699	-6.773*	-4.269*
		(2.020)	(1.153)	(2.979)	(1.958)
	Lagged confirmed COV-19 cases p.c.	2.137	-6.573	-7.529	45.302
		(17.054)	(14.996)	(20.810)	(36.197)
	Lagged confirmed COV-19 deaths p.c.	325.700	280.957	-709.197	512.372
		(578.627)	(450.184)	(639.362) (491.423)
	Confirmed COV-19 cases p.c.	-0.615	2.965	-10.248	-8.838
		(3.537)	(2.085)	(8.472)	(6.000)
	Confirmed COV-19 deaths p.c.	-212.282*	76.330	-84.867	-242.935*
		(80.470)	(56.498)	(160.257) (109.129)
	Household size	-0.145**	-0.211***	-0.186** -0.457***
		(0.046)	(0.051)	(0.056)	(0.083)

Table F :

 F Robustness Checks

		Gatherings Handshake	Stores	Curfew	N	Clusters
		A. March 22 vs March 24
	Full Sample	5.420***	2.819***	11.967*** 12.446*** 47,366	142
		(0.821)	(0.709)	(1.420)	(1.501)
	Western and Northern Europe	4.798***	2.809***	11.293*** 11.600*** 20,029	37
		(0.824)	(0.577)	(1.682)	(1.453)
	B. Effect of a strict lockdown on pooled data
	Full Sample	2.721***	0.852	5.558***	7.193*** 94,544	155
		(0.647)	(0.591)	(0.968)	(1.006)
	Western and Northern Europe	3.303***	2.058***	7.394***	8.146*** 37,745	38
		(0.401)	(0.420)	(0.801)	(0.815)
	C. Countries with no change in their lockdown policy
	Full Sample	8.043***	3.392**	14.051*** 14.886*** 66,337	103
		(1.188)	(1.113)	(1.299)	(1.279)
	Western and Northern Europe	8.367***	4.454***	14.899*** 14.864*** 28,172	29
		(1.168)	(0.938)	(1.422)	(1.206)

Note. Standard errors are clustered at the country-gender level. Significance levels: * 5%, * * 1%, * * * 0.1%.

  The table below provides the DiD estimate in (1) using weights. The weights provide representativity on the country level by age, income quintile, and education.

	H Replication of the results on weighted data
																(b) Handshake
		.02											.04
													.02
		0
	Day FE											Day FE	0
		-.02											-.02
		-.04							UK		Control	-.04
		20	21	22	23	24	25	26	27	28	29	30	20	21	22	23	24	25	26	27	28	29	30
						Day in March									Day in March
					(c) Stores closure								(d) Total curfew
		.15											.2
		.1
													.1
		.05
	Day FE	0										Day FE	0
		-.05											-.1
		-.1											-.2
		20	21	22	23	24	25	26	27	28	29	30	20	21	22	23	24	25	26	27	28	29	30
						Day in March									Day in March

Table G :

 G DiD estimates of the effect of the UK lockdown using weighted data Note. Standard errors are clustered at the country-gender level. Significance levels: * 5%, * * 1%, * * * 0.1%.

		Gatherings Handshake	Stores	Curfew	N	Clusters
		D. Weighted data
	Perceived norm	7.079***	3.397*	13.313*** 16.698*** 90,396	94
		(1.473)	(1.343)	(2.066)	(1.679)
	Western and Northern Europe	7.447***	3.040	15.487*** 18.092*** 37,357	26
		(1.756)	(1.837)	(2.548)	(2.224)

Table H :

 H Heterogeneity of the DiD estimate according to individual covariates B. Income bracket (the direct effect is part of the model FE) Note. Standard errors are clustered on the country-gender level (N = 94, 544; 155 clusters). Significance levels: * 5%, * * 1%, * * * 0.1%.

		Gatherings Handshake	Stores	Curfew
	A: Gender (the direct effect is part of the model FE)
	Post x UK	13.228***	7.957***	17.567*** 18.120***
		(0.816)	(0.547)	(1.000)	(1.047)
	Post x UK x Female	-3.599***	-2.964***	-2.863*** -2.562***
		(0.351)	(0.102)	(0.217)	(0.126)
	Post x UK	6.142***	3.193***	10.268*** 13.022***
		(0.656)	(0.674)	(1.537)	(1.856)
	Post x UK x Income quintile	0.295	-0.015	0.633	0.223
		(0.369)	(0.315)	(0.561)	(0.633)
	C. Years of education
	Post x UK	9.449***	5.049***	15.936*** 12.795***
		(1.362)	(1.160)	(1.027)	(1.978)
	Years of education	-0.023	0.004	-0.125*** -0.298***
		(0.018)	(0.014)	(0.026)	(0.034)
	Post x UK x Years of education	-0.127***	-0.115***	-0.179**	0.050
		(0.033)	(0.021)	(0.055)	(0.049)
		D. Household size
	Post x UK	6.503***	2.870**	12.578*** 12.383***
		(0.833)	(1.055)	(1.332)	(1.471)
	Household size	0.184**	0.108	0.290***	0.472***
		(0.056)	(0.064)	(0.060)	(0.064)
	Post x UK x Household size	0.329	0.100	0.125*	0.595***
		(0.221)	(0.084)	(0.063)	(0.121)
		29

Table I :

 I Heterogeneity of the DiD estimate according to subjective perception variables Note. Standard errors are clustered on the country-gender level (N = 94, 544; 155 clusters). Significance levels: * 5%, * * 1%,

		Gatherings Handshake	Stores	Curfew
	A. Misestimation of Covid cases
	Post x UK	7.260***	3.059*	12.649*** 13.544***
		(1.194)	(1.177)	(1.376)	(1.303)
	Mistake	-0.002**	-0.003***	-0.003**	-0.001
		(0.001)	(0.001)	(0.001)	(0.001)
	Post x UK x Mistake	0.011	0.008*	0.025***	0.038***
		(0.010)	(0.003)	(0.004)	(0.004)
	B. Subjective effectiveness of containment measures
	Post x UK	8.441***	4.780*	17.471*** 14.315***
		(1.250)	(2.067)	(1.403)	(2.332)
	Subjective Effectiveness	0.581***	0.516***	0.944***	1.153***
		(0.147)	(0.151)	(0.181)	(0.226)
	Post x UK x Subjective Effectiveness	-0.272	-0.409	-1.124***	-0.114
		(0.507)	(0.727)	(0.283)	(0.287)
	C. Subjective trust in government
	Post x UK	6.260***	3.855**	10.357*** 12.423***
		(0.719)	(1.210)	(1.048)	(1.028)
	Trust in Government	2.696***	2.454***	2.387***	2.064***
		(0.098)	(0.124)	(0.166)	(0.220)
	Post x UK x Trust in Government	0.028	-0.538	0.535	0.242
		(0.497)	(0.648)	(0.570)	(0.450)
	D. Government was truthful
	Post x UK	7.705***	5.230***	11.710*** 11.366***
		(0.702)	(1.321)	(0.861)	(1.212)
	Government was truthful	2.450***	2.267***	2.053***	1.595***
		(0.104)	(0.122)	(0.158)	(0.206)
	Post x UK x Government was truthful	-0.290	-0.796	0.192	0.637**
		(0.432)	(0.650)	(0.334)	(0.226)

* * * 0.1%.

Responses are not representative but representativity can be reconstructed using country-specific weights. We include all countries that had more than

respondents and completed the survey before March 30. We use the May 21 release of the data, which fixes some issues with the initial weight construction.2 The verbatim of the announcement is provided in the Online Appendix, Section A.2.

These changes all are statistically significant, as shown in the Online Appendix, Section B.

Our data does not allow us to directly measure the relationship between mobility and norms. In the Online Appendix, Section C, we report tentative results based on questions in the survey about the intention to stay at home.

We focus on the 'containment and closure' category and restrict only to mandatory policies, disregarding simple recommendations from the governments.

The outcome variable, y id , denotes either one of the four perceived social norms, or one of the four measures of misperceptions as defined in Section 3.1.1.

In the main tables we only report the estimates of the β parameters; the full results tables are provided in the Online Appendix, Section D. Also note that we do not control for normative beliefs in our preferred regressions on perceived social norms, since they are likely to be endogenous to unobserved heterogeneity generating differences perceived social norms. The robustness check available from authors upon request, shows that the results still holds when normative beliefs are controlled for and, if anything, are stronger both statistically and in terms of magnitude.

This interpretation is further substantiated by the analysis of the heterogeneity of the response of perceived social norms to the UK lockdown. When interacting the treatment effect with subjective perception variables in separate models, the only dimension of heterogeneity that seems to matter is how well individuals are informed about COVID itself, measured as the gap between their estimate of the number of COVID cases and the actual number in their country. The higher that gap, the more the perception of the social norm relative to the curfew variable shifts up. These results are provided in the Online Appendix, Section I, along with the results from interactions with individual covariates. Non of these interactions with socio-economic variables are significant, except for gender.

Chris Roth for very useful feedback at earlier stages of this project. This work has been funded by a French government subsidy under the framework of the Investissements d'avenir programme reference ANR-17-EURE-001.

Online Appendix A Sample information A.1 Variables and data source

The entire set of variables available in the data is described in FWH. We only describe below the variables used as the main outcomes in the analysis. Perceived social norms. Our measure of perceived social norms come from questions about the perception of others' beliefs about Coronavirus measures:

• sob social : How many of 100 people in your country do you think believe that participation at social gatherings should be cancelled because of the coronavirus right now? [slider ranging from 0 to 100 -initiated at 0]

• sob handshake: How many of 100 people in your country do you think believe that one should not shake other people's hands because of the coronavirus right now? [slider ranging from 0 to 100initiated at 0]

• sob stores: How many of 100 people in your country do you think believe that all shops in your country other than particularly important ones, such as supermarkets, pharmacies, post offices, and gas stations, should be closed because of the coronavirus right now? [slider ranging from 0 to 100initiated at 0]

• sob curfew : How many of 100 people in your country do you think believe there should be a general curfew in your country (with the exception of grocery shopping, necessary family trips, and the commute to work) because of the coronavirus right now? [slider ranging from 0 to 100 -initiated at 0] Misperception. To build a measure of misperception, we rely on questions about personal norms:

• fob social : "What do you think: should people in your country cancel their participation at social gatherings because of the coronavirus right now?" [No = 0; Yes = 1]

• fob handshake: "What do you think: should people in your country not shake other people's hands because of the coronavirus right now?" [No = 0; Yes = 1]

• fob stores: "What do you think: should all shops in your country other than particularly important ones, such as supermarkets, pharmacies, post offices, and gas stations, be closed because of the coronavirus right now?" [No = 0; Yes = 1]

• fob curfew: "What do you think: should there be a general curfew in your country (with the exception of grocery shopping, necessary family trips, and the commute to work) because of the coronavirus right now?" [No = 0; Yes = 1]

For each policy, we compute the weighted average of this variable at the country level, separately before and after March 23. The weights aim at restoring the national representativity of the sample regarding observed heterogeneity available in the data. However, for some countries the dataset did not include the necessary information to construct weights. Thus, the total sample shrinks from 94,544 to 91,182 for models that study misperception as an outcome. Note that the European sample is not affected by this.

Weights. The dataset also contains census information about the distribution of the population in each country over age, gender, education, income and household composition (assuming independence in the population between these characteristics). We use this additional source of information to build weights rescaling the observations available in the sample to make them representative of the country population.


Prof. Dr Sourav Kar

Subhash Bairagi

Ketaki Kar

Dr Thierry Roisnel

Dr Vincent Dorcet

Sundargopal Ghosh
email: sghosh@iitm.ac.in

Mr Mr S S Kar

Ms K Bairagi

Ghosh

Metal Coordinated Tri-and Tetraborane Analogues

Keywords: Chalcogen, Metallaheteroborane, Tantalum, Tetraborane, Triborane 10

A series of triborane and tetraborane analogues have been isolated and structurally characterized utilizing chalcogenatoborate ligands Li[BH3(EPh)] (E = S or Se). Thermolysis of [Cp*TaCl4] in the presence of Li[BH3(SPh)] afforded bimetallic tantallaheteroborane [(Cp*Ta)2(µ-η 3 :η 3 -B2H4S)(µ-η 2 :η 2 -SBH3)] (1) and hexasulfido trimetallic complex [(Cp*Ta)3(µ-S)4(µ-SPh)2] (2). Compound 1 is a fused ditantallaheteroborane, in which both di-and triborane analogues are stabilized by two tantalum atoms. In an attempt to synthesize the selenium analogues of 1 and 2, roomtemperature reaction of [Cp*TaCl4] with Li[BH3(SePh)] was carried out, which afforded bimetallic tantallaheteroborane [(Cp*Ta)2{µ-η 3 :η 3 -B3H6(SePh)}{µ-SePh}2] (3), monometallic tantallaheteroboranes [Cp*Ta(SePh)2{B4H8-n(SePh)n}] (4: n = 0, 5: n = 1), and trimetallic species [(Cp*Ta)3(µ-Se)4{µ-Se2(Se)}] (6). Compound 3 is the rarest example of triborane analogue {B3H6(SePh)} in the coordination sphere of two tantalum atoms. Whereas compounds 4 and 5 are examples of unsaturated metallaheteroboranes, in which the tetraborane analogues are stabilized in the coordination sphere of tantalum. One of the unique features of 3 and 5 is the presence of terminal B-SePh. Compound 6 has similar Ta3Se6 trisbutterfly core as that of 2 with additional bridging selenide unit. All the compounds have been characterized by NMR spectroscopy, mass spectrometry, IR spectroscopy and single-crystal X-ray diffraction studies.

10.

Introduction

Lower boranes, such as diborane, triborane, and tetraborane are very special because of their unique bonding, abnormal structure, and unusual reactivities. 1,2 Some of them have significantly been employed in many organic syntheses, such as, catalytic diboration and borylation reactions. 1b-c,2 Most of the triboranes and tetraboranes are typically isolated in ring form. 1a Interestingly, the chain forms of them are not very usual as with the increase of boron atoms they tend to form clusters. 3 However, utilizing transition metal templates these smaller boranes have been isolated both in chain and ring forms (Scheme 1). [4][5][6][7][8][9] In this connection, one suitable approach was developed by Fehlner and co-workers 10 employing cyclopentadienyl metal chlorides and monoborane reagents that led to the isolation of metal(s) coordinated smaller borane molecules. For example, recently we have isolated a classical [B2H5] -species in the coordination sphere of tantalum template. 9a Likewise, the triborane species I and II were stabilized in the coordination spheres of dicobalt and dimolybdenum, respectively. 4,5c The tetraborane IV, shown in Scheme 1, is stabilized at dichromium template. 6a-c Recently, Braunschweig, Marder, and co-workers have isolated a tetraborane species V which is stabilized at diruthenium template. 8a Apart from distinctive structural and bonding features, these metallaboranes, comprising of lower boranes, have a wide range of applications in catalysis, cyclotrimerization, borylation, etc. However, the development in this field found out to be very slow due to lack of alternative synthetic strategy and thus, search for an alternative synthetic strategy became essential. Interestingly, the progress in this field was significantly enhanced by the discovery of isolobal analogy 12 and electroncounting rules [13][14][15] that provided the basis for understanding the interrelationships among structures and compositions. Indeed, the replacement of one/two boron atoms of these smaller boranes with chalcogen atoms led to the stabilization of these species. 16,17 For example, we have recently explored the reactivity of Li[BH3(EPh)] (E = S or Se) with [Cp2VCl2] that yielded chalcogen included divanadaboranes having similar structural features with that of [B2H6] complexes. 16 On the other hand, treatment of Li[BH3(EPh)] (E = S or Se) with [CpNbCl4] yielded chalcogen incorporated triborane analogue III. 16 As a result, with an objective of isolating triborane and tetraborane analogues, we have explored the chemistry of [Cp*TaCl4] with chalcogen containing ligands, Li[BH3(EPh)] (E = S or Se) under diverse reaction conditions. Herein, in this article, we report the synthesis and characterization of several tantallaheteroboranes, which are analogues of triborane and tetraborane species.

Results and Discussion

Reactivity of [Cp*TaCl4] with Li[BH3(EPh)] (E = S or Se).

In an attempt to synthesis smaller boranes in the coordination sphere of tantalum, the reaction of [Cp*TaCl4] with four equivalents of Li[BH3(SPh)] was carried out at elevated conditions. The reaction afforded fused ditantallaheteroborane 1 (9% yield, Rf = 0.89) and fused trimetallic hexa-sulfido complex 2 (10% yield, Rf = 0.62) (Scheme 2). When the reaction was carried out with Li[BH3(SePh)] at room-temperature, it yielded ditantallaheteroborane 3 (12% yield, Rf = 0.28), monometallic tantallaheteroboranes 4 (20% yield, Rf = 0.34) and 5 (8% yield, Rf = 0.32), and fused trimetallic heptaselenido complex 6 (10% yield, Rf = 0.24) (Scheme 2). The formation of these metallaheteroboranes and chalcogen-ligated metal complexes is the concurrence of several reactions in one pot that vary from the binding of the anionic ligands, salt elimination, B-B formation, BH3-EPh cleavage, etc. The detailed characterizations of these molecules are described below.

Ditantallaheteroborane 1. Compound 1 was isolated as yellow solid in 9% yield. The 11 B{ 1 H} NMR of 1 exhibits three resonances, appeared at δ = 31.8, -12.0, and -22.6 ppm with equal intensity. The peaks in the negative region indicate boron attached to electronegative sulfur atom. The resonance at δ = 2.09 ppm in the 1 H NMR spectrum suggests the existence of one kind of Cp* environment. Further, the 1 H NMR spectrum of 1 displays peaks at δ = -7.99 and -10.19 ppm, which indicate the presence of bridging Ta-H-B protons. The mass spectrum of 1 displays a molecular ion peak at m/z 753.1644 [(M-H) + NH4] + . All these spectroscopic data were not enough to reveal the structure of 1. As a result, we have carried out a single-crystal Xray analysis on a suitable crystal of compound 1.

The solid-state X-ray structure of 1, shown in Figure S1, evidently shows the core geometry as an edge-fused tantallaheteroborane [(Cp*Ta)2(µ-η 3 :η 3 -B2H4S)(µ-η 2 :η 2 -SBH3)]. The spectroscopic data nicely corroborate with the solid-state structure of 1. For example, the 11 B{ 1 H} chemical shifts of 1 for the sulfur-connected boron atoms appeared in the upfield region. The 11 B{ 1 H} resonances of 1 at δ = 31.8, -12.0, and -22.6 ppm are assigned to B1, B2, and B3, respectively, by means of calculated 11 B NMR. [START_REF]The calculated 11 B chemical shifts of 3 appeared at δ = 23[END_REF] The Ta-Ta bond distance of 2.763(6) Å in 1 is significantly shorter as compared to the Ta-Ta bond distances of [(TaCp*)3(μ3-S)3(μ-S)3B(SH)] [START_REF] Kar | [END_REF] (c.a. 3.106 Å) and [(TaCp*)2(μ-H)(B2H5) (SCH2S)2] 9a (3.2903(8) Å). However, it is comparable with those of [(TaCp*)2(μ-Se){B3H6(SePh)}] 16 (2.815(1) Å) and [(Cp*TaBr)2(B2H6)] 20 (2.83 Å). Further, the WBI 21 value of 0.85 for Ta-Ta bond along with the contour line diagram 22 of Laplacian of electron density of 1 support a strong Ta-Ta bonding interaction (Figure 1b). As shown in Figure S1, the geometry of 1 can be considered as the fusion of two clusters, trigonal bipyramidal {Ta2B2S} and tetrahedron {Ta2BS}. The {Ta2B2S} fragment of cluster 1 has trigonal bipyramidal geometry, which is structurally identical to [{NbCp(EPh)}2{B2H4E}] 16 (E = S or Se) and [(Cp*MoCl)2 B3H7]. 4 The other part of cluster 1, i.e., tetrahedron {Ta2BS}, has similar structural features as that of diborane(6) species in bimetallic template. Therefore, compound 1 can also be viewed as a fused cluster where the triborane analogue and diborane analogue are stabilized in a ditantalum coordination sphere. 10.1002/ejic.202100687

Accepted Manuscript

European Journal of Inorganic Chemistry Triborane analogue 3. Compound 3 was isolated as purple solid in 12% yield. The 11 B{ 1 H} NMR spectrum of 3 shows three equivalents chemical shifts at δ = 24.5, 17.2, and 11.3 ppm. The 1 H chemical shift at δ = 2.20 ppm suggests the existence of one kind of Cp* protons, which is further confirmed by 13 C{ 1 H} NMR. Further, the 1 H NMR spectrum shows peaks at δ = -7.00 and -7.76 ppm with a ratio of 2:2 that indicates the existence of four Ta-H-B bridging protons. The 1 H{ 11 B} NMR spectrum shows peaks at δ = 6.38 and 6.07 ppm with a 1:1 ratio, which may be due to the terminal B-H protons. The mass spectrum of 3 displays a molecular ion peak at m/z 1140.0769 [M] + . All these spectroscopic data were not adequate to predict the identity of 3 until a single-crystal X-ray diffraction analysis was carried out.

The solid-state X-ray structure of 3 displays a bimetallic metallaheteroborane [(TaCp*)2{µ-η 3 :η 3 -B3H6(SePh)}{µ-SePh}2] (Figure 2). The geometry of 3 is trigonal bipyramidal, in which one of the boron atoms and two tantalum atoms are in the equatorial positions, whereas the other two boron atoms are in the axial positions. The Ta-Ta bond is bridged by two {SePh} ligands and is slightly longer (2.7917(4) Å) than that of 1. Further, the contour line map along the Ta1-Ta2-Se2 plane of 3 presents BCP and the bond path between Ta centers (Figure S27). The WBI of 0.83 between the Ta centers of 3 additionally supports the presence of strong Ta-Ta bonding interaction. The tantalum centers of 3 are at +4 oxidation state. On the other hand, the av. B-B bond distance of 3 (1.66 Å) is somewhat shorter than the B-B bond distances in other metallaboranes and metallaheteroboranes. 9a,16 In order to assign the boron atoms, we have calculated 11 B NMR chemical shifts for 3. The calculated chemical shifts at δ = 17.7, 12.2, and 7.8 ppm correspond to B2, B3, and B1, respectively, that corroborate with the experimental 11 B{ 1 H} NMR with an error range of 3.5-7 ppm. One of the key features of 3 is the activation of one of the B-H bonds and the formation of the B-Se bond.

Besides the existence of B3H8-metal complexes, the number of structurally characterized triboranes at the coordination sphere of metals is very limited. 4,5 Compound 3 can be viewed as the triborane analogue stabilized in the coordination sphere of two tantalum atoms and is one of the potential entries to the limited series of transition metal coordinated triboranes. The 4), Ta1-B2 2.392( 7), Ta1-B3 2.429( 7), Ta2-B2 2.397( 7), Ta2-B1 2.423( 7), Ta2-Se2 2.7064(6), B1-B2 1.654(10), Se3-B2 2.024( 7); Ta2-Se2-Ta1 62.012( 15), Ta2-B1-Ta1 70.09( 18), B1-B2-B3 132.5(6).

Electronic structure analyses of 1 and 3. As bimetallic 1 comprises of diborane and triborane analogues and bimetallic 3 consists triborane analogues, a theoretical investigation of their electronic structure and bonding became necessary. Computational analyses of 3 show a large HOMO-LUMO gap for 1 (3.509 eV) than that of 3 (3.037 eV). The HOMO-1 of both 1 (Figure 1b) and 3 (Figure 3b) depict the d orbital overlap of two Ta centers, which along with WBI and contour line diagram of Laplacian of electron density (Figures 1b andS27) support the strong Ta-Ta bonding in 1 and 3. The contour map of 1 perpendicular to Ta1-Ta2 bond (Figure 1c) shows BCPs and the bond path between B1-B2 and B2-S1 (represent triborane analogue) and between B3-S2 (represent diborane analogue). The contour map of 3 along B1-B2-B3 plane represents BCPs and the bond path between all these boron centers, which represent triborane analogue (Figure 3c). Further, the HOMO of 3 signifies the delocalized orbitals over one of the Ta-B-Ta bonds and localized p orbital on the Se atom of B-Se bond (Figure 3a). The NBO analysis 23 of 1 and 3 shows that all the boron and tantalum centers have negative natural charges, whereas all the sulfur atoms (for 1) and selenium atoms (for 3) have positive natural charges (Table S1). The natural charge analysis and natural valence population analysis of 1 and 3 indicate that the tantalum and boron centers are acting as acceptors, whereas sulfur/selenium atoms are behaving as donors.

10.1002/ejic.202100687

Accepted Manuscript

European Journal of Inorganic Chemistry Tetraborane analogues, 4 and 5. Compounds 4 and 5 were isolated as yellow solids in 20% and 8% yields, respectively. The 1 H NMR of 4 and 5 show one Cp* environment at δ = 2.02 and 1.98 ppm, respectively. In addition, compound 4 show three 1 H chemical shifts in the negative region at δ = -0.28, -2.03, and -3.04 ppm with 2:2:2 ratio, which may correspond to terminal B-H, bridging B-H-B or Ta-H-B hydrogens, respectively. In addition, 1 H{ 11 B} spectrum of 4 show two chemical shifts at δ = 3.12 and 4.2 ppm, which may correspond to terminal B-H. Whereas compound 5 shows two additional chemical shifts at δ = -0.90, and -2.62 ppm with 2:2 ratio, which correspond to bridging B-H-B or Ta-H-B hydrogens. The 11 B{ 1 H} NMR of 4 and 5 show three resonances at δ = 7.9, 3.3, and -2.8 ppm; and δ = 11.4, 5.0, and -5.2 ppm, respectively with 2:1:1 ratio. The mass spectrum of 4 displays a molecular ion peak at m/z 566.1468 [(M-SePh) + CH3CN] + . However, these spectroscopic data were not enough to identify the core geometry of 4 and 5.

Therefore, we have performed the single-crystal X-ray diffraction analysis on the suitable crystal of 4 and 5. As presented in Figure 4 S1). This may be due to the higher electronegativity of Cl compared to that of Se. Thus, we believe that the Ta in 4 and 5 acts as an acceptor, whereas it is a donor in [Cp*TaCl2{B4H8}]. 18), Ta2-Se3 2.5870 (19), B7-B8 1.84(3), B6-B8 1.75(3); B8-B7-Ta2 98.6(10), B5-Ta2-B7 62.8( 7), B5-B8-B7-93.8(13); 5: Ta1-B1 2.508(11), Ta1-B2 2.277( 12), Ta1-Se1 2.5499(11), Ta1-Se2 2.5608(10), B1-B2 1.723( 16), B2-B3 1.663( 16), B2-B4 1.689( 16), B4-Se3 1.969(11); B3-Ta1-B1 63.7( 4), B2-B1-B4 57.5(6), B3-B2-B4 64.3 (7), B3-B2-B1 102.1(8), B1-B2-Ta1 76.3(6).

10.1002/ejic.202100687

Accepted Manuscript

European Journal of Inorganic Chemistry Trimetallic polychalcogenide, 2 and 6. Both complexes 2 and 6 were isolated as green solids. The 1 H NMR spectrum of 2 shows peaks at δ = 2.24, and 2.11 ppm in 2:1 ratio. On the other hand, the 1 H NMR spectrum of 6 shows chemical shifts at δ = 2.34, and 2.24 ppm in 2:1 ratio. The 1 H NMR of 2 and 6 reveal the presence of dissimilar Cp* protons, which is further confirmed by 13 C{ 1 H} NMR spectra. Although all their spectroscopic data have similar pattern, 1 H NMR spectrum of 2 has peaks in the phenyl region. The mass spectra of 2 and 6 show molecular ion peaks at m/z 1294.1066 [M] + , and 1502.6188 [M+H] + , respectively. All the spectroscopic data were not adequate to envisage the identity of 2 and 6. A clear explanation eluded us until the solid-state X-ray structure analysis of 2 and 6 were carried out. The solid-state X-ray structures of 2 and 6, shown in Figure 6, show that both the molecules are consist of a Ta3 triangular core that can be viewed as fused trisbutterfly. In the case of 2, four monosulfide and two {SPh} ligands bridged the edges of the Ta3-triangular framework. Whereas four monoselenide and one triselenide ligand bridged the edges of the triangular Ta3 framework of 6. One of the interesting features of 6 is the existence of an extra selenide unit above the Ta3Se6 core. This additional selenide unit is not coordinated to any metal, instead bonded to two of the selenium atoms of fused trisbutterfly Ta3Se6 core. Two of the Ta-Ta bond distances in both 2 and 6 differ significantly from the other one. Although the observed Ta1-Ta1 distance of 2 (2.9622( 15) Å) and Ta2-Ta2 distance of 6 (3.0865( 19) Å) are consistent with normal Ta-Ta bond length, Ta1-Ta2 bond lengths of 2 (3.2192( 12) Å) and 6 (3.3311(15) Å) are slightly higher. [START_REF] Kar | [END_REF]24 This may be due to the presence of phenyl rings and an additional selenide group in 2 and 6, respectively.

Table 1. Selected structural parameters of trimetallic polychalcogenide complexes of group 5 metals.

Compounds

Av. dM-M (in Å) [a] Av. dM-E (in Å) [b] Ref. Note that there are few examples of these types of fused trisbutterfly complexes in the literature (Table 1). 24,25 For example, recently utilizing Li[BH2Se3] we have isolated the polychalcogenide trimetallic complexes having Ta3Se6 and Ta3Se8 core. But the earlier attempts to isolate their S analogues utilizing Li[BH2S3] were failed. Now, utilizing phenyl incorporated chalcogenatoborate ligand Li[BH3(SPh)], we are able to isolate the Ta3S6 core (2). On the other hand, heptaselenide 6 is the only example of its type after [Cp + Nb3S7] (Cp + = C5Me4Et). 25 The MO analysis shows that HOMO-LUMO energy gaps of 2 (2.48 eV), and 6 (2.50 eV) are quite higher. Both the HOMOs of 2 and 6 show that d orbitals of each Ta atoms are overlapped with each other and delocalized to form the Ta3 triangular skeleton (Figures S30a andS30b). Also, we have checked the Laplacian plot of electron density along the Se1-Se3-Se1 plane of 6, which displayed BCPs and bond path between all these Se atoms (Figure S30c).

UV-vis absorption studies of complexes 1-6. The UV-vis absorption spectroscopy was very helpful to modulate the optical properties of complexes 1-6. The UV-vis spectra of them reveal multiple bands around 280-700 nm (Fig. 7). The high-energy absorption bands around 280-290 nm point out the π-π* transition of Cp* ligands, and that is characteristic of most of the Cp* based-metal complexes. The low-energy bands around 311-627 nm have been assigned to charge transfer bands. In order to get information about the electronic transitions, time-dependent DFT calculations were carried out (Figures S31-S42 and Tables S2-S7). The molecular orbitals related to the most intense electronic transitions of 1-6 are shown in Fig. S37-S42. The absorption bands around 311-420 nm of complexes 1-6 may correspond to the intramolecular MLCT transitions. In complexes 1, 3, 4, and 5, the absorptions around 445-495 nm may be assigned to the electronic transitions corresponding to HOMOLUMO. The HOMOs of 1, 3, 4, and 5 are mostly centred on ligands and the LUMOs are localized on d orbitals of Ta with very little contribution from ligand. The absorptions around 445-495 nm, obtained from TD-DFT calculations, may be assigned to intramolecular LMCT transitions. The low-intensity absorptions near 603 and 627 nm for complexes 2 and 6, respectively, may be due to intramolecular LMCT transitions. They correspond to HOMO-1LUMO transition in which the HOMO-1 is largely localized on the chalcogen atoms S and Se for complexes 2 and 6, respectively. Both the LUMOs are centered on the d orbitals of Ta with very little contribution from the ligand.

Conclusion

In summary, we have synthesized and structurally characterized several tantallaheteroborane species, which can be viewed as the result of heteroborane fragment "growth" around a Ta-Ta bond. For example, triborane analogue and diborane analogue are stabilized around the Ta-Ta bond in 1. In 3, triborane analogue stabilized around Ta-Ta bond. On the other hand, tetraborane analogues are stabilized in the coordination sphere of Ta. Thus, the isolation and characterization of these unique metallaheteroborane species established a new methodology for the stabilization of diborane, triborane, and tetraborane type species utilizing metal coordination spheres. Further, the theoretical studies revealed that tetraborane species 4 and 5 have reactive Se centers, which can undergo coordination/cluster growth reaction. The reactivity study with metal carbonyls and alkynes is underway.

Experimental Section

General Procedures and Instrumentation. All syntheses were carried out in flame-dried glassware under an argon atmosphere using conventional glovebox or standard schlenk line techniques. Solvents were distilled underneath of Ar atmosphere using standard methods.

[Cp*TaCl4] 26 and Li[BH3(EPh)] 27,28 (E = S and Se) were synthesized according to the literature methods, while other commercial reagents such as [LiBH4•THF], Ph2S2, Ph2Se2 powder were used as received (Aldrich) without further purification. The reaction mixture was separated into pure compounds using thin layer chromatographic techniques on 250-µm diameter aluminum supported silica gel TLC plates (MERCK TLC Plates). Note that the reactions, extractions, and work-up were done under Ar-atmosphere, and during all these processes properly distilled solvents were used. In particular, we have done separation using TLC plates inside beakers which were filled with Ar before and after filling with eluting solvents. All the NMR spectra were recorded on Bruker 400 MHz and Bruker 500 MHz FT-NMR spectrometers. 1 H and 13 C{ 1 H} shifts are referenced to residual 1 H and 13 C{ 1 H} signals in the deuterated solvent, while 11 B{ 1 H} resonance is referenced to the external standard of a sealed tube that contained [Bu4N(B3H8)] in [D6] benzene (δB = -30.07 ppm). 29 Infrared spectra were recorded on a PerkinElmer Spectrum 400 FT-IR spectrometer. ESI mass spectra were acquired on a Bruker MicroTOF-II mass spectrometer. UV-vis absorption spectra were recorded on a Thermo Scientific (Evolution 300) UV-vis spectrometer. Note that, because of low yields and higher sensitivity, elemental analysis of the compounds could not be performed. The solvent was removed in vacuo, and the residue was extracted with n-hexane and filtered through a frit using 3 cm of celite. After removing the solvent from the filtrate, the crude materials were subjected to chromatographic work-up on TLC plates (20% CH2Cl2 in hexane) which yielded yellow 1 (0.015 g, 9%) and green 2 (0.019 g, 10%). The reaction mixture was allowed to come to room temperature over 1 hour under the stirring condition and continued for 24 h. The solvent was removed in vacuo, and the residue was extracted with n-hexane and filtered through 3 cm of celite. After removal of the solvent from the filtrate, the crude materials were subjected to chromatographic work-up on TLC plates (20% CH2Cl2 in hexane which yielded purple 3 (0.030 g, 12%), yellow 4 (0.059 g, 20%), yellow 5 (0.029 g, 8%), and green 6 (0.022 g, 10%). X-ray Structure Determination. Crystal data for 1 was obtained using Bruker AXS Kappa APEX-II CCD diffractometer with graphitemonochromated MoKα (λ = 0.71073 Å) radiation at 150 K. The crystal data for 2, and 4-6 were collected and integrated Bruker AXS Kappa APEX-III CCD diffractometer with graphite-monochromated MoKα (λ = 0.71073 Å) radiation at 296 K. The crystal data for 3 was collected and integrated using a D8 VENTURE Bruker AXS diffractometer with graphite-monochromated MoKα (λ = 0.71073 Å) radiation at 150 K. The structures were solved by heavy atom methods using SHELXS-97 or SIR92 [START_REF] Sheldrick | SHELXS-97[END_REF] and refined using SHELXL-2018. [START_REF] Sheldrick | [END_REF] Olex2 is utilized to draw the structures. 32 Crystallographic data have been deposited with the Cambridge Crystallographic Data Center as supplementary publication no. 2008774 (1), 2082990 (2), 1914732 (3), 2083518 (4), 2045971 (5), and2082991 (6). These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif. Computational Details. All molecules were fully optimized using b3lyp functional 33 in conjunction with the 6-31g(d)-sdd basis set using the Gaussian 09 [START_REF] Frisch | Gaussian 09, Revision C.01[END_REF] program. For the optimization of all molecules, multiplicity = 1 is considered. All compounds were fully optimized in gaseous state using their X-ray crystallographic coordinates. NBO analyses were carried out with the NBO partitioning scheme 24 as employed in the Gaussian 09. Note that significant algorithmic differences between NBO3 and NBO5 are particularly apparent in details of natural population analysis for transition metals and rare-earth species. [START_REF] Weinhold | Discovering Chemistry with Natural Bond Orbitals[END_REF] Wiberg bond indexes (WBI) 22 were obtained on NBO analysis. The QTAIM analysis 23 was performed utilizing Multiwfn V.3.6 package. [START_REF] Lu | [END_REF] The 11 B NMR chemical shifts were calculated with respect to B2H6 (B3LYP B shielding constant 93.5 ppm) and converted to the usual [BF3.OEt2] scale using the experimental 11 B chemical shift of B2H6, 16.6 ppm. All the optimized structures and orbital graphics were produced using the Gaussview 37 and Chemcraft [START_REF] Zhurko | [END_REF] .

Synthesis of [(

  11

Scheme 1 .

 1 Scheme 1. Various types of metal-coordinated tri-and tetraboranes (For clarity, two µ-EPh units attached to Nb-Nb bond are omitted in III; VI: Dur = 2,3,5,6-tetramethylphenyl).

  Scheme 2. Syntheses of ditantallaheteroboranes (1 and 3), tantallaheteroboranes (4 and 5) and trimetallic polychalcogenide complexes (2 and 6).

Figure 1 .

 1 Figure 1. (a) HOMO-1 of 1 depicts Ta-Ta bonding interaction; (b) and (c) Contour line diagrams of the Laplacian of electron density along the Ta1-S2-Ta2 and a plane perpendicular to Ta1-Ta2 bond planes of 1, respectively.

  [Ta2B3] core of 3 possesses trigonal bipyramidal geometry, which is geometrically identical to that of electronically unsaturated transition metal coordinated triborane species [(Cp*MoCl)2B3H7]. 4 Although several M2B3 cores are known with open geometry, to the best of our knowledge 3 is the second example with closo-geometry after [(Cp*MoCl)2B3H7]. According to Wade's skeleton electron counting rule, 13 the number of skeletal electron pairs (SEP) required for the trigonal bipyramid is six (CVE = 42). Compound 3 has six skeletal electron pairs (CVE = 42); thus, it is electronically saturated.

Figure 2 .

 2 Figure 2. Molecular structure of 3. Note that hydrogen atoms of phenyls are not shown for clarity. Selected bond lengths (Å) and angles (°) of 3: Ta1-Ta2 2.7917(4), Ta1-B2 2.392(7), Ta1-B3 2.429(7), Ta2-B2 2.397(7), Ta2-B1 2.423(7), Ta2-Se2 2.7064(6), B1-B2 1.654(10), Se3-B2 2.024(7); Ta2-Se2-Ta1 62.012(15), Ta2-B1-Ta1 70.09(18), B1-B2-B3 132.5(6).

Figure 3 .

 3 Figure 3. (a) HOMO and (b) HOMO-1 of 3; (c) Contour line diagram of the Laplacian of electron density of 3 along the B1-B2-B3 plane of 3.

  , the solid-state X-ray analysis reveals compound 4 as [Cp*Ta(SePh)2{B4H8}] and compound 5 as [Cp*Ta(SePh)2{B4H7(SePh)}]. Compounds 4 and 5 can be viewed as tetraborane analogues stabilized in the coordination sphere of one tantalum that represent a square pyramidal TaB4 core, where the tantalum atoms are attached to Cp* and two {SePh} ligands. The only difference between 4 and 5 is the presence of terminal B-SePh in 4. Both 4 and 5 have 6 SEPs (CVE = 32), however, the square pyramid core needs 7 SEPs for electronic saturation. Thus, compounds 4 and 5 can be viewed as electronically unsaturated species, isoelectronic with earlier reported [Cp*TaCl2{B4H8}]. 7 In 4 and 5, and [Cp*TaCl2{B4H8}], the tantalum atoms are at +5 oxidation state. Although there are many examples of tetraborane stabilized in the coordination sphere of two metals, 6,9a monometal stabilized tetraborane species are very few. To investigate the effect of substitution of Cl by {SePh} ligand, we have carried out computational analyses of [Cp*TaCl2{B4H8}], 4, and 5. The HOMO-LUMO energy gap for 4 (3.49 eV) and 5 (2.98 eV) are smaller as compared to that of [Cp*TaCl2{B4H8}] (4.12 eV) (Figure 5). The MO analyses reveal that HOMO of 4 is localized on the Se atom (p orbital) of SePh unit attached to the metal center, whereas the HOMO of 5 is centered on the SePh unit attached to boron. On the other hand, the LUMOs of 4 and 5 are mostly centered on tantalum atom (dorbital) along with a little contribution from the Se atom (p orbital) of SePh unit attached with the metal center. The NBO analysis shows that the tantalum atom has a negative natural charge in 4 and 5, and it is positive in [Cp*TaCl2{B4H8}] (Table

Figure 4 .

 4 Figure 4. Molecular structure of 4 (left) and 5 (right). Selected bond lengths (Å) and angles (°) of 4: Ta2-B5 2.47(2), Ta2-B6 2.296(18), Ta2-Se3 2.5870(19), B7-B8 1.84(3), B6-B8 1.75(3); B8-B7-Ta2 98.6(10), B5-Ta2-B7 62.8(7), B5-B8-B7-93.8(13); 5: Ta1-B1 2.508(11), Ta1-B2 2.277(12), Ta1-Se1 2.5499(11), Ta1-Se2 2.5608(10), B1-B2 1.723(16), B2-B3 1.663(16), B2-B4 1.689(16), B4-Se3 1.969(11); B3-Ta1-B1 63.7(4), B2-B1-B4 57.5(6), B3-B2-B4 64.3(7), B3-B2-B1 102.1(8), B1-B2-Ta1 76.3(6).

Figure 5 .

 5 Figure 5. Frontier molecular orbitals of [Cp*TaCl2{B4H8}], 4, and 5.

Figure 6 .

 6 Figure 6. Molecular structure of 2 (left) and 6 (right). Note that Cp* and hydrogens of phenyl groups are not shown for clarity. Selected bond lengths (Å) and angles (°) of 2: Ta1-Ta1 2.9622(15), Ta1-Ta2 3.2192(12), S1-Ta1 2.427(4), S2-Ta1 2.628(4), S3-Ta1 2.427(4); Ta2-S1-Ta1 84.26(15), Ta2-S2-Ta1 77.24(12); 6: Ta1-Ta2 3.3311(15), Ta2-Ta2 3.0865(19), Se1-Ta1 2.632(3), Se2-Ta1 2.463(2), Se1-Se3 2.385(4);Se3-Se1-Ta1 95.83(11)

Figure 7 .

 7 Figure 7. Combined UV-vis spectra of 1-6 in CH2Cl2.

  In a flame-dried 50 mL Schlenk tube under Ar atmosphere, a toluene solution of [Cp*TaCl4] (0.200 g, 0.44 mmol, in 20 mL) was chilled to -78 ºC. Then a freshly prepared toluene solution of Li[BH3SPh] (4 equivalents, in 15 mL) was transferred to it through a cannula. The reaction mixture was allowed to come to room temperature over 1 hour under the stirring condition and refluxed at 80 °C for 24 h.

1:

  MS (ESI + ): m/z calculated for [(C20H37B3S2Ta2-H) + NH4] + : 753.1852, found: 753.1644. 11 B{ 1 H} NMR (160 MHz, [d8]-toluene, 22 °C): δ (ppm) = 31.8 (br, 1B), -12.0 (br, 1B), -22.6 (br, 1B); 1 H NMR (500 MHz, C6D6, 22 °C): δ (ppm) = 6.96 (br, B-Ht), 2.09 (s, 30H; 2×Cp*), -7.99 (d, 2H, Ta-H-B), -10.19 (d, 2H, Ta-H-B); 1 H{ 11 B} NMR (500 MHz, [d8]-toluene, 22 °C): δ (ppm) = 6.81 (s, 1H, B-Ht), 2.08 (s, 30H; 2×Cp*), 0.019 (s, 1H, 10.1002/ejic.202100687 Accepted Manuscript European Journal of Inorganic Chemistry B-Ht), 0.006 (s, 1H, B-Ht), -8.12 (d, 2H, Ta-H-B), -10.30 (d, 2H, Ta-H-B); 13 C{ 1 H} NMR (125 MHz, C6D6, 22 °C): δ (ppm) = 110.1 (s, C5Me5), 13.6 (s, C5Me5); IR (dichloromethane, cm -1 ): ṽ = 2453 (B-Ht); UV-Vis [CH2Cl2, λ, nm]: 343, 451. 2: MS (ESI + ): m/z calculated for [(C42H55S6Ta3)] + : 1294.1068, found: 1294.1066. 1 H NMR (500 MHz, C6D6, 22 °C): δ (ppm) = 6.87-6.86 (m, Ph), 2.24 (s, 30H; 2×Cp*), 2.11 (s, 15H; 1×Cp*); 13 C{ 1 H} NMR (125 MHz, C6D6, 22 °C): δ (ppm) = 136.9-126.8 (s, Ph), 119.1, 115.4 (s, C5Me5), 13.4, 13.2 (s, C5Me5); UV-Vis [CH2Cl2, λ, nm]: 311, 353, 420, 494, 603. In a flame-dried 50 mL Schlenk tube under Ar atmosphere, a toluene solution of [Cp*TaCl4] (0.200 g, 0.44 mmol, in 20 mL) was chilled to -78 ºC. Then a freshly prepared toluene solution of Li[BH3SePh] (4 equivalents, in 15 mL) was transferred to it via cannula.

3 : 4 :

 34 MS (ESI + ): m/z calculated for [C38H51Ta2B3Se3] + : 1140.0771, found: 1140.0769. 11 B{ 1 H} NMR (160 MHz, CDCl3, 22 °C): δ (ppm) = 24.5 (br, 1B), 17.2 (br, 1B), 11.3 (br, 1B); 1 H NMR (500 MHz, C6D6, 22 °C): δ (ppm) = 7.96-6.98 (m, Ph), 2.20 (s, 30H; 2×Cp*), -7.00 (s, 2H, Ta-H-B), -7.76 (s, 2H, Ta-H-B); 1 H{ 11 B} NMR (500 MHz, C6D6, 22 °C): δ (ppm) = 7.53-7.09 (m, Ph), 6.38 (t, 1H, B-Ht), 6.07 (t, 1H, B-Ht), 2.28 (s, 30H; 2×Cp*), -7.24 (s, 2H, Ta-H-B), -8.09 (s, 2H, Ta-H-B); 13 C{ 1 H} NMR (125 MHz, C6D6, 22 °C): δ (ppm) = 137.4-125.7 (s, Ph), 110.5 (s, C5Me5), 13.9 (s, C5Me5); IR (dichloromethane, cm -1 ): ṽ = 2448 (B-Ht); UV-Vis [CH2Cl2, λ, nm]: 335, 495. MS (ESI + ): m/z calculated for [(C22H33TaB4Se2 -SePh) + CH3CN] + : 566.1491, found: 566.1468. 11 B{ 1 H} NMR (160 MHz, C6D6, 22 °C): δ (ppm) = 7.9 (br, 1B), 3.3 (br, 1B), -2.8 (br, 2B); 1 H NMR (500 MHz, C6D6, 22 °C): δ (ppm) = 7.99-6.85 (m, Ph), 4.37 (br, B-Ht), 3.13 (br, B-Ht), 2.02 (s, 15H; 1×Cp*), -0.28 (s, 2H, B-Ht), -2.03 (s, 2H, B-H-B), -3.04 (s, 2H, Ta-H-B); 1 H{ 11 B} NMR (500 MHz, C6D6, 22 °C): δ (ppm) = 7.98-6.85 (m, Ph), 4.20 (s, 1H, B-Ht), 3.12 (s, 1H, B-Ht), 2.02 (s, 15H; 1×Cp*), -0.28 (s, 2H, B-Ht), -2.03 (s, 2H, B-H-B), -3.04 (s, 2H, Ta-H-B); 13 C{ 1 H} NMR (125 MHz, C6D6, 22 °C): δ (ppm) = 131.8-127.9 (s, Ph), 118.1 (s, C5Me5), 12.5 (s, C5Me5); IR (dichloromethane, cm -1 ): ṽ = 2548, 2442 (B-Ht); UV-Vis [CH2Cl2, λ, nm]: 372, 495. 5: 11 B{ 1 H} NMR (160 MHz, CDCl3, 22 °C): δ (ppm) = 11.4 (br, 2B), 5.0 (br, 1B), -5.2 (br, 1B); 1 H NMR (500 MHz, C6D6, 22 °C): δ (ppm) = 7.92-6.87 (m, Ph), 3.59 (br, B-Ht), 3.49 (s, B-Ht), 1.98 (s, 15H; 1×Cp*), -0.90 (s, 2H, B-H-B), -2.62 (s, 2H, Ta-H-B); 13 C{ 1 H} NMR (125 MHz, C6D6, 22 °C): δ (ppm) = 137.6-125.4 (s, Ph), 118.3 (s, C5Me5), 12.2 (s, C5Me5); IR (dichloromethane, cm -1 ): ṽ = 2545, 2440 (B-Ht); UV-Vis [CH2Cl2, λ, nm]: 381, 445. 6: MS (ESI + ): m/z calculated for [(C30H45Se7Ta3) + H] + : 1502.6247, found: 1502.6188. 1 H NMR (500 MHz, C6D6, 22 °C): δ (ppm) = 2.34 (s, 30H; 2×Cp*), 2.24 (s, 15H; 1×Cp*); 13 C{ 1 H} NMR (125 MHz, C6D6, 22 °C): δ (ppm) = 117.1, 114.3 (s, C5Me5), 14.9, 14.6 (s, C5Me5); UV-Vis [CH2Cl2, λ, nm]: 325, 374, 400, 627.

1:

  C20H37B3S2Ta2, Mr = 735.94, triclinic, space group P-1, a = 9.4502(9) Å, b =11.3156(10) Å, c = 12.0193(12) Å, α = 71.843(3)°, β = 88.776(4)°, γ = 85.061(3)°, V = 1216.7(2) Å 3 , Z = 2, ρcalc = 2.009 g/cm3, μ = 9.162 mm -1 , F(000) = 700.0, R1 = 0.0275, wR2 = 0.0563, 5527 independent reflections [2θ ≤ 54.968°] and 564 parameters. 2: C43H57Cl2S6Ta3, Mr = 1379.99, tetragonal, space group P42/n, a = 12.0855(16) Å, b =12.0855(16) Å, c = 30.920(4) Å, α = β = γ = 90°, V = 4516.2(13) Å 3 , Z = 4, ρcalc = 2.030 g/cm3, μ = 7.677 mm -1 , F(000) = 2656.0, R1 = 0.0768, wR2 = 0.1761, 3987 independent reflections [2θ ≤ 49.990°] and 315 parameters.

3 : 4 :

 34 C38H49B3Se3Ta2, Mr = 1136.98, monoclinic, space group P21/c, a = 20.0953(16) Å, b = 9.9318(7) Å, c = 19.6758(16), α = 90°, β = 105.574(3), γ = 90°, V = 3782.8(5)Å 3 , Z = 4, ρcalc =1.996 g/cm 3 , μ = 8.694mm -1 , F(000) = 2160.0, R1= 0.0364, wR2 = 0.0809, 8651 independent reflections [2θ ≤ 55.014°] and 311parameters C22H33B4Se2Ta, Mr = 679.59, monoclinic, space group P21/c, a = 9.7935(15) Å, b = 18.224(3) Å, c = 28.933(6) Å, α = 90.000(5)°, β = 90.02(2)°, γ = 90°, V = 5163.9(16) Å 3 , Z = 8, ρcalc = 1.748 g/cm 3 , μ = 7.083 mm -1 , F(000) = 2608.0, R1 = 0.0525, wR2 = 0.0914, 9094 independent reflections [2θ ≤ 50.074°] and 677 parameters 5: C28H37B4Se3Ta, Mr = 834.64, orthorhombic, space group Pbca, a = 20.3246(13) Å, b = 14.8799(8) Å, c = 20.6315(13) Å, α = β = γ = 90°, V = 6239.5(7) Å 3 , Z = 8, ρcalc = 1.777 g/cm 3 , μ = 7.039 mm -1 , F(000) = 3200.0, R1 = 0.0392, wR2 = 0.0650, 5493 independent reflections [2θ ≤ 49.998°] and 353 parameters. 6: C31.30H47.60Cl2.60Se7Ta3, Mr = 1611.42, orthorhombic, space group Pnma, a = 16.827(2) Å, b = 16.111(2) Å, c = 15.2247(19) Å, α = β = γ = 90°, V = 4127.6(9) Å 3 , Z = 4, ρcalc = 2.593 g/cm 3 , μ = 14.296 mm -1 , F(000) = 2946.0, R1 = 0.0828, wR2 = 0.1579, 3764 independent reflections [2θ ≤ 49.998°] and 252 parameters.

Acknowledgements 10.1002/ejic.202100687

This work was funded by SERB, New Delhi, India, Grant No. CRG/2019/001280. S.K. and S.B. thank IIT Madras and K.K. thank DST-INSPIRE for fellowships. We thank P. K. Sudhadevi Antharjanam and Dr. B. Varghese for X-ray structure analyses. The computational facility, IIT Madras is gratefully acknowledged.

Accepted Manuscript

European Journal of Inorganic Chemistry

Entry for the Table of Contents

Diborane, triborane analogue, and tetraborane analogue stabilized in the coordination sphere of tantalum atom(s). New early transition metal coordinated triborane and tetraborane analogues have been synthesized utilizing chalcogenatoborate ligands Li[BH3(EPh)] (E = S or Se) and structurally characterized. Also, theoretical calculations have given insight into their bonding and electronic structures.

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