Cristian Pasquaretta
email: cristian.pasquaretta@univ-tlse3.fr

Raphaël Jeanson

Christophe Andalo

Lars Chittka
email: l.chittka@qmul.ac.uk

Mathieu Lihoreau

Analysing plant-pollinator interactions with spatial movement networks

Keywords: bumblebees, foraging, honeybees, movement ecology, pollination, route optimization, spatial networks

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Introduction

Bees play a key role in the reproduction of wild and cultured plants. Over recent years, their widespread declines have raised considerable concern for food security and the sustainability of our ecosystems [START_REF] Goulson | Bee declines driven by combined stress from parasites, pesticides, and lack of flowers[END_REF][START_REF] Klein | Why bees are so vulnerable to environmental stressors[END_REF]. Central to understanding the impact of pollinator loss on plant reproduction is the foraging behaviour of bees [START_REF] Thomson | Pollen transport and deposition by bumble bees in Erythronium: influences of floral nectar and bee grooming[END_REF][START_REF] Waser | Flower constancy: definition, cause, and measurement[END_REF]. Most bees are central-place foragers, meaning that they collect food (nectar and pollen) to provision their brood in a single nest [START_REF] Michener | The Bees of the World[END_REF]. By exploiting plants and developing foraging routes to visit them, individual bees may bias pollen flow and fashion the genetic structure of plant populations, therefore calling for more research of bee spatial strategies at the individual and collective levels [START_REF] Ohashi | Trapline foraging by pollinators: Its ontogeny, economics and possible consequences for plants[END_REF][START_REF] Burkle | The future of plant-pollinator diversity: Understanding interaction networks acrosss time, space, and global change[END_REF][START_REF] Mayer | Pollination ecology in the 21st Century: key questions for future research[END_REF].

Historically, bees were assumed to use simple movement rules that would yield maximal energy gains to exploit patchily distributed resources, such as moving between nearest unvisited flowers [START_REF] Ohashi | Trapline foraging by bumble bees: IV. Optimization of route geometry in the absence of competition[END_REF], making short trips after encountering highly rewarding flowers [START_REF] Chittka | Foraging dynamics of bumble bees: correlates of movements within and between plant species[END_REF] or keeping constant heading directions between visiting flowers [START_REF] Pyke | The flight directionality of bumblebees: Do they remember where they came from?[END_REF].

While these rules of thumb may hold true when bees forage at small spatial scales (within an inflorescence or a flower patch) mounting evidence shows that this is not the case at larger spatial scales, when bees move between distant locations (flower patches or plants). In these conditions, foragers of many bee species tend to develop stable foraging routes (sometimes called traplines in analogy to the fixed circuits that trappers follow when examining a number of traps distributed widely in space) that they follow for several hours or days (e.g. Euglossine bees [START_REF] Janzen | Euglossine bees as long-distance pollinators of tropical plants[END_REF]bumblebees: Heinrich 1976;[START_REF] Thomson | Trapline foraging by bumble bees: II. Definition and detection from sequence data[END_REF]honeybees: Buatois & Lihoreau, 2016). This routing behaviour is based on the acquisition of spatial memories encoding the location of the different food resources, the colony nest site and other prominent environmental features (e.g. visual landmarks) [START_REF] Collett | Spatial memory in insect navigation[END_REF]. With training, bumblebees and honeybees can learn to find the shortest path to visit a few artificial flowers (equivalent to natural flower patches) once and return to the nest (Bombus impatiens: [START_REF] Ohashi | Trapline foraging by bumble bees: IV. Optimization of route geometry in the absence of competition[END_REF]Bombus terrestris: Lihoreau et al., 2012a; Apis mellifera: [START_REF] Buatois | Evidence of trapline foraging in honeybees[END_REF], an optimisation behaviour analogous to solving the Travelling Salesman Problem in graph theory [START_REF] Cook | pursuit of the traveling salesman: mathematics at the limits of computation[END_REF]. This mathematical problem is notoriously difficult (if not impossible) to solve for large graphs, because the number of possible paths increases factorially with the number of nodes in the graph (e.g. 6 paths for 3 nodes, > 3 million paths for 10 nodes), and finding efficient solutions often requires complex algorithms and systematic approaches [START_REF] Polyakovskiy | A comprehensive benchmark set and heuristics for the traveling thief problem[END_REF][START_REF] Dorigo | Ant-Q: A reinforcement learning approach to the traveling salesman problem[END_REF].

While there is evidence that bees exhibit routing behaviour in nature [START_REF] Heinrich | the foraging specializations of individual bumble-bees[END_REF][START_REF] Janzen | Euglossine bees as long-distance pollinators of tropical plants[END_REF], to what extent these observations in simplified experimental conditions can be extrapolated to the field, where individuals may interact to exploit numerous highly variable resources scattered across large landscapes, is an open question.

Field data on such multi-destination routes among flower patches are even more complex and challenging to analyse, and conventional behavioural metrics do not suffice to capture detailed information about routing behaviour [START_REF] Thomson | Trapline foraging by bumble bees: II. Definition and detection from sequence data[END_REF][START_REF] Makino | Findings on spatial foraging patterns of bumblebees (Bombus ignitus) from a bee-tracking experiment in a net cage[END_REF][START_REF] Makino | Does interaction between bumblebees (Bombus ignitus) reduce their foraging area?: bee-removal experiments in a net cage[END_REF][START_REF] Makino | Longer visits on familiar plants?: testing a regular visitor's tendency to probe more flowers than occasional visitors[END_REF][START_REF] Lihoreau | Monitoring flower visitation networks and interactions between pairs of bumble bees in a large outdoor flight cage[END_REF]. We argue that network statistics derived from graph theory hold considerable promise to characterise these complex movement patterns at the individual and collective levels, and to identify the decision rules underpinning spatial strategies. In developing routes between flowers, foragers form movement networks embedded in space [START_REF] Barthélemy | Spatial networks[END_REF], where 'nodes' are feeding locations (flower patches or plants) and 'edges' are flight paths between them (see examples in Figures 1A-E) [START_REF] Thomson | Trapline foraging by bumble bees: II. Definition and detection from sequence data[END_REF][START_REF] Lihoreau | Monitoring flower visitation networks and interactions between pairs of bumble bees in a large outdoor flight cage[END_REF]. These spatial movement networks are directed, meaning that individuals move from one particular location to another (movement vectors). Networks are also weighted so that the thickness of edges is proportional to the frequency of movements between nodes. Because most bee species are central-place foragers, their spatial movement networks also include the nest site, a specific node at which every flower visitation sequence starts and ends. Therefore, in principle, an optimal movement network for a bee connects all flowers and the nest using the shortest possible path (optimal network in Figure 1E). Discrete temporal network analysis can then be performed depending on the time intervals with which a visitation matrix is built. For instance, matrices may be developed by considering flower visits made in a single foraging bout (dynamic network) or by cumulating the flower visits of several foraging bouts (static network). A major advantage of network statistics is that they allow for analyses of very large spatial datasets and the derivation of new empirically testable hypotheses (e.g. [START_REF] Perna | Animal transportation networks[END_REF][START_REF] Jacoby | Emerging network-based tools in movement ecology[END_REF]. Several analytical packages (e.g. igraph, sna, tnet packages in R, graph-tool in Python, UCINET) and both local metrics (e.g. measures describing the level of importance of a node in a network) and global metrics (e.g. measures describing the general level of connectivity of the entire network) can be readily calculated to characterize space use by pollinators from an individual-based point of view to measure, compare and predict their behaviour across different temporal scales.

In a recent field survey, [START_REF] Dupont | Spatial structure of an individual-based plant-pollinator network[END_REF] applied an individual-based plant-pollinator network analysis to flower visitation data of different bumblebee species. The study showed significant modularity in space use by bees based on plant characteristics, so that foragers tended to visit patches of aggregated plants with numerous flowers and use taller plants to move from one module to another [START_REF] Dupont | Spatial structure of an individual-based plant-pollinator network[END_REF]. Although the analytical approach developed in this study is very appealing, field surveys only provide partial information about the foraging experience of individual bees, the location of their nest relative to different plant patches and the temporal dynamics of their foraging patterns. All these parameters are critical in determining bee foraging behaviour [START_REF] Chittka | Cognitive ecology of pollination: animal behaviour and floral evolution[END_REF]. Experimental advances on model bee species, such as bumblebees and honeybees, using artificial flowers delivering controlled rates of food resources combined with automated movement tracking, now allow for collecting high resolution spatial and temporal data on bee foraging patterns in complex, yet controlled, environments (e.g. motion detection cameras on flowers: [START_REF] Lihoreau | Monitoring flower visitation networks and interactions between pairs of bumble bees in a large outdoor flight cage[END_REF]Radio Frequency Identification (RFID): [START_REF] Ohashi | An automated system for tracking and identifying individual nectar foragers at multiple feeders[END_REF]harmonic radars: Lihoreau et al., 2012b;QR tags: Crall et al. 2015;3D video tracking: Ings & Chittka, 2008).

Extensive recordings of individual based data using these semi-field approaches provide an interesting opportunity to start examining the cognitive processes underpinning the foraging patterns of bees and how they change across time in ecologically relevant conditions.

Here we describe how spatial network statistics can be used to analyse the foraging patterns of bees both at local and global levels. We illustrate the potential of this approach for comparative analyses by statistically comparing spatial optimisation in the movement patterns of bees of the same species or, of different species across environments varying in spatial scales, number of flowers and flower configurations using standard network metrics. We used published movement datasets of bumblebees and honeybees of known age, foraging experience and colony origin, foraging in arrays of artificial flowers in the lab and in the field. To validate the approach, we compared our results with analyses of more conventional behavioural metrics used in previous studies, such as the number of re-visits to flowers and overall travel efficiency (distance/number of flowers visited).

Materials and methods

Experimental data

We analysed six datasets of bee flower visitation sequences. Three datasets were obtained on the bumblebee Bombus terrestris (experiment 1: Lihoreau et al., 2012a;experiment 2: Lihoreau et al., 2011;experiment 3: Lihoreau et al., 2012b). The three other datasets were obtained on the honeybee Apis mellifera (experiments 4-6: [START_REF] Buatois | Evidence of trapline foraging in honeybees[END_REF].

All the datasets were generated following the same general methodology and are thus comparable. In all experiments bees were individually marked (coloured number tags or paint dots on the thorax) and maintained in colony nest boxes (bumblebees) or hives (honeybees) equipped with a transparent, colourless, entrance tube. The tube was fitted with a series of shutters to control all departure and arrival of foragers at the colony. Workers collected sucrose solution (40% w/w) on artificial flowers outside the colony. Flowers consisted of a blue plastic landing platform (diameter = 60mm) with a yellow feeding spot in the middle. Bees were initially pre-trained on a flower from which they could collect ad libitum sucrose solution. Each individual was tested alone. A regular forager that made at least five foraging bouts (foraging trips starting and ending at the nest colony box) in one hour was selected. The crop capacity of this forager was estimated by averaging the total volume of sucrose solution collected from a training flower over another three foraging bouts. The forager was then tested with all test flowers placed in a specific spatial arrangement (see experimental arrays in Figure 2). During the test, each flower provided the same amount of sucrose solution, chosen so that the bee had to visit all flowers to fill its nectar crop to capacity before returning to the colony nest box (e.g. 1/5 th of the crop capacity available in each flower in an array of five flowers). Flowers were refilled by the experimenter at the end of each foraging bout, meaning that any revisit to a flower within the same foraging bout was not rewarding. Bees were tested for 22 to 80 consecutive foraging bouts in the same array of flowers. All flower visits (when a bee landed on a flower) were recorded and used to reconstruct the complete foraging history of each bee.

Experiments were conducted in six different arrays, varying in their spatial scale, their number of flowers and the spatial configuration of flowers. Experiments 1, 2 and 4 (Figure 2A,B,D) were completed in flight rooms at small spatial scales and with controlled illumination [START_REF] Lihoreau | Trade-off between travel distance and prioritization of high-reward sites in traplining bumblebees[END_REF]Lihoreau et al., 2012a;[START_REF] Buatois | Evidence of trapline foraging in honeybees[END_REF]. Experiments 3, 5 and 6 (Figure 2C,D,E) were completed in outdoor open fields at small spatial scale for experiment 5 and large spatial scales for experiments 3 and 6 (Lihoreau et al., 2012b;[START_REF] Buatois | Evidence of trapline foraging in honeybees[END_REF]. Details about the spatial arrangement of flowers, the number of bees tested and the numbers of foraging bouts per bee are given in Figure 2.

Network analyses

We built spatial networks of bee foraging movements in which flowers were nodes and movements were edges (Figure 1). Edges weight corresponded to the frequency of movement between flowers.

To describe foraging movements and compare them across experimental conditions and species, we calculated three local network metrics describing the role of each flower in the bee movement network and one global network metric to infer on the efficiency of the network structure.

Local network measures

At a local level, we calculated the "weighted clustering coefficient", which assesses the degree to which nodes tend to cluster together [START_REF] Barrat | The architecture of complex weighted networks[END_REF]. Here a high clustering value indicates that neighbouring flowers of a given flower are themselves highly connected, i.e. frequently re-visited (Figure 1B). We used the "Kleinberg's authority score" [START_REF] Kleinberg | Authoritative sources in a hyperlinked environment[END_REF] to measure the relative importance of a node in a network (Figure 1C). Given A, an individual movement matrix across flowers, the Kleinberg's authority score is defined as the principal eigenvector of the inverted matrix t(A)*A. This metric assigns large values to flowers that are most often used, while accounting for the number of visits to adjacent flowers (i.e. flowers connected by at least one edge). Therefore a high Kleinberg's authority score indicates that a specific flower is more often visited than all its neighbour flowers. This may be the case, for instance, at the early stages of a route development when bees often return to a reference flower from which they explore and attempt to locate new flowers [START_REF] Ohashi | Trapline foraging by bumble bees: IV. Optimization of route geometry in the absence of competition[END_REF][START_REF] Lihoreau | Travel optimization by foraging bumblebees through readjustments of traplines after discovery of new feeding locations[END_REF]2016).

We calculated the "weighted betweenness centrality". This metric reflects the importance of a node as intermediary of the network, based on the number of shortest paths connecting all pairs of nodes that pass through the focal node [START_REF] Opsahl | Structure and evolution of weighted networks[END_REF]. In a bee movement network a high weighted betweenness centrality characterises a flower that is acting as a bridge among multiple other flowers (Figure 1D).

Because our aim was to study general trends of spatial optimization by bees across time at the network level (route efficiency) and not at the node level (role played by individual flowers), for all the local metrics we calculated mean values over all flowers at each foraging bout. Betweenness scores were normalized following an algorithm that weights the betweenness value for the number of flowers visited in the network [START_REF] Freeman | Centrality in social networks conceptual clarification[END_REF]. Authority scores were scaled from 0 to 1. Clustering coefficients vary between 0 and 1 and need no normalization. In these conditions, an optimal network (in which a bee would visit all flowers once and return to the nest by travelling the shortest distance to visit all flowers) and a suboptimal network (in which a bee would travel longer distances for visiting the same amount of flowers) would be characterised by the maximum average betweenness of 0.5, the maximum average authority score of 1, and the minimum average clustering coefficient of 0 (Figure 1E).

Global network measures

At the global level, we examined the triadic structures of the network -i.e. motifs [START_REF] Milo | Network motifs: Simple building blocks of complex networks[END_REF], which represent triadic patterns of connection between nodes in a directed network. Network motifs can be representative of various biological processes such as information flow [START_REF] Nandi | Social insect colony as a biological regulatory system: modelling information flow in dominance networks[END_REF], resource exchange [START_REF] Quevillon | Social, spatial, and temporal organization in a complex insect society[END_REF] or disease spread [START_REF] Waters | Information processing in social insect networks[END_REF]. In a bee movement network the analyses of network motifs might help identifying behavioural rules underpinning trapline formation (Figure 1F) while allowing for unbiased comparison across different datasets (Shizuja & McDonald, 2015). Whereas a detailed temporal network analysis of motifs might be used to better understand the mechanisms of network functionality [START_REF] Kovanen | Temporal motifs in timedependent networks[END_REF], here we used a discrete approach by counting all the 16 possible triadic motifs to connect three flowers (including the nest) observed at each foraging bout and thus not strictly related to the exact temporal sequence of visits on flowers (Figure 1F). For each experiment, we compared the triadic motifs of the observed bee foraging networks at each foraging bout to those of the theoretical optimal network connecting all flowers and the nest using the shortest possible path. Since only two out of the 16 possible triadic motifs (Figure 3A-F) can be observed in the optimal movement network (Figure 1E), these global measures inform us about the overall efficiency of the routes developed by bees.

Data analyses

Local network measures

All analyses were conducted in the statistical environment R (i.e. version 3.2.3). For each foraging bout of each bee we extracted weighted clustering coefficient values, authority scores and weighted betweenness centrality values of each flower, using the functions "clustering_local_w" and "betweenness_w" in the tnet package [START_REF] Opsahl | Structure and evolution of weighted networks[END_REF] and the function "authority.scores" in the igraph package [START_REF] Csardi | The igraph software package for complex network research[END_REF]. We ran three different regression models for weighted betweenness, authority and weighted clustering coefficient values using the sequential number of foraging bouts, type of array (i.e. small or large spatial scale), species (i.e. bumblebee or honeybee) and all the interactions among these predictors as fixed effects. We used individual identity nested in experimental array as a random effect in all models. We carried out model selection for the three different parameters ranking candidate models according to their Akaike Information Criterion [START_REF] Akaike | Prediction and Entropy[END_REF]. We used beta regression for the three averaged local network measures (clustering coefficient, weighted betweenness centrality and authority scores) because their values were constrained between 0 and 1. We also applied a zero inflation method using the Beta Inflated (BEINF) family function from the gamlss package [START_REF] Rigby | Generalized additive models for location, scale and shape[END_REF]. Model selection of the Beta regression mixed models are shown in the supplementary materials (Tables S1, S2 andS3). Because network metrics are correlated, we applied a Bonferroni correction by setting the alpha level of significance at 0.017 [START_REF] Tylianakis | Habitat modification alters the structure of tropical host-parasitoid food webs[END_REF].

Global network measures

Motifs were calculated using the "triad.census" function in the "igraph package" [START_REF] Csardi | The igraph software package for complex network research[END_REF]. Only two out of the 16 possible triadic motifs (motif 2 and 6: Figure 3A-F) are representative of the optimal movement network (Figure 1E). Depending on the number of flowers in the array, motif 1 (triadic structure where the three nodes -A, B, C -have no connection among them, i.e. the empty graph A, B, C) can also occur and being represented for a maximum of 7 times in a network with 7 flowers. Motif 2 (triadic structure with a single connection between the three nodes, i.e. A>B, C) and motif 6 (triadic structure where A>B>C are all connected by two directed lines) of the optimal movement network can also occur at different frequencies depending on the network size (i.e. for 7 flowers: 21 and 7; for 6 flowers: 12, 6; for 5 flowers: 5, 5; as indicated by red horizontal lines in Figure 3). We analysed the tendency of bees to modify their motifs frequency with time by applying a generalized linear mixed effect model for count data (i.e. GLMM with Zero Inflated Poisson distribution error) using the observed frequency for each motif and for each dataset as response variable, the number of foraging bouts as predictor, and individual identity as random effect.

Other measures

To illustrate the benefits of using the network approach relative to more conventional analyses, we also calculated non-network measures used in previous studies for assessing the ability of bees to develop efficient routes [START_REF] Lihoreau | Trade-off between travel distance and prioritization of high-reward sites in traplining bumblebees[END_REF]Lihoreau et al., 2012a;Lihoreau et al., 2012b;[START_REF] Buatois | Evidence of trapline foraging in honeybees[END_REF]. For each foraging bout of each bee we calculated the number of revisits to flowers and the distance travelled (assuming straight lines between flowers) divided by the number of flowers visited. Both measures of route efficiency are expected to decrease with increasing network efficiency, and reach a minimum in an optimal movement network. We applied a GLMM for count data to study the impact of experience (foraging bout) on the number of revisits to flowers and a linear mixed effect model (LMM) for the travelled distance divided by the number of flowers visited. Both models were run for each experiment using individual identity as random effect.

Results

Local network measures

The average weighted betweenness centrality increased as bees accumulated foraging experience in the six experiments (estimatebout = 0.066, standard error (se) = 0.004, t = 17.11, P < 0.001), indicating that individuals tended to visit all flowers at a similar frequency by the end of training (Figure 4). This tendency was stronger in large spatial scale arrays (estimatesmall_array = -0.067, se = 0.005, t = -13.55, P < 0.001). Interestingly, in small spatial scale arrays bumblebees showed higher average weighted betweenness centrality (estimatehoneybees = -1.172, se = 0.164, t = -7.15, P < 0.001) and a tendency to develop optimal networks faster (estimatehoneybees = -0.020, se = 0.008, t = -2.533, P = 0.011) than honeybees (Figure 4).

The average Kleinberg's authority scores also increased as bees accumulated experience in the six experiments (estimatebout = 0.083, se = 0.03, t = 2.781, P = 0.004), meaning that all flowers became equally important in the network. For both bee species, the average authority scores were lower in small spatial scale arrays than in large spatial scale arrays (estimatesmall_arrays = -0.446, se = 0.103, t = -4.334, P < 0.001). However, honeybees had larger average authority scores than bumblebees in the small spatial scale arrays (estimatesmall_arrays_honeybees = 0.582, se = 0.111, t = 5.229, P < 0.001) meaning that they tended to use all possible connections between flowers equally whereas bumblebees only used a few.

The average clustering coefficient tended to decrease with time, as bees accumulated foraging experience (Figure 6). Specifically, bumblebees showed a significant decrease in average clustering coefficient while honeybees maintained stable values throughout the experiments (estimatebout_honeybees= 0.018, se = 0.004, t = 4.185, P < 0.001). Honeybees showed completely different trend at small spatial scales, by increasing their average clustering coefficient scores with experience (estimatehoneybees_small_arrays = 0.407, se = 0.148, t = 2.752, P = 0.006). This again illustrates the much reduced route optimisation efficiency of honeybees in comparison to bumblebees at small spatial scales (Figure 6).

Overall, these changes in all three local network measures were more pronounced at larger spatial scales, where flowers were distant from each other and from the colony nest, both for bumblebees and honeybees (Figures 4, 5 and6).

Global network measures

While bees initially used the 16 possible motifs to link flowers, they gradually reduced the number of motifs to only use two of them by the end of training (motifs 2 and 6), a behaviour that is characteristic of route optimisation (Figure 3). This tendency was less pronounced for honeybees at small spatial scales (Figures 3D and3E). Analyses of the frequency usage of each motif confirmed that honeybees at small spatial scales often presented opposite tendencies than honeybees at large spatial scales or bumblebees at all spatial scales (Figure 3D: motifs 3, 7, 8 and 15; Figure 3E: motifs 4, 5, 10 and 15) (for detailed motifs analysis see Table S4-S9).

Other measures

Conventional statistics for bee movement analyses showed trends towards a general increase in movement efficiency with experience. In all experiments bees decreased the number of revisits to flowers as they accumulated foraging bouts (Table S10). Bees also tended to decrease their travelled distance divided by the number of visited flowers, except in the case of honeybees foraging in small spatial scale arrays (Table S10).

Discussion

Network analyses are increasingly used in behavioural and ecological research, providing a whole new range of metrics to describe and model interactions between individuals and their environment [START_REF] Croft | Exploring animal social networks[END_REF][START_REF] Jeanson | Long-term dynamics in proximity networks in ants[END_REF][START_REF] Pinter-Wollman | The dynamics of animal social networks: Analytical, conceptual, and theoretical advances[END_REF]. In pollination ecology, this approach has proved particularly powerful to describe interactions between plant and pollinator species, for instance using undirected bipartite networks based on field surveys of pollinator abundance (e.g. [START_REF] Fontaine | Functional diversity of plant-pollinator interaction webs enhances the persistence of plant communities[END_REF][START_REF] Bascompte | Plant-animal mutualistic networks: The architecture of biodiversity[END_REF][START_REF] Campbell | A network model for plant-pollinator community assembly[END_REF][START_REF] Burkle | Plant-pollinator interactions over 120 years: Loss of species, co-occurrence, and function[END_REF][START_REF] Coux | Linking species functional roles to their network roles[END_REF]. Here we show how spatial network analyses can be developed to study the movement patterns of individual bees exploiting multiple feeding locations at various spatial and temporal scales in simplified experimental conditions. We argue that this approach may prove particularly helpful to analyse pollinator movements in more complex and ecologically realistic experimental designs and to generate new empirically testable hypotheses for pollination ecology research.

As illustrated above, bee movement patterns can be described in terms of local and global network metrics that change predictably as individuals accumulate foraging experience. For instance, in a simple situation where only one bee exploits a stable array of flowers refilled between each foraging bout, both average betweenness values and average authority scores increased with time. By contrast the average clustering of flowers decreased with time as bees started to develop optimal or suboptimal stable movement networks. This tendency for optimisation of spatial movement networks was also reflected in the dynamics of motif usage, resulting in bees increasing their usage of the only two motifs representative of an optimal foraging route. Interestingly, and in accordance with previous studies (e.g. [START_REF] Saleh | Traplining in bumblebees (Bombus impatiens): a foraging strategy's ontogeny and the importance of spatial reference memory in short-range foraging[END_REF]Lihoreau et al., 2012a;[START_REF] Buatois | Evidence of trapline foraging in honeybees[END_REF], we found that bumblebees and honeybees rarely use optimal spatial networks at small spatial scales, where the cost of using a longer (suboptimal) path may be negligible. By contrast, foragers bees always used optimal spatial networks at large spatial scales, suggesting that they use more complex optimisation movement rules in more costly conditions. These results were confirmed with more conventional statistical approaches (e.g. flower re-visits, travel efficiency), thereby validating our approach.

Importantly, the global network approach, based on motif analyses, brought new insights into the spatial behaviour of bees. For instance the foraging patterns of honeybees were characterised by frequent back and forth movements between flowers (Figure 6D -i The aim of this exploratory study was to introduce spatial network analyses for characterising bee movement patterns using relatively standard metrics. Further developments of this approach will provide a powerful, complementary, analytical tool to conventional behavioural metrics in order to inform researchers about spatial processes that are not captured by other measures. This approach should focus more on global measures of path optimality (e.g. network path length, geodesic distance " [START_REF] Wasserman | Social network analysis: Methods and applications[END_REF] to discriminate these different scenarios. For instance, network triads give new information about specific movement routines that may be repeated within a route but that are hardly detectable with current measures of sequence repeatability [START_REF] Thomson | Trapline foraging by bumble bees: II. Definition and detection from sequence data[END_REF][START_REF] Ayers | Determinism as a statistical metric for ecologically important recurrent behaviors with trapline foraging as a case study[END_REF]. Ultimately, a major challenge for future studies will be to consider the high levels of heterogeneity among flower resources that bees may face in nature, taking into account variation in resource reward quantity and quality, signals, and competition among foragers in addition to spatial constraints of resource locations, in order to extend our approach to field conditions. Experimentally, bumblebees foraging in arrays of artificial flowers providing different nectar rewards face a trade off between maximising their nectar intake rate and minimizing travel distances when developing traplines [START_REF] Lihoreau | Trade-off between travel distance and prioritization of high-reward sites in traplining bumblebees[END_REF]. Analyses on non-averaged local metrics could be used to capture the effect of resource diversity in network formation, and bring new insights into how bees integrate memories of multiple individual flowers in their spatial memory. The Kleinberg's authority score likely informs us about how bees use flowers as reference points relative to neighbouring flowers, perhaps to locate new flowers at the beginning of route formation. The weighted clustering coefficient is a mean to determine the level of connections between sub-groups flowers, a measure that should greatly vary during the process of route optimisation. Other network measures, not used here, may also help understand how bees change their foraging area with experience or in the face of competition (e.g. modularity in [START_REF] Dupont | Spatial structure of an individual-based plant-pollinator network[END_REF].

While some of the predictions tested here may seem rather intuitive, our analysis of bumblebee and honeybee movement patterns in relatively simple foraging conditions aims at illustrating how network statistics could serve future research in field and semi-field conditions. Motif network analyses offer the possibility to statistically compare networks to each other, either for the same individuals at different stages of route formation, or between different individuals, and between different species.

Characterising the spatial foraging strategies of a wider range of pollinators, including wild and managed species is a key challenge of pollination ecology in order to identify and compare the real impact of these species on pollination services [START_REF] Garibaldi | Wild pollinators enhance fruit set of crops regardless of honey bee abundance[END_REF]. For instance, our preliminary analysis suggests that at small spatial scales bumblebees display more efficient spatial movements than honeybees. Bumblebees tended to reach a frequency of each triadic structure that would lead to an optimal foraging network, whereas honeybees often showed the opposite behaviour. A possible explanation is the difference of social life style between these two pollinator species. Honeybees, in contrast to bumblebees, have evolved a unique food recruitment system (the waggle dance) by which successful foragers communicate locational information about food resources to their nestmates upon their return to the hive [START_REF] Frisch | The dance language and orientation of bees[END_REF][START_REF] Dornhaus | Benefits of recruitment in honey bees: effects of ecology and colony size in an individual-based model[END_REF]. These insects may thus invest less in individual sampling and efficient route learning than species lacking the means to communicate foraging locations, such as bumblebees [START_REF] Buatois | Evidence of trapline foraging in honeybees[END_REF]. Another possibility is the difference of typical foraging range between the two species. While bumblebees rarely cover more than three kilometres to exploit floral resources [START_REF] Osborne | Bumblebee flight distances in relation to the forage landscape[END_REF], honeybees can travel more than ten kilometres within a single foraging trip [START_REF] Pahl | Large scale homing in honeybees[END_REF], suggesting that they are better adapted to long flights and could start exhibiting optimisation movement patterns at larger spatial scales than bumblebees. Systematic comparisons of both species across a wider range of spatial scales will be needed to test these hypotheses.

Another key advantage of network analyses is that they allow for working on complete (raw) datasets and thus reduce the risks of arbitrarily discarding important information. In the case of pollinators, such approach may allow identification of specific movement patterns that occur at the early stage of route learning, for instance exploration flights to locate flowers and store them in spatial memory, or exploitation flights to return to familiar locations [START_REF] Woodgate | Life-long radar tracking of bumblebees[END_REF]. Further development of pollinator movement networks may also include detailed dynamic temporal analyses of flower visitation sequences, which might reveal differential effect of the individual experience on the probability to optimize the foraging route. Stochastic agent-based methods [START_REF] Snijders | Introduction to stochastic actor-based models for network dynamics[END_REF] recently applied to animal social networks [START_REF] Boucherie | A longitudinal network analysis of social dynamics in rooks corvus frugilegus: repeated group modifications do not affect social network in captive rooks[END_REF][START_REF] Pasquaretta | Understanding dynamics of information transmission in Drosophila melanogaster using a statistical modeling framework for longitudinal network data (the RSiena package)[END_REF], may also prove useful to integrate rate of change of flower visitation sequences. New metrics could be developed to estimate network efficiency in order to account for the specificity of the structure of bee spatial movement based on individual experience. For instance, the direct integration of probability values based on the spatial distances between flowers will allow for a finer calculation of local network metrics which could be used to characterize the individual learning process and compare the likelihood to obtain an optimal foraging route depending on the early spatial experience of the bee. Explicit consideration of the nest as a specific node in the network, different from flowers, may also bring useful information about bee network dynamics and efficiency.

For all these reasons, we believe that pollinator movement networks constitutes a highly promising conceptual framework for studying plant-pollinator systems from a mechanistic point of view in complement to more conventional behavioural measures. Ultimately, a comprehensive understanding of bee movement patterns between plants may provide new fundamental insights into pollination processes and the genetic structuralism of plant populations. The development of optimal routes by individual bees between particular plants can have important and predictable effects on plant reproduction and inbreeding [START_REF] Ohashi | Trapline foraging by pollinators: Its ontogeny, economics and possible consequences for plants[END_REF]. Advances in DNA pollen analyses (see [START_REF] Clare | The promise of genomics in the study of plant-pollinator interactions[END_REF]and metabarcoding;[START_REF] Pornon | Using metabarcoding to reveal and quantify plant-pollinator interactions[END_REF] now allow identification of flower species visited by individual bees during a given foraging trip. One can readily downscale the approach at an intraspecific level by using pollen DNA and more variable genetic markers (e.g. microsatellite; [START_REF] Arif | Interpretation of electrophoretograms of seven microsatellite loci to determine the genetic diversity of the Arabian Oryx[END_REF] to identify individual plants visited by pollinators and infer patterns of pollen flow within a plant population that can then be verified by paternity analyses using plant progeny genotypes for these markers [START_REF] Bernasconi | Seed paternity in flowering plants: an evolutionary perspective[END_REF]. Coupling these approaches with existing models of bee movements (Lihoreau et al., 2012b;[START_REF] Reynolds | A simple iterative model accurately captures complex trapline formation by bumblebees across spatial scales and flower arrangements[END_REF][START_REF] Becher | BEESCOUT: A model of bee scouting behaviour and a software tool for characterizing nectar/pollen landscapes for BEEHAVE[END_REF] will provide critical information about how the foraging strategies of bees directly influence pollen transfer and plant mating patterns across landscapes, and therefore a better assessment of consequences of bee declines on pollination.

Contribution of the authors

ML designed and conducted the experiments; CP built and analysed the networks; CP, RJ, CA, LC and ML wrote the manuscript. All authors gave final approval for publication. Authors declare no competing interests.

Funding

CP is funded by a grant of the Federal University of Toulouse (IDEX UNITI) to CA, RJ and ML. LC is supported by ERC grant SpaceRadarPollinator. ML is supported by an ANR Jeune Chercheur (ANR-16-CE02-0002-01). (Lihoreau et al., 2012a). B. Experiment 2: bumblebees in the lab [START_REF] Lihoreau | Trade-off between travel distance and prioritization of high-reward sites in traplining bumblebees[END_REF]. C. Experiment 3: bumblebees in the field (Lihoreau et al., 2012b). D. Experiment 4: honeybees in the lab [START_REF] Buatois | Evidence of trapline foraging in honeybees[END_REF]). E. Experiment 5: honeybees in the field [START_REF] Buatois | Evidence of trapline foraging in honeybees[END_REF]. F. Experiment 6: honeybees in the field [START_REF] Buatois | Evidence of trapline foraging in honeybees[END_REF]. Spatial scales are provided for each array (i.e. SMALL or LARGE). Distribution of all possible network triadic motifs across foraging bouts. For each motif, the x-axis represents the temporally ordered foraging bouts. Red horizontal lines indicate the frequency of each motif expected in the optimal network. Best fitted lines obtained from generalized linear models using foraging bouts as predictor and frequency of motif as response variable are shown for each motif along with their standard errors (blue line and shaded grey area). Significant effects of time on the frequency of each motif are highlighted with asterisks.

GLMM estimates, Z-values and P-values for each motif in each experiment are available in Tables S4-S9.

  .e. motifs 7 & 8) and disproportionate usage of specific flowers or local hubs (Figure 6D -i.e. motif 4).

Figure 1 .

 1 Figure 1. Examples of local and global metrics calculated on a bee spatial movement network. Nodes of the network (white circles) represent flowers (F1-F6) and the colony nest (black square). Edge directions indicate individual movements between flowers and the nest. Edge thickness is proportional to the frequency of bee movements from one flower to another (i.e. edge weights). In this hypothetical network, from A to E, the forager tends to increase the number of visited flowers with experience (t0, t0 + 1, t0 + 2, t0 + n) while reducing both the number of revisits to flowers and the time needed to visit all (i.e. network optimization). Examples of local network measures are shown (black arrows): 1) High clustering coefficient calculates the degree to which neighbours of a given node are themselves highly connected; 2) Authority score indicates the existence of highly visited nodes;3) High betweenness centrality value counts the number of shortest paths that pass through a focal node. (F) Hypothetical network illustrating two common network motifs (red arrows) in bee movement data (motifs 3 and 6, see Figure3).

Figure 2 .

 2 Figure 2. Spatial arrangements of the artificial flowers (F1-F6) and the colony nest (black square) in the six experiments under investigation (scale is in meters). Number of bees (n) and foraging bouts (fb) are shown for each experiment. A. Experiment 1: bumblebees in the lab (Lihoreau et al., 2012a). B. Experiment 2: bumblebees in

  Figure 3.

Figure 4 .

 4 Figure 4. Average weighted betweenness centrality values for each individual bee at each foraging bout. Black lines and grey shaded areas represent respectively the best fitted lines and their standard errors obtained from zeroinflated mixed effect models built using foraging bouts as fixed effect and individual identity as random (see details in the methods). Spatial scales are provided for each graph (i.e. SMALL -a,b,d,e -or LARGE -c,f -; see also Figure 2).

  Figure 5.Average authority score values for each individual bee at each foraging bout. Black lines and grey shaded areas represent respectively the best fitted lines and their standard errors obtained from zeroinflated mixed effect models built using foraging bouts as fixed effect and individual identity as random (see details in the methods).Spatial scales are provided for each graph (i.e. SMALL -a,b,d,e -or LARGE -c,f -; see also Figure2).

Average clustering coefficient values for each individual bee at each foraging bout. Black lines and grey shaded areas represent respectively the best fitted lines and their standard errors obtained from zeroinflated mixed effect models built using foraging bouts as fixed effect and individual identity as random (see details in the methods). Spatial scales are provided for each graph (i.e. SMALL -a,b,d,e -or LARGE -c,f -; see also Figure 2).

Foraging bouts Clustering coefficient

Supplementary material legends:


Franck Ulm

Yann Cornaton

Jean-Pierre Djukic

Michael J Chetcuti

Vincent Ritleng

Hydroboration of Alkenes Catalysed by a Nickel N-Heterocyclic Carbene Complex: Reaction and Mechanistic Aspects

Keywords: nickel, hydroboration, alkene, N-heterocyclic carbene, Ni(I) active species

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Introduction

Boronic acid and ester derivatives are important starting materials in molecular synthesis and are well-known partners for classical transformations, such as the Petasis reaction, 1 Chan-Lam coupling, 2 conjugate addition reactions, [START_REF] Berthon-Gelloz | Boronic Acids. Rhodium-and Palladium-Catalyzed Asymmetric Conjugate Addition of Organoboronic Acid[END_REF] and, most impressively, Suzuki-Miyaura cross-couplings, [START_REF] Suzuki | [END_REF] but their traditional production methodology involves a metal-halogen exchange with an organoalkali reagent and trialkylborates, [START_REF] Hall | Boronic Acids. Structures, Properties, and Preparation of Boronic Acid Derivatives: Overview of their Reactions and Applications[END_REF] which is far from being satisfying from an environmental perspective. Subsequently, new methods were developed through the direct borylation of aryl halides, mostly catalysed by Pd. 6 More recent advances have allowed the hydroboration of alkenes, [START_REF] Fu | Transition Metal-Catalyzed Hydroboration of Olefins[END_REF] a reaction which is of great interest since the substrates are readily available and it creates new C-B bonds by the most straightforward and atom-thrifty synthetic route.

The main drawback of this methodology is that it is principally based on noble metals, such as rhodium and iridium. [START_REF] Fu | Transition Metal-Catalyzed Hydroboration of Olefins[END_REF] The decrease in non-renewable natural resources has indeed become a global concern for the future, and precious transition metals, are, just like to fossil fuels, limited and thus strategic resources. This can be monitored by the tremendous increase of their prices over the last decade. New directions for homogeneous catalysis should thus not only address energy issues by developing highly reactive catalysts, but should also favour the use of earth-abundant materials as catalysts.

In this context, complexes based on first-row transition metals, [START_REF] Obligacion | [END_REF] most notably copper, 9 cobalt, 10 iron, 11 and manganese 12 have recently emerged as alternative catalysts for this process. In contrast, although it has shown promise for the hydroboration of alkynes, 13 the 1,4-hydroboration of 1,3-dienes, 14 or more recently for formal hydroborations making use of a diboron reagent with a proton source, 15 there are to our knowledge only three reports of the nickel-catalysed hydroboration of alkenes. 16 The first one involved an activated nickel powder that showed relatively low activity and selectivity. 16a In the two other examples, well-defined nickel(II) pre-catalysts were used, which showed excellent activity and selectivity. Hence, in 1996, Srebnik et al. reported that the half-sandwich triphenylphosphine nickel complex, [Ni(Cp)Cl(PPh3)] (Cp = η 5 -C5H5), catalyses the selective hydroboration of trans-4-octene and styrene with HBPin to give 4-pinacolboryloctane and 1-phenyl-2pinacolborylethane in high yields (Scheme 1, eq. 1). 16b In contrast, Schomaker et al. recently reported that the heteroleptic NHC-phosphine nickel complex, [NiCl2(IMes)(PCy3)] (IMes = 1,3-dimesitylimidazol-2-ylidene), catalyses the Markovnikovselective hydroboration of styrenes with good efficiency in the presence of KOt-Bu (Scheme 1, eq. 2). 16c Remarkably, no dehydroborylation product was observed in both cases, but the reaction scopes were rather limited, and no mechanistic study was carried out. Scheme 1. Previously reported nickel-catalysed hydroboration of alkenes. 16b,c [a] F. Ulm, Prof. M. J. Chetcuti, Prof. V. Ritleng Université de Strasbourg Ecole européenne de Chimie, Polymères et Matériaux CNRS, LIMA UMR 7042 F-67000 Strasbourg, France E-mail: michael.chetcuti@unistra.fr, vritleng@unistra.fr [b] Dr. Y. Cornaton, Dr. J.-P. Djukic Université de Strasbourg CNRS, Institut de Chimie de Strasbourg UMR 7177 F-67000 Strasbourg, France [c] Prof. V. Ritleng Institut Universitaire de France 1 rue Descartes, F-75000 Paris, France Supporting information for this article is given via a link at the end of the document.((Please delete this text if not appropriate))

In parallel, efforts from our group and others towards the diversification of pseudo-trigonal [Ni(η 5 -C5R5)L(NHC)] (+) species and the study of their catalytic activity in a large array of reactions, have allowed their establishment as a highly versatile platform for important organic transformations. 17 Most notably, interesting activities have been obtained for the hydrosilylation of carbonyl 18 and imine 19 derivatives. Thus, the half-sandwich nickel complex, [Ni(Cp)Cl(IMes)] (1a), was shown to efficiently catalyse the hydrosilylation of a vast array of aldehydes, ketones, aldimines and ketimines (over 60 examples!) under mild conditions in the presence of a catalytic amount of sodium borohydride. 18a,19 This precedent, together with (i) the scarcity of nickel-catalysed alkene hydroborations, 16 (ii) the electronic and structural proximity of [Ni(Cp)Cl(PPh3)] and 1a, (iii) the renewed interest in the fascinating chemistry of nickel, 20 and (iv) the necessity to gain a better understanding of its reaction paths in order to be able to tame its reactivity, prompted us to the enter this challenging field with a series of [Ni(Cp † )L(NHC)] (+) complexes (Cp † = Cp, Cp* (η 5 -C5Me5); L = Cl -, NCMe, NHC = IMes, IPr (1,3-bis(2,6-diisopropylphenyl)imidazol-2-ylidene), ICy (1,3-dicyclohexylimidazol-2-ylidene) and to try to unravel the mechanism at play.

Herein, we show that the Cp* complex, [Ni(Cp*)Cl(IMes)] (2a), efficiently catalyses the anti-Markovnikov hydroboration of alkenes with HBCat (catecholborane) in the presence of a catalytic amount of KOt-Bu. Notably, the selectivity can be reversed for some styrene derivatives by using HBPin (pinacolborane) instead of HBCat. A combination of experiments gives some insight to the mechanism. The latter is proposed to go through a Ni(I)/Ni(III) cycle after initial reduction of the nickel(II) precursor by a tert-butoxo-catecholato-borohydride species.

Results and Discussion

Initial studies focussed on the hydroboration of styrene with HBPin in CH2Cl2 at room temperature, conditions under which the complex [Ni(Cp)Cl(PPh3)] (1 mol%) had been reported to quantitatively convert styrene to 1-phenyl-2-pinacolborylethane in 18 h (Scheme 1, eq. 1). 16b Disappointingly however, absolutely no conversion was observed under these conditions with the closely related complexes, 1a and [Ni(Cp)Cl(IPr)] (1b). Intrigued by this negative result, we reinvestigated the reaction with [Ni(Cp)Cl(PPh3)] and were unable to reproduce Srebnik's result.

We thus decided to investigate the reaction in toluene at 60 °C in the presence of 3 mol% of nickel precatalyst and 6 mol% of KOt-Bu. 16c Under these conditions, 1a proved again to be unreactive (Fig. 1). A first hit was observed with 1b with 30% conversion after 18 h and 64% Markovnikov selectivity, but the Cp derivatives proved to be globally poorly reactive, as was also illustrated by the very poor conversion observed with [Ni(Cp)Cl(ICy)] (1c). A net gain of activity was observed with the electron-richer Cp* derivatives, notably with 2a that allowed 75% conversion with a 40:60 anti-Markonikov/Markovnikov (AM/M) ratio. The IPr derivative 2b proved a little less active in this case, with 59% conversion after 18 h, and showed no selectivity. Complex 2a was thus chosen for the optimization study of the reaction conditions (Table 1). The promising result obtained in 15 h at 60 °C (entry 1) prompted us to decrease the temperature to 25 °C. This resulted in a much better selectivity with a AM/M ratio of 26:74, but the conversion decreased to 62 % (entry 2). Running the reaction for 24 h at 25 °C allowed us to almost reach the conversion observed after 15 h at 60 °C (entry 3). Carrying out the same (%) [b] AM/M (%) [b] 1 [a] Reaction conditions: styrene (1.04 mmol), 2a (3 mol%), KOt-Bu (6 mol%) in toluene (2 mL). [b] Conversions and AM/M ratio determined by 1 H NMR spectroscopy with 1,3,5-trimethoxybenzene as an internal standard; average values of at least two runs. [c] Reaction run with NaOt-Bu or LiOt-Bu instead of KOt-Bu. catalysis at 60 °C led to full conversion, but still with a low selectivity (entry 4). Finally, increasing the number of equivalents of HBPin to 2.5 allowed us to observe full conversion as well, but surprisingly with an even better AM/M ratio of 20:80 than at room temperature (entry 5). However, the impossibility, at least in our hands, to cleanly separate the isomers by column chromatography led us to explore the reaction with HBCat. A similar result to HBPin (1.2 equiv.) at 60 °C (entry 1) was observed with HBCat, with 73 % conversion and a 50:50 AM/M ratio after 15 h reaction (entry 6). Increasing the number of equivalents to 1.8 and 2.5 allowed the conversion to reach 83 and 100%, respectively, but with a reverse regioselectivity (entries 7 and 8), as was recently observed with an aryloxy-tethered NHC-Fe(II) catalyst. 21 Indeed, in this case, the linear isomer was the major product, and a 85:15 AM/M ratio was obtained when 2.5 equiv. of HBCat were used (entry 8). In light of the increased selectivity observed at room temperature with 1.2 equiv. of borane (entries 2 and 3), we then decided to check if a similar tendency could be observed in the presence of 2.5 equiv. of borane. The anti-Markovnikov isomer was the sole product formed under these conditions, but the conversion was only 33 % after 15 h (entry 9). Finally, the replacement of potassium tert-butoxide by sodium or lithium tert-butoxide had no consequence on the reaction (entry 10).

With these optimized conditions in hand (2.5 equiv. borane, (%) [b] AM/M (%) [b] Yield (%) H NMR spectroscopy with 1,3,5-trimethoxybenzene as an internal standard; average values of at least two runs. [c] Isolated yield of the AM isomer. [d] [NiCp*(NCMe)(IMes)]PF6 (3a) was used as precatalyst instead of 2a.

toluene, 60 °C, 15 h), we then examined the scope of the hydroboration of alkenes catalysed by 2a with HBCat (Table 2). Electron-neutral and electron-rich styrenes were all fully converted with high linear selectivity (entries 1-5). In the cases of 4-methoxystyrene and 2-methylstyrene, the linear isomer was actually the sole product (entries 3 and5). Electron-poor styrenes were hydroborated with conversions ranging from moderate in the case 4-trifluoromethylstyrene (entry 9) to full with 2-bromo-and 4-fluoro-styrenes (entries 7 and8). With the exception of 2-bromostyrene, which was converted with a poor selectivity, the other substrates all gave good to excellent linear selectivity. In all cases where the branched isomer was formed as a minor product, it decomposed on the silica column, 22 allowing the isolation of the pure AM isomer in yields ranging from 38 % in the case of 4-trifluoromethylstyrene (entry 9) to 86 % for 4-methylstyrene (entry 4). The reaction is not limited to styrenes, and vinylcyclohexane was fully converted to the linear isomer, allowing its isolation with 60 % yield (entry 10). Cisstilbene was also hydroborated with good efficiency (80 %), but the resulting product decomposed on the column (Fig. 2). In addition, a number of substrates performed either poorly or nonselectively. Thus, trans-stilbene and 1-phenylcyclohexene gave no conversion at all, and 1-methylstyrene, 4-cyanostyrene, cinnamyl chloride and 1-heptene [START_REF]A possible explanation for the observation of a mixture of products with 1-heptene may be due alkene chain isomerization[END_REF] gave complicated mixtures despite good to excellent conversions (Fig. 2). As catalysts that can enable different regioselectivities are invaluable for the construction of a diverse set of value-added compounds, [START_REF] Obligacion | [END_REF] we next also briefly investigated the reaction scope with HBPin to check if the observed reversal of selectivity with styrene was general (Table 3). Electron-rich and electron-poor styrenes such as 4-methoxystyrene, 2-bromostyrene and 4trifluoromethylstyrene were also converted to the branched isomer with good to high regioselectivities (entries 2-4). Surprisingly however, 2-and 4-methylstyrene gave the linear isomer quasi-exclusively (entry 5 and 6). Although substrate dependent regioselectivity is observed every now and then, [9][10][11][12] and had, in particular, been noted with the closely related [Ni(Cp)Cl(PPh3)] for styrene and 4-octene (Scheme 1), 16b it is to our knowledge rarely observed within a series of simple styrene derivatives. We therefore did not pursue our substrate scope investigation with HBPin any further. (%) [b] AM/M (%) [b] Yield (%) [a] Reaction conditions: alkene (1.0 mmol), HBPin (2.5 mmol), 2a (3 mol%), KOt-Bu (6 mol%) in toluene (2 mL) at 60 °C for 15 h. [b] Conversions and AM/M ratio determined by 1 H NMR spectroscopy with 1,3,5trimethoxybenzene as an internal standard; average values of at least two runs. [c] Isolated yield of the AM/M mixture. [d] The AM:M ratio was difficult to evaluate due to the possible presence of debromoborylation products. [START_REF] Bheeter | [END_REF] [e] The low isolated yields are due to massive decomposition during the chromatographic purification.

To gain insight to the mechanism, we first checked whether the hydroboration process was the result of a true homogeneous catalysis by conducting the hydroboration of styrene with HBCat in the presence of 190 equivalents of Hg relative to 2a. No inhibition was observed, nor a change of selectivity, and thus a process catalysed by nickel particles is unlikely. 25 Owing to the propensity of nickel to easily access multiple oxidation states, 20 we then checked whether the reaction involves a radical by performing control experiments in the presence of radical scavengers. The addition of 1 equiv. of TEMPO or galvinoxyl (relative to styrene) at t0 completely inhibited the reaction (Scheme 2). Furthermore, the addition of 3 mol% TEMPO limited the conversion to 55 % after 15h reaction, and the addition of 1 equiv. TEMPO after 7 h reaction to 76 % (vs. 100% without radical scavenger). This suggested the presence of radicals not only during the activation phase but during the catalytic cycle itself. This point being established, we then recorded a cyclic voltammogram of the pre-catalyst (1 mM) in CH3CN (0.1 M NBu4PF6). As the latter tended to generate a deposit at the surface of the carbon electrode that altered the reproducibility of the measurements, the electrochemical characterization was carried out with the cationic derivative, [Ni(Cp*)(NCMe)(IMes)]PF6 (3a), of 2a that shows a similar catalytic activity (Table 2,entry 2). At a scan rate of 200 mV.s -1 , a quasi-reversible oxidation process can be observed at E1/2ox = 0.16 V vs. Fc/Fc + (Ep = 154 mV), and a quasi-reversible reduction peak is seen at E1/2red = -1.75 V (Ep = 190 mV) (Fig. 3). By analogy with the electrochemical data reported by Crabtree for the Cp derivative 1a (E1/2ox = 0.03 V and E1/2red = -1.51 V vs. Fc/Fc + , v = 100 mV.s -1 ), 26 these values most likely correspond to Ni(II)/Ni(III) oxidation and Ni(II)/Ni(I) reduction processes, while the irreversible oxidation and reduction peaks observed at -0.25 V and -1.48 V (vs. Fc/Fc + ) potential would correspond to ligand-centred redox processes. Nevertheless, the Cp* ligand has been described 'to act as an electron density buffer', 27 which might mean that neither of these redox processes are purely metal centred, and could explain the counter-intuitive observation of a higher Ni(II)/Ni(III) oxidation potential for 3a with respect to 1a. In parallel, stoichiometric studies were conducted to try to identify reaction intermediates. Thus, we monitored the reaction of 2a with 1 equiv. of HBcat and 1 equiv. of KOt-Bu by 1 H NMR in C6D6 from 253 to 298 K. At 293 K, signals belonging to a Cp*-Ni(IMes) species were unambiguously identified (Fig. 4). Though a little broad, these signals are found at the same chemical shifts as those of 2a, suggesting that most of the starting TEMPO (1 equiv.) at t = 0: < 1% conv. Galvinoxyl (1 equiv.) at t = 0: < 1% conv.

No radical scavenger: 100% conv. TEMPO (3 mol%) at t = 0: 55% conv. TEMPO (1 equiv.) at t = 7 h: 76% conv. complex is unreacted under these conditions. Nevertheless, a singlet observed at 4.47 ppm is assigned to molecular H2. Furthermore, another singlet, observed at -22.9 ppm and present in a ratio of ca. 5% when compared to 2a, is assigned to a nickel-hydride species by analogy with the corresponding signal of [Ni(Cp)H(IMes)]. 18a Albeit to a low extent, this suggests that a reaction has well occurred at the nickel centre. In addition to these observations, the proton of the starting HBCat is only observed in very minor proportions, and the singlet belonging to the tert-butoxide anion has shifted from 1.05 to 1.28 ppm, which corresponds to the shift observed when the latter is reacted with HBCat in the absence of nickel pre-catalyst, and thus suggests that the main reaction occurred between these two species under these conditions.

To gain further insight into this reaction, we next recorded the 11 B NMR spectrum of a 1:1 mixture of HBCat and KOt-Bu in C6D6 at room temperature (Fig. 5). In agreement with the data reported by the groups of S. P. Thomas 28 and T. B. Clark 29 for the reaction of HBPin with NaOt-Bu, several peaks are observed, which can be attributed to BH3 (or more likely to B2H6) at -13.3 ppm, to (t-BuO)BCat at 25.8 ppm, and most importantly to an alkoxo-catecholato-borohydride species, [H(t-BuO)BCat] -( 4), at 8.2 ppm, that has been described to act as a universal reducing agent for a number of iron, cobalt, nickel and manganese complexes in various hydrofunctionalization reactions. 12b, 28,[START_REF] Brown | For relevant borohydride species[END_REF] The addition of this preformed mixture (6 mol%) and HBCat (2.5 equiv.) to 2a (3 mol%), previously solubilized in toluene in the presence of styrene, resulted in a catalytic system that demonstrated similar activity to when 4 is generated in situ (Scheme 3), thus suggesting that this species could also act as the pre-catalyst activator here. We were intrigued by the observation of a strong effervescence at the beginning of each catalytic reaction, i.e.: immediately after the addition of HBCat, and this independently of the presence or absence of styrene (the latter being indifferently added before or after HBCat). So, we next conducted a piezometric study in order to quantify the amount of H2 produced. For that purpose, we used a thermostatically controlled double-walled Schlenk tube that is connected to a pressure transducer, which allows the real-time monitoring of the pressure inside the Schlenk (Fig. S1). 31 Using this experimental set-up, we measured the production of 1 equiv. of H2 per mole of nickel when 83 equiv. HBCat were added to a 1:2 mixture of 2a and KOt-Bu in toluene at room temperature. Similarly, the reaction of 2a with 2 equiv. of KOt-Bu and 2 equiv. of HBCat produced 1 equiv. of H2 per mole of nickel. In contrast, the reaction of 1 equiv. 2a with 1 equiv. KOt-Bu and 1 equiv. of HBCat only produced 0.5 equiv. of H2 per mole of nickel.

In view of these data, we considered the possible implication of the nickel hydride complex [NiCp*H(IMes)] (5a), that would act as the true catalytic precursor 18a and would be reduced with concomitant H2 release to the Ni(I) active species, [NiCp*(IMes)] (6a), whose IPr analogues (Cp and Cp*) have already been isolated 32 and shown to be catalytically competent in Suzuki couplings. 33 To try to validate this possibility, we then prepared 6a by reacting 2a with KC8 (or Na/Hg) in THF at -78 °C (Scheme 4). The generation of 6a was established by 1 H NMR spectroscopy. Two highly deshielded singlets at 107 and 31 ppm, integrating for 15 and 2 protons respectively (Fig. S2), could indeed be assigned to the protons of the Cp* group and of the imidazolylidene ring by comparison with the reported data for [NiCp*(IPr)]. 32 However, despite repeated attempts, we have been unable to isolate it pure due to its high sensitivity. Nevertheless, we still attempted the hydroboration of styrene with HBCat in the presence of impure 6a (3 mol%). 70 % conversion was observed after 15 h at 60 °C, with a 60:40 AM/M ratio (Scheme 5). Despite the reduced performance and selectivity compared to 2a and KOt-Bu, which may be attributed to the presence of impurities, this result, observed in the absence of KOt-Bu, tended to confirm the implication of 6a in the catalytic cycle. From that point on, different mechanisms for the hydroboration of styrene by HBCat catalysed by 6a were then considered. Density functional theory (DFT) computations at the PBE-D3(BJ)/def2-TZVPP level of theory were carried out to discriminate between the different hypothesis that were formulated. For this study, only reaction intermediates (local energy minima) were considered, and no transition state (energy saddle-points) were searched for. Thus, only the thermodynamics of the reactions were studied, with no insight into the kinetics. Reaction Gibbs energies computed at this level of theory are compiled in Table 1 at both temperatures considered in the experimental part of this work, i.e.: at 25 °C and 60 °C.

Two reactions were considered for the formation of the Ni(I) catalyst 6a from the Ni(II) hydride 6a: (i) one where 5a would react with an equivalent of 4, which would act as a reductant, to generate 6a and one equivalent of H2; (ii) the other where two molecules of 5a would react together to generate two equivalents of 6a and one of H2. In these two reactions, both reactants should lose a hydrogen radical. Both of these reactions have been found to be endergonic with the former being largely less favourable than the latter at both 25 °C (ΔrG 0 = 53.66 vs. 13.82 kcal/mol) and 60 °C (ΔrG 0 = 52.38 vs. 13.12 kcal/mol). Examples of reactions similar to the latter have been known for more than 40 years, 34 and even if this reaction is endergonic, the equilibrium should be shifted toward the formation of 6a as a consequence of the law of mass action since H2 mostly escapes the solution as a gas, as observed experimentally.

The first step of the catalytic cycle was initially supposed to be an oxidative addition of 6a to HBCat to generate a Ni(III) intermediate, as CV measurements suggested a Ni(I)/Ni(III) catalytic cycle could be amenable. However, all DFT attempts to optimize such a structure led instead to the "agostic" adduct 7a where the H-B bond of the HBCat attractively interacts with the Ni(I) centre in an exergonic fashion at both 25 °C (ΔrG 0 = -6.77 kcal/mol) and 60 °C (ΔrG 0 = -4.94 kcal.mol). Mapping the spin density of this adduct revealed an important single electron population on the hydrogen involved in the agostic interaction, giving it a strong hydrogen radical character (Fig. S3). From this agostic intermediate, two mechanisms have been considered: (i) a first one where the B-H bond would undergo an homolytic fission to generate a boron radical that will then be captured by the styrene forming a carbon radical and 5a (Scheme 6); or (ii) a second one where an adduct 8a between 7a and a styrene (Fig. S4) would homolytically break the B-H bond and release the same carbon radical as in the previous mechanism and 5a (Scheme 7). In both cases, the carbon radical would then react with 5a to regenerate 6a and yield the final hydroboration product. Figure 6 shows the Gibbs energy profiles for both considered mechanisms of the catalytic cycle, leading to both products (AM and M) at 25 °C and 60 °C. The second step of both these mechanism, the only one by which they differ, is endergonic but the reaction Gibbs energy is more than twofold larger in mechanism 1 than in mechanism 2, at both considered temperatures. The final product AM is predicted to be more stable than its regioisomer M, in agreement with the experimental results. The difference of stability between AM and Scheme 6. Proposed catalytic mechanism 1 (outer-sphere transfer), through the release of a boron radical. generate the corresponding nickel hydride species 5a, possibly through a σ-bond metathesis mechanism, which contrasts with the commonly proposed formation of a putative nickel alkoxide intermediate that would then react with the borane 16c (or silane 18b35 ) to generate the Ni(II) hydride intermediate. Then, in an initiation step, two 5a could react together to generate the catalytically active Ni(I) species 6a (Scheme 8). 36 The latter would then form an "agostic" intermediate 7a, where the B-H bond of the borane interacts with the Ni(I). Styrene would then form an adduct 8a with 7a before homolytically breaking the B-H bond, hence regenerating 5a and releasing a carbon radical. This carbon radical would finally react with 5a, to yield the hydroboration product and regenerating 6a (Scheme 7). Importantly, this mechanism is in agreement with our previous observation, in the related hydrosilylation reaction of carbonyl derivatives catalysed by 1a, 18a where we noted that although a Ni(II)-H species is most probably the true catalytic precursor, there is no insertion of the C=O or C=C double bond into this Ni(II)-H bond.

Conclusions

In conclusion, we have shown that the [NiCp*Cl(IMes)] complex 2a is an efficient precatalyst for the hydroboration of alkenes in the presence of a catalytic amount of KOt-Bu. With HBCat, about ten styrene derivatives and vinylcyclohexane have been converted to the linear product with yields ranging from moderate to very good depending on the substrate. The use of HBPin instead of HBCat allowed to obtain the branched product as the major one in the cases of styrene, 4trifluoromethylstyrene and 4-methoxystyrene.

Mechanistic studies strongly suggest the initial generation of a the nickel-hydride complex 5a by reaction of 2a with the in situ formed tert-butoxo-catecholato-borohydride species [H(t-BuO)BCat] -(4), as evidenced by 1 H and 11 B NMR spectroscopy. Two molecules of the latter would then react together to generate two equivalents of the Ni(I) species 6a and one equivalent of H2, as suggested by combined experimental and theoretical studies. The latter would then act as the active species through a catalytic cycle involving an agostic intermediate 7a and a styrene adduct 8a that would homolytically break the B-H bond of the borane. These unprecedented studies with only the fourth nickel hydroboration catalyst reported to date 16 shed light both on the potential of nickel as another base metal for this important transformation, and on the fact that appropriately designed nickel(I) species may be an interesting lead for future research in this domain.

Experimental Section

General comments

All reactions were carried out using a glovebox or standard Schlenk techniques under an atmosphere of dry argon. Solvents were distilled from appropriate drying agents under argon. Unless otherwise specified, solution NMR spectra were recorded at 298 K on Bruker Avance I 300 MHz, or Bruker Avance III HD 400 MHz spectrometers operating at 300.13 or 400.13 MHz for 1 H, at 75.47 or 100.61 MHz for 13 C and at 96.29 or 128.38 MHz for 11 B. The chemical shifts are referenced to the residual deuterated or 13 C solvent peaks. Chemical shifts (δ) and coupling constants (J) are expressed in ppm and Hz respectively. The catalyst precursors 1a, 37 1b, 17b 1c, 38 2a, 39 2b, 39 and 3a 17f were prepared according to published procedures.

General procedure for the hydroboration of alkenes

In an oven dried Schlenk tube were added 2a (17 mg, 0.0318 mmol, 3 mol%), KOt-Bu (7 mg, 0.0624 mmol, 6 mol%), and toluene (2 mL), containing the internal standard (trimethoxybenzene, 0.6 mg/mL). This was followed by the addition of HBCat (0.266 mL, 2.50 mmol, 2.5 equiv.) or HBPin (0.363 mL, 2.50 mmol, 2.5 equiv.) and of the desired alkene (1.00 mmol, 1 equiv.). The resulting reaction mixture was stirred in a preheated oil bath at 60 °C for 15 h. The solution was then cooled to room temperature and an aliquot of the mixture was removed by syringe in order to determine the conversion and the isomeric ratio by 1 H NMR spectroscopy. The rest of the solution was filtered through a plug of silica that was washed with CH2Cl2. The resulting filtrate was dried under high vacuum to give a pale orange solid (with HBCat) or a pale yellow oil (with HBPin). The purification procedure was performed rapidly because of the fast degradation of the desired products, especially with HBCat. 22 The branched isomer, in particular, was found to be very unstable upon filtration over the silica plug, allowing the isolation of the pure linear isomer with HBCat and generating (in some cases) an increase of the linear/branched ratio with HBPin.

Synthesis of [NiCp*(IMes)] (6a)

In a glovebox, a Schlenk tube was charged with a stirring bar and 2a (300 mg, 0.562 mmol). The Schlenk tube was then laid in a horizontal position in order to introduce sparkling orange shavings of KC8 (84 mg, 0.621 mmol) without touching the purple powder. In this position, the Schlenk tube was closed and taken out of the glovebox. 2a was then dissolved in THF without touching KC8 (10 mL). While putting the Schlenk tube in a vertical position, the system was plunged into a bath at -78 °C. The temperature was allowed to slowly increase to room temperature and the heterogeneous purple medium was stirred for 4 days. After this time, the resulting dark yellow suspension was filtered through a thin pad of Celite under argon and the filtrate was concentrated under vacuum. The resulting brown powder was dissolved in a small amount of pentane and stored at -28 °C overnight. The mother liquor was removed with a syringe to yield 6a as a shining yellow-brown powder (234 mg, 0.470 mmol, 84 %) that was dried under high vacuum. 1 H NMR (C6D6,400.13 MHz): δ 107.31 (s v.br.,15H,C5Me5),30.95 (s br.,2H,NCH),5.29 (s br.,4H,3.57 (s,6H,2.21 (s,6H,, 1.42 (s, 6H, o-Me).

Control experiments

Investigation of the mercury effect: An oven dried Schlenk tube was charged with 2a (17 mg, 0.0318 mmol, 3 mol%), KOt-Bu (7 mg, 0.0624 mmol, 6 mol%), and toluene (2 mL), containing the internal standard (trimethoxybenzene, 0.6 mg/mL). This was followed by the addition of Hg (1.2 g, 5.98 mmol, 188 equiv.), HBCat (0.266 mL, 2.50 mmol, 2.5 equiv.), and styrene (0.115 mL, 1.00 mmol, 1 equiv.). The resulting reaction mixture was stirred in a preheated oil bath at 60 °C for 15 h. The solution was then cooled to room temperature and an aliquot of the mixture was removed by syringe in order to determine the conversion and the isomeric ratio by 1 H NMR spectroscopy. A conversion of 100 % with a 90:10 AM/M ratio was observed.

Investigation of the radical scavenger effect: An oven dried Schlenk tube was charged with 2a (17 mg, 0.0318 mmol, 3 mol%), KOt-Bu (7 mg, 0.0624 mmol, 6 mol%), and toluene (2 mL), containing the internal standard (trimethoxybenzene, 0.6 mg/mL). This was followed by the addition of HBCat (0.266 mL, 2.50 mmol, 2.5 equiv.), styrene (0.115 mL, 1.00 mmol, 1 equiv.) and TEMPO (156 mg, 1.00 mmol, 1 equiv. (at t = 0 or 7 h) or 5 mg, 0.0320 mmol, 3 mol%) or galvinoxyl (422 mg, 1.00 mmol, 1 equiv.). The resulting reaction mixture was stirred in a preheated oil bath at 60 °C for 15 h. The solution was then cooled to room temperature and an aliquot of the mixture was removed by syringe in order to determine the conversion by 1 H NMR spectroscopy. Complete inhibition of the reaction was observed when 1. 0 equiv. TEMPO or galvinoxyl was added at t = 0 h. 55% conversion was observed when 3 mol% TEMPO was added at t = 0 h. 76% conversion was observed when 1.0 equiv. TEMPO was added at t = 7h.

1 H NMR follow-up of a 1:1:1 mixture of 2a/HBCat/KOt-Bu: An oven dried Schlenk tube was charged with 2a (32 mg, 0.0599 mmol), KOt-Bu (7 mg, 0.0624 mmol) and freeze-pump-thaw degassed C6D6 (2 mL). The resulting mixture was cooled -25 °C before the addition of HBCat (6.4 μL, 0.0598 mmol). The reaction mixture was then vigorously stirred for several seconds prior to the transfer of an aliquot of 0.6 mL into an NMR tube placed in a bath at -25 °C. 1 H NMR spectra were then recorded from 253 to 298 K.

11

B NMR analysis of a 1:1 mixture of HBCat/KOt-Bu: An oven dried Schlenk tube was charged with KOt-Bu (42 mg, 0.375 mmol) and freezepump-thaw degassed C6D6 (2 mL). The resulting mixture was cooled -25 °C before the addition of HBCat (40 μL, 0.375 mmol). The reaction mixture was then vigorously stirred for several seconds prior to the transfer of an aliquot of 0.6 mL into an NMR tube placed in a bath at -25 °C. 11 B NMR spectra were then recorded from 253 to 298 K.

Hydroboration of styrene catalysed by 2a with 4:

To an oven dried Schlenk tube were added HBCat (0.266 mL, 2.50 mmol, 2.5 equiv.) and KOt-Bu (7 mg, 0.0624 mmol, 6 mol%) in toluene (2 mL), containing the internal standard (trimethoxybenzene, 0.6 mg/mL) in order to form 4. This mixture was stirred for 5 min at room temperature before adding 2a (17 mg, 0.0318 mmol, 3 mol%) and styrene (0.115 mL, 1.00 mmol). The resulting reaction mixture was then stirred in a preheated oil bath at 60 °C for 15 h. The solution was finally cooled to room temperature and an aliquot of the mixture was removed by syringe in order to determine the conversion and the isomeric ratio by 1 H NMR spectroscopy. A conversion of 100 % with a 89:11 AM/M ratio was observed.

Hydroboration of styrene catalysed by 6a:

In an oven dried Schlenk tube were added 6a (15 mg, 0,0301 mmol, 3 mol%) and toluene (2 mL), containing the internal standard (trimethoxybenzene, 0.6 mg/mL). This was followed by the addition of HBCat (0.266 mL, 2.50 mmol, 2.5 equiv.) and styrene (0.115 mL, 1.00 mmol, 1 equiv.). The resulting reaction mixture was stirred in a preheated oil bath at 60 °C for 15 h. The solution was then cooled to room temperature and an aliquot of the mixture was removed by syringe in order to determine the conversion and the isomeric ratio by 1 H NMR spectroscopy. A conversion of 70 % with a 60:40 AM/M ratio was observed.

Cyclic voltammetry

The cyclic voltammogram of complex 3a (1 mM in CH3CN) was recorded with a Voltalab 50 potentiostat/galvanostat (Radiometer Analytical MDE150 polarographic stand, PST050 analytical voltammetry and CTV101 speed control unit) controlled by the Voltamaster 4 software. A conventional three-electrode cell (10 cm 3 ) was used in our experiments with a glassy carbon disk (s = 0.07 cm 2 ) set into a Teflon rotating tube as a working electrode, a Pt wire as a counter electrode, and a KCl (3 M)/Ag/AgCl reference electrode (+210 mV vs. NHE). Prior to each measurement, the surface of the glassy carbon electrode was carefully polished with 0.3 m aluminum oxide suspension (Escil) on a silicon carbide abrasive sheet of grit 800/2400. Thereafter, the glassy carbon electrode was copiously washed with water and dried with paper towel and argon gas. The electrode was installed into the voltammetry cell along with a platinum wire counter electrode and the reference electrode. The 1 mM solution of 3a was vigorously stirred and purged with O2-free (Sigma Oxiclear cartridge) Ar for 15 min before the voltammetry experiment was initiated, and maintained under an Ar atmosphere during the measurement procedure. The voltammogram was recorded at 23(1) °C with 0.1 M NBu4PF6 as supporting and inert electrolyte. The voltage sweep rate was set at 200 mV.s -1 , and the cyclic voltammogram was recorded from +0.5 V to -2.2 V vs. Fc/Fc + .

Piezometric studies 31

2a, KOt-Bu and toluene were introduced in a double-walled Schlenk vessel of 28 mL, thermostated at 20 °C under Ar. After the resulting mixture was stirred for a few minutes, a Mykrolis A332984-007 absolute pressure-to-voltage transducer was air-tightly screwed to the neck of the glass vessel and connected to a Pico-Log analog-logic converter/datalogger board interfaced to a computer. This allowed the measurement of the pressure of hydrogen (computed from a linear absolute pressure-output voltage relationship) developed in the known overhead volume of the sealed reactor as a function of time. The absence of leaks was preliminarily checked by applying a moderate pressure of argon gas. HBCat was swiftly injected into the vessel via a lateral glass valve, which was tightly closed immediately upon injection to avoid gas leaks. Several experiments have been performed with varying amounts of reagents: (i) 2a (48 mg, 0.0899 mmol), KOt-Bu (20 mg, 0.178 mmol, 2 equiv.) and HBCat (0.799 mL, 7.496 mmol, 83 equiv.) in toluene (6 mL); (ii) 2a (144 mg, 0.270 mmol), KOt-Bu (61 mg, 0.544 mmol, 2 equiv.) and HBCat (60 μL, 0.563 mmol, 2 equiv.) in toluene (12 mL); (iii) 2a (144 mg, 0.270 mmol), KOt-Bu (30 mg, 0.267 mmol) and HBCat (29 μL, 0.272 mmol) in toluene (12 mL).

Computational details

Geometry optimizations of the different species thought to be involved in the reaction mechanism were performed at the density functional theory (DFT) level of theory, using the ORCA program system 40 version 4.2.0. The Perdew-Burke-Ernzerhof (PBE) functional 41 augmented with Grimme's D3 dispersion correction with a Becke-Johnson (BJ) damping function 42 was used for all calculations. All computations were carried out using Karlsruhe's second-generation default triple-ζ valence with two sets of polarization functions (def2-TZVPP) basis set 43 . Solvent effects were accounted for in all computations by using the conductor-like polarizable continuum model (CPCM), 44 simulating toluene (ε=2.4, n=1.497) as a solvent. Geometry optimizations by the quasi Newton update procedure with the BFGS update were carried out in all cases with integration grid accuracy 5 to 7, an energy gradient convergence criterion of 10 -4 Eh/a0, and a tight SCF convergence criterion. All thermodynamic data have been evaluated at 298.15 K and 333.15 K. 3D molecular structures and isosurfaces were produced using Jmol.

FULL PAPER

Entry for the

Figure 1 .

 1 Figure 1. Pre-catalysts' screening for the hydroboration of styrene with HBPin.

Figure 2 .

 2 Figure 2.Substrates that performed either poorly or non-selectively with HBCat or that gave a product that decomposed.

Scheme 2 .

 2 Scheme 2. Effect of radical inhibitors.

Figure 3 .

 3 Figure 3. Cyclic voltammogram of 3a: 1 mM 3a in a 0.1 M NBu4PF6 solution in CH3CN with a glassy C working electrode, a Pt wire counter electrode, and a Ag/AgCl, KCl 3 M reference electrode. Referenced to a 2mM Fc/Fc + external standard: E1/2 = 0.48 V vs. AgAgCl, KCl 3 M. Scan rate = 200 mV.s -1.

Figure 4 .

 4 Figure 4.

1 H

 1 NMR (C6D6, 293 K) spectrum of a 2a / HBCat / KOt-Bu (1:1:1) mixture.

  Figure 5. 11 B NMR (C6D6, 298 K) spectrum of a HBCat / KOt-Bu (1:1) mixture.

Scheme 3 .

 3 Scheme 3. Addition of preformed 4 to a catalytic reaction mixture.

Scheme 4 .Scheme 5 .

 45 Scheme 4. Synthesis of 6a.

Scheme 7 .Figure 6 .

 76 Scheme 7. Proposed catalytic mechanism 2 (inner-sphere transfer), through the formation of the adduct 8a.

Scheme 8 .

 8 Scheme 8. Proposed mechanism for the generation of the Ni(I) active species 6a.

  the air-stable Ni(II) precursor [NiCp*Cl(IMes)] to the [Ni(I)Cp*(IMes)] active species provides an efficient catalyst for the regioselective hydroboration of alkenes.FranckUlm, Yann Cornaton Jean-Pierre Djukic, Michael J. Chetcuti,

Table 1 .

 1 Hydroboration of styrene with HBPin or HBCat catalysed by 2a

	Entry	Borane	Temp.	Time	Conv.
		(equiv.)	(°C)	(h)

Table 2 .

 2 Hydroboration of alkenes with HBCat catalysed by 2a

	[a]

Table 3 .

 3 Hydroboration of styrenes with HBPin catalysed by 2a

	[a]

Table 4 .

 4 Reaction Gibbs energies computed at the PBE-D3(BJ)/def2-TZVPP level of theory

	Reaction			ΔrG 0 at 25 °C	ΔrG 0 at 60 °C
						(kcal/mol)	(kcal/mol)
	5a + HBCatOt-Bu -→ 6a + BCatOt-Bu •-	53.66	52.38
					+ H2
	5a → 6a + ½ H2	13.82	13.12
	6a + HBcat →7a	-6.77	-4.94
	7a → 5a + Bcat •	43.85	42.14
	7a + styrene → 8a	17.80	19.74
	Bcat	• + styrene → AM	•	-41.96	-40.29
	Bcat	• + styrene → M	•	-26.72	-25.08
	8a → 5a + AM	•	-14.84	-16.79
	8a → 5a + M	•		0.40	-1.58
	AM	• + 5a → 6a + AM	-12.82	-12.95
	M • + 5a → 6a + M	-24.77	-24.87

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Acknowledgements

MJC and VR are grateful to the Université de Strasbourg and the CNRS for their financial help. The Institut Universitaire de

. YC and JPD thank the Centre de Calcul de l'Université de Strasbourg for providing access to the HPC facilities for the computational part of this work.