Helen Metcalfe
email: helen.metcalfe@rothamsted.ac.uk

Jana Bürger

Christoph Von Redwitz

Alicia Cirujeda

Silvia Fogliatto

Denise F Dostatny

Bärbel Gerowitt

| Michael Glemnitz

José L González-Andújar

| Eva

Hernández Plaza

Jordi Izquierdo

Michaela Kolářová

Jevgenija Ņečajeva

Sandrine Petit

Gyula Pinke

Matthias Schumacher

| Lena Ulber

Francesco Vidotto

Guillaume Fried

The utility of the 'Arable Weeds and Management in Europe' database: Challenges and opportunities of combining weed survey data at a European scale

published or not. The documents may come

three case studies repeating previously published national scale analyses with data from a larger spatial extent. The case studies, originally done in France, Germany and the UK, explore various aspects of weed ecology (community composition, management and environmental effects and within-field distributions) and use a range of statistical techniques (canonical correspondence analysis, redundancy analysis and generalised linear mixed models) to demonstrate the utility and versatility of the AWME database. We demonstrate that (i) the standardisation of abundance data to a common measure, before the analysis of the combined dataset, has little impact on the outcome of the analyses, (ii) the increased extent of environmental or management gradients allows for greater confidence in conclusions and (iii) the main conclusions of analyses done at different spatial scales remain consistent. These case studies demonstrate the utility of a

Europe-wide weed survey database, for clarifying or extending results obtained from studies at smaller scales. This Europe-wide data collection offers many more opportunities for analysis that could not be addressed in smaller datasets; including questions about the effects of climate change, macro-ecological and biogeographical issues related to weed diversity as well as the dominance or rarity of specific weeds in Europe.

K E Y W O R D S
abundance measures, arable plants, cover estimates, data collection, management, nomenclature, plot size, sampling bias, weed community, weeds

| INTRODUCTION

Weed vegetation surveys are commonly used in weed science to assess the impacts of agricultural practices on weed flora (e.g., [START_REF] Pinke | The influence of environment, management and site context on species composition of summer arable weed vegetation in Hungary[END_REF], determine causes of yield losses (e.g., [START_REF] Adeux | Mitigating crop yield losses through weed diversity[END_REF], monitor conservation efforts (e.g., [START_REF] Kolářová | Impact of site conditions and farming practices on the occurrence of rare and endangered weeds on arable land in The Czech Republic[END_REF] and map species distributions (e.g., [START_REF] Hanzlik | Occurrence and distribution of important weed species in German winter oilseed rape fields[END_REF]. Many surveys are designed for a particular purpose and so the collected data, and associated metadata, are specific to the particular research question. As such, the resulting local databases can contain different methodologies and data types [START_REF] Bürger | Two sides of one medal: arable weed vegetation of Europe in agronomical weed surveys compared to phytosociological data[END_REF]. Despite such discrepancies, there is potential for added benefits when surveys are analysed in combination, as demonstrated by the success of several plot-vegetation databases (e.g., European Vegetation Archive [EVA] [START_REF] Chytrý | European Vegetation Archive (EVA): an integrated database of European vegetation plots[END_REF],

European Weed Vegetation Database [START_REF] Küzmič | European Weed Vegetation Databasea gap-focused vegetation-plot database[END_REF]). The Arable Weeds and Management in Europe (AWME) database [START_REF] Bürger | Arable Weeds and Management in Europe[END_REF] provides a new resource for combining arable weed survey data and complementary management information from across Europe.

The value of combining data or findings from multiple studies is clear, as illustrated by several meta-analyses aiming at improving our understanding of the response of weed communities to drivers of change (e.g., [START_REF] Gu | Annual intercropping suppresses weeds: a meta-analysis[END_REF][START_REF] Richner | Reviewing change in the arable flora of Europe: a meta-analysis[END_REF]. Meta-analyses use previously published results to understand the net effect of a specific driver on weed community response. However, the utility of this approach is limited by the accessibility of published statistical results and appropriate measures of confidence in published articles. There is, therefore, scope to provide more robust analyses by returning to the raw data, as demonstrated by the success of similar data collections in adjacent scientific disciplines (e.g., CESTES database [START_REF] Jeliazkov | A global database for metacommunity ecology, integrating species, traits, environment and space[END_REF], which is dedicated to analyses at the metacommunity level including species traits). However, the key challenges facing analysts using the AWME database (Table 1) has not been widely explored.

Here, we will explore the utility of the AWME data collection using three case studies. In each case study, we will focus on an analysis previously published using data from a national scale weed survey (each of which is a component dataset within the AWME database).

Each of the original studies posed a different question about weed communities and their ecology. Using a three-stage process we will determine whether (a) the data contained within AWME allow this question to be addressed at the European scale, (b) it is possible to overcome key challenges associated with analysing data gathered for different purposes and (c) the conclusions of the original publication and our reanalysis remain consistent across scales. Through this work, we aim to examine the utility of the AWME data collection for

European scale analysis and guide future analysts in the best practice for using the AWME data collection to avoid key challenges associated with data collections of this kind.

| MATERIALS AND METHODS

| The AWME database

In 2019, the working group Weeds and Biodiversity of the European Weed Research Society set out to form a data collection of primary arable weed vegetation records. The resulting AWME [START_REF] Bürger | Arable Weeds and Management in Europe[END_REF] database currently comprises 36 surveys of arable weed vegetation conducted between 1996 and 2018 across 12 countries (Tables S1 andS2) and contains >40 000 observations of weed vegetation. The unifying feature of these records is that each consists of a list of species found on a plot of a specific size from an arable field or its margin. Observations are complemented by metadata including the survey date and geographic coordinates. The distinguishing feature of the AWME database (from other collections such as EVA) is that observations are supplemented with information on the agricultural management of the survey site, making the data more useful to agronomists and weed scientists seeking to understand the impact of agricultural practices on weed communities. These agricultural T A B L E 1 Key challenges associated with the analysis of data coming from multiple weed vegetation surveys and potential solutions that are incorporated within the Arable Weeds and Management database and our analyses. (vi) Disparity in plot size between surveys

Plot sizes vary according to the purpose of the survey, and available resources. Observations on larger plots will likely have higher species richness, and the co-occurrence of species may depend on plot size [START_REF] Chytrý | Plot sizes used for phytosociological sampling of European vegetation[END_REF].

Information about survey methodology and plot size are included within AWME so that the user may make an informed decision as to which approach best suits their needs.

Retained all plot sizes in analysis (FR and DE) as previous work has shown that analysing data from varying plot sizes does not introduce strong bias [START_REF] Peterka | Is variable plot size a serious constraint in broad-scale vegetation studies? A case study on fens[END_REF]) Accounted for differences between surveys (not just plot size) by including the survey as a random effect (UK).

management data include information on crop, previous crops and rotations, tillage or weed control treatments. The 36 included weed surveys were conducted using different combinations of sampling design and methodology with varying levels of complexity. Whilst some studies had a narrow focus on a single crop, study region, or growing season, other studies were designed at a national scale sampling many crops and/or growing seasons. Different surveys focussed on distinct parts of the field, for example, to study edge effects or to compare plots with and without herbicide treatments. Most of the surveys in AWME were done just before crop harvest, when most weed species were mature, however others focussed on earlier crop growth stages concentrating on significant time points for weed management decision-making. Various abundance measures (e.g., counts, cover) were used to record species occurrence. These differences between surveys give rise to several key challenges for analysis. Many of these are addressed directly within AWME, whilst others were important to consider during our analyses (Table 1).

| The case studies

We selected three case studies where analyses had previously been [START_REF] Heard | Weeds in fields with contrasting conventional and genetically modified herbicide-tolerant crops. I. Effects on abundance and diversity[END_REF] to study the effect of landscape features, environment and management on weed diversity and abundance in arable fields.

| Analysis

To recreate the case studies, we kept the analytical methods as true to each of the original publications as possible.

We used canonical correspondence analyses (CCA; ter [START_REF] Ter Braak | Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis[END_REF] for the FR case study. Following Lososová et al.

(2004), we tested for gross and net effects of each explanatory variable on weed species composition. The explanatory variable considered were latitude ( N), longitude ( E), mean annual temperature ( C), annual precipitation (mm), soil pH, crop type, previous crop, herbicide treatment (presence/absence), position in the field (core/edge), sampling season and year of sampling. Separate CCAs with a single explanatory variable were used to test gross effects.

The effect of a particular variable after partitioning out the effect shared with the other explanatory variables (i.e., net effect) was tested using partial CCAs (pCCA), each with a single explanatory variable and the other 10 (9) variables used as covariates (see Step 1 below for details of explanatory variables). Significances were tested by 1000 permutation tests. We used the ratio of a particular canonical eigenvalue over the sum of all eigenvalues (total inertia) as a measure of the proportion of variation explained by each factor. We used the cca() function from the vegan package in R [START_REF] Oksanen | LUCAS Soil, the largest expandable soil dataset for Europe: a review[END_REF] to calculate the CCA.

In the DE case study, we compare the combined effect of three groups of variables on weed species composition in the DE case. We [START_REF] Legendre | Studying beta diversity: ecological variation partitioning by multiple regression and canonical analysis[END_REF]. Similar to the approach for the FR case, variance partitioning calculates gross and net effects.

separated
In this case, gross effect was calculated by using all variables of a group and the net effect by using the variables of the other groups of covariates. Each of the groups were formed by different explanatory variables. For the variation partitioning, we used Hellinger transformation to avoid horseshoe effects and to reduce the weight of rare species [START_REF] Legendre | Ecologically meaningful transformations for ordination of species data[END_REF]. We used 500 permutations of the analysis to test for significance. In the data from AWME, there were some correlations between environmental variables. However, to keep the analysis as similar as possible to the original study we opted to retain all variables in our analyses. We used the vegan package in R [START_REF] Oksanen | LUCAS Soil, the largest expandable soil dataset for Europe: a review[END_REF] to calculate the RDA and the variance partitioning respectively.

In contrast to the multivariate analyses in the FR and DE case studies, we used generalised linear mixed effects models (GLMMs) in the UK case study to investigate the effect of crop, herbicide treatment (presence/absence) and position in field (core/edge) on weed species richness and abundance. Species richness and weed abundance (obtained using count data) were assumed to follow a Poisson distribution and the rescaled data (see Table 1) were assumed to follow a normal distribution. We used the canonical link function (natural logarithm for Poisson responses, identity for normal responses). We estimated the dispersion parameter to account for over and under dispersion. We considered the following terms in the fixed effects model: position in field (core/edge), crop type, herbicide treatment (presence/absence). We also included the second and third-order interactions between these fixed effects. Terms were selected using backwards elimination according to the largest p-value given by an approximate F-test when that term was dropped [START_REF] Kenward | Small sample inference for fixed effects from restricted maximum likelihood[END_REF]. The final predictive model was chosen when all remaining terms gave significant values (p ≤ 0.05) for an F test when dropped from the model. All statistical analyses were done using R (R Core Team, 2022), the GLMMs were fitted using Genstat [START_REF] Payne | The guide to GenStat release 16-part 2: statistics[END_REF] to correspond with the original publication.

To address our aims objectively, we took a three-step approach to separate the effect of any data transformations and changes in scale.

| Step 1: Reframing the scope

To address some of the challenges associated with combining disparate datasets several of the variables used in the original studies have been consolidated or simplified within AWME (Table 1) as such it was necessary to redefine the scope of each of our case studies and repeat the analysis from the original publications using only the original data in the form as it is contained within AWME. This gave us a baseline result within the original spatial extent and before any additional data transformations.

In

Step 1 of case study FR, we redefined the scope of the analysis to include only 11 of the original 14 explanatory variables analysed by In their original study, which is the focus of our UK case study, [START_REF] Metcalfe | The contribution of spatial mass effects to plant diversity in arable fields[END_REF] did repeated analyses on datasets from the same fields before and after herbicide application. However, datasets of this kind are rare in AWME and so we redefined the scope of the analysis to instead include herbicide treatment (presence/absence) as an explanatory variable. We also included crop type and field part (core/ edge; in the original publication this was a continuous variable representing transects with samples at various distances from the edge).

| Step 2: Transforming the response variables

To address some of the key challenges identified in Table 1 it was necessary to transform our response variables to allow compatibility across the different survey data sets. Here, we trialled three different approaches: For FR and DE, we transformed all data to presence/ absence and the [START_REF] Barralis | Méthode d'étude des groupements adventices des cultures annuelles: application à la Côte d'Or[END_REF] scale respectively (the six Barralis classes: '+', '1', '2', '3', '4' and '5' represented 0.0005, 0.5, 1.5, 11.5, 35.5 and 75.5 individuals/m 2 respectively). Whilst for the UK case study, we standardised the response variable within each survey data set to have zero mean and unit variance. We repeated the statistical analyses with the transformed response variables, again using only the data from within the original spatial extent. This step allowed us to understand better the robustness of any transformations or changes in analysis made to address the differences in abundance measure.

| Step 3: Scaling up to the European scale

In Step 3, we again repeated each analysis with the transformed response variable used in Step 2 but at a wider spatial extent incorporating all relevant data from AWME from across Europe (Figure 1).

This final stage allowed us to assess whether the changes introduced in the previous two steps leave sufficient remaining records to make data analysis possible at a continental scale and to better understand whether results obtained from analyses at a national scale are truly representative of universal concepts within weed ecology.

We avoided the issue of spatial biases in the FR case study by randomly selecting one observation from fields with multiple records across all three steps of our analysis. To account for potential spatial bias (Table 1) in the European scale analysis of the other two case studies, we additionally trialled a spatial subsampling procedure (DE, see Figure S1) and fitting variograms to the response variable to test for spatial autocorrelation (UK), however, these were found to be unnecessary and so the results are not presented here.

| RESULTS

In our FR case study, crop type was the top-ranked explanatory variable in all three steps of our analysis (Table 2). The relative importance of longitude was notable at the European scale where it was the second most important explanatory variable (rank 7 at national scale). The importance of pH and precipitation at the national scale (rank 4 and 5 respectively) was less marked at the European scale (rank 8 and 7 respectively). Most of the weed community composition differences between crop types is related to differences in crop sowing date expressed on CCA axis 1, from autumn-sown crops on negative to spring-sown crops on positive loadings (Figure 2).

In our DE case study, the net effect of environment was lower at the European scale than at the national scale, however the combined effect of environment, management and year increased from 10.5 to 15.8 (%) for gross effect and from 0.1 to 2.4 (%) net effect (E Â M Â Y in Table 3). Focusing only on environmental variables (Figure 3), the combination of climate and geographical position explained most of the variation, whilst the net effects of climate, geographical position and soil were relatively small.

In our UK case study, both species richness and abundance were consistently higher at the field edge than in the field core (Figure 4).

We also consistently find a strong effect of crop on both species richness and abundance (Table 4). Herbicide treatment was only found to have a significant effect at the European scale.

For all three case studies, despite the rescoping of the questions to include fewer variables with decreased resolution, the first step of

Variables

Step 1. France (abundance)

Step 2. France (presence-absence)

Step 3. Europe (presence-absence)

Group of variables

Step 1. Germany (in count)

Step 2. Germany (in Barralis scale)

Step 3. Europe (in Barralis scale)

Gross effect (%) Net effect (%) Gross effect (%) Net effect (%) Gross effect (%) Net effect (%)

Environmental (E) 7.9 6.5 Whilst the order of importance of variables tended to remain similar to the previous steps in all three case studies there were some notable changes in this final step, primarily in the geographic and climatic variables.

In the FR case study, the main difference between the two spatial scales was the relative importance of soil and climatic variables. At the scale of France, soil pH was the first environmental variable, followed by precipitation, with less importance of longitude, latitude and temperature. Yet at the scale of Europe, longitude was the second most important variable immediately after crop type, and the influence of temperature was stronger at this scale. The effect of year was also stronger at the European scale. Similarly, in the DE case study, the combination of climate and geographical location explained most of the variation due to the environment at the European scale, whilst the net effects of climate, geographical location and soil were relatively small at the scale of Germany.

| DISCUSSION

The consistency in results between the original studies and those we obtained in step one of our analyses indicates that despite the T A B L E 4 Final generalised linear mixed model terms and their significance for both abundance and species richness at all three stages of the iterative analysis

Fixed effect

Step 1. UK (counts) N = 24 432

Step 2. UK (rescaled to zero mean and unit variance) N = 24 432

Step consolidation of several environmental and management variables and an associated reduction in the resolution of the data, this has little impact on the ability to answer important ecological questions using the data stored within AWME. In all three case studies, we were able to alter the scope of the question slightly to allow the inclusion of additional data sets from across Europe.

We identified several key challenges associated with combining data from multiple surveys. Some of these challenges are addressed within the AWME database itself, but for others it was necessary to address them in our analysis (Table 1). Through our three case studies, we highlighted some exemplary solutions to the challenges of combining disparate datasets. There is inherent data loss when analysing data from multiple sources as not all information is available from each source. In the case studies, we found that the resolution of explanatory variables was often coarser than in the original studies. There was also information loss from the exclusion of incomparable records or in the transformation of response variables (e.g., from counts to presence/absence). We addressed the challenge of different species abundance metrics by transforming the data to a common scale, which is known to influence the outcome of ordination analyses [START_REF] Otypková | Effects of plot size on the ordination of vegetation samples[END_REF]. However, we found that this transformation had little influence in our analysis. In case studies FR and DE, there was minimal impact on the percentage of explained inertia, and in case study UK, the variables identified as significant in the GLMM remained similar in each step of the analysis. This may be explained by the fact that the original datasets from France, Germany and the UK, were collected on a national scale representing a long gradient of 'heterogeneous' data with almost unique species composition in each plot. In this case, presence-absence data is sufficient to describe between-site variation. Whereas, in the case of more homogeneous data at the scale of a small region where many species are distributed in most sites, species abundance becomes the main source of between-site variation and switching to presence-absence data will have a more serious impact [START_REF] Austin | The application of quantitative methods to vegetation survey: II. Some methodological problems of data from rain forest[END_REF]). These findings suggest that future monitoring approaches aiming at analysis of species composition could focus on achieving a large sample size and reduce the sampling effort on each plot by estimating species abundance rather than counting individuals. This could allow a broader range of environments and/or management practices to be considered for the same sampling effort.

It is interesting to note that whilst the trend in the results observed for the UK dataset and the European dataset were similar in our UK case study, the magnitude of the abundance and species richness metrics diverged between the datasets. For both metrics, the absolute values of predictions for herbicide-treated and untreated plots in the UK were very similar whilst at the European scale values were high in the untreated plots and much lower in the plots which had received herbicide. This exemplifies some of the key challenges described in Table 1. For the UK data, the herbicide-treated and untreated data come from the same plots which were sampled before and after herbicide treatment and so we would expect the weed communities to remain similar with a loss of some individuals and species following treatment. However, in the rest of the AWME database the treated and untreated plots may come from vastly different surveys with different plot sizes and or different methodologies. It is also likely that the choice of the data collector to conduct a survey with or without herbicide treatment reflects the typical agronomy of the field, farm or region being surveyed. As such, survey data from sites with low or no herbicide use could be expected to have higher weed species richness and abundance than those where herbicide use is common [START_REF] Hyvönen | Weed species diversity and community composition in cropping practices at two intensity levels-a six-year experiment[END_REF]. The choice to rescale the data within each dataset led to information loss on the absolute size of effect, however, it allowed us to consider all datasets with information on our variables of interest and the step-wise analysis confirmed that this technique was effective in allowing us to understand the relative effects of our explanatory variables.

In all three case studies, we found some consistency in the conclusions that could be drawn at the national scale and at the European scale, particularly in terms of the role of management practices. In fact in all three cases, we saw an increase in the certainty of predictions or in the explanatory power of the fitted model. This is primarily due to the additional data incorporated into the analysis, but it also indicates that the patterns observed at the national scale are largely supported by the additional datasets as any contradictory data would likely weaken the strength of the results.

Where we observed differences in the results between the national scale and the continental scale was largely in the role of the environment. In the FR case study, crop management variables were the key drivers of weed community composition at the national scale with soil pH and precipitation being the most important environmental drivers. This result contrasted with other studies that indicated a stronger effect of environmental gradients (e.g., [START_REF] Lososová | Weed vegetation of arable land in Central Europe: gradients of diversity and species composition[END_REF][START_REF] Šilc | Formalized classification of the weed vegetation of arable land in Slovenia[END_REF]. However, when we repeated the analysis at the European scale the effect of longitude was much more important (second most important explanatory variable). However, even at this continental scale, the main difference between weed communities was still determined by the crop type, meaning there are more similarities between weed communities of a given crop in different European regions than between weed communities of two different crops within the same region. In France, a complex gradient of soil pH, precipitation and longitude opposed weed vegetation of dry calcareous regions in Eastern France to weed vegetation of more rainy acidic regions of Western France [START_REF] Fried | Environmental and management factors determining weed species composition and diversity in France[END_REF]. Soil pH is recognised as one of the most structuring factors clearly differentiating acidophilic and basophilic weed assemblages [START_REF] Hüppe | Syntaxonomische Fassung und Übersicht über die Ackerunkrautgesellschaften der Bundesrepublik Deutschland[END_REF][START_REF] Pinke | Effects of environmental factors on weed species composition of cereal and stubble fields in western Hungary[END_REF]. The soil effect seems less visible at the European scale may be due to a stronger differentiation of weed communities along longitudinal and temperature gradients.

Interestingly, in the FR case study, sampling season was the second most important gross effect at both the national and European scale. Therefore, the importance of the crop type variable is partly supported by warm continental countries (Pannonian plain of Hungary) or Mediterranean countries (Italy, Southern France) where the growing season is long enough to grow summer crops ( Čarni et al., 2011). In northern Europe, the growing season is shorter and the differences between weed communities of winter and spring crops are less important. This difference could explain previous discrepancies between studies when reporting the relative importance of management [START_REF] Hallgren | Data diving with crossvalidation: an investigation of broad-scale gradients in Swedish weed communities[END_REF] versus environmental factors [START_REF] Lososová | Weed vegetation of arable land in Central Europe: gradients of diversity and species composition[END_REF].

Beyond the case studies presented here, the large geographical extent covered by AWME makes it a particularly valuable resource to address questions where (i) a sufficiently large environmental gradient may not be present in national or regional surveys, like macroecological patterns or climate change effect prediction (space-for-time substitution) or (ii) an effect may be hypothesised to change with scale. Potential future studies using AWME could (a) test the abundant-centre hypothesis [START_REF] Sagarin | The 'abundant centre' distribution: to what extent is it a biogeographical rule?[END_REF] which assumes that a species becomes more abundant at the centre of its range, where the environmental conditions are most favourable, (b) test the theory of species assembly [START_REF] Booth | Assembly theory applied to weed communities[END_REF] according to hierarchical filters starting from a true regional pool, (c) predict responses to climate change and/or extreme events using a time-for-space substitution, (d) predicting the spread of invasive or troublesome weeds by identifying combinations of management practices, soil and climates suitable for these species to establish, (e) disentangling the effects of management systems and single management measures and (f) examining relationships between weed management, weed abundance/weed pressure and weed diversity.

We have demonstrated the utility of gathering weed survey datasets into a European-scale database and explored the challenges and opportunities that such a database presents. We demonstrated that the European scale allows us to confirm and enrich previous works.

Our case study results should encourage us to use existing datasets to tackle more ambitious issues which require the perspective of a larger geographical area or a range of spatial scales as these can be combined with minimal loss of information despite different methodologies. The AWME database is a growing collection, and we welcome new data contributions and requests for data for analysis.

  The utility of the 'Arable Weeds and Management in Europe' database: Challenges and opportunities of combining weed survey data at a European scale Helen Metcalfe, Jana Bürger, Christoph Von Redwitz, Alicia Cirujeda, Silvia Fogliatto, Denise F Dostatny, Bärbel Gerowitt, Michael Glemnitz, José L González-andújar, Eva Hernández Plaza, et al. To cite this version: Helen Metcalfe, Jana Bürger, Christoph Von Redwitz, Alicia Cirujeda, Silvia Fogliatto, et al.. The utility of the 'Arable Weeds and Management in Europe' database: Challenges and opportunities of combining weed survey data at a European scale. Weed Research, 2022, 63 (1), pp.1 -11. 10.1111/wre.12562. hal-04028758

  published posing a range of ecological questions regarding weed communities. The original publications interrogated a national scale weed survey, and each of these national scale surveys are now included within the AWME data collection. Our first case study (FR) examined the important environmental and management factors determining weed species composition in France. The original publication by Fried et al. (2008) used data from a French national weed survey (Biovigilance Flore). The second case study (DE) was a more focussed study excluding the effect of crop type by focussing on maize crops to understand the role of the environment and management in weed community composition. In their original analysis published in 2015, de Mol et al. interrogated weed survey data from German maize crops. Our third case study (UK) follows Metcalfe et al. (2019) who used data from a national weed survey in the UK (Farm Scale Evaluations,

Fried

  et al. (2008) (retaining latitude [ N], longitude [ E], mean annual temperature [ C], annual precipitation [mm], soil pH, crop type, previous crop, herbicide treatment [yes/no], position in the field [core/ edge; in the French data all records were taken in field cores], sampling season [spring, summer, autumn, winter] and year of sampling).We excluded minor crops represented in fewer than 100 fields and simplified the previous crop variable into five categories (autumnsown dicot crop, autumn-sown monocot crop, spring-sown dicot crop, spring-sown monocot crop, other-including fallow and pluriannual forage crops) which characterised the legacy effect of past disturbances[START_REF] Gaba | Agroecological weed control using a functional approach: a review of cropping systems diversity[END_REF], the sowing date influencing the timing of disturbances and the type of crop being partly related to the nature of the disturbances (types of herbicides). To reduce noise due to rare species, we only retained the 217 weed species that occurred in more than 50 fields ($1% of the analysed fields).For step one of the DE case study, we redefined the scope of the analysis to include the previous crop, tillage (± plough), longitude ( E), latitude ( N), three climate variables (precipitation of the warmest quarter of the year [mm], minimum and mean yearly temperature[ C] from WorldClim data version 2.1[START_REF] Fick | WorldClim 2: new 1-km spatial resolution climate surfaces for global land areas[END_REF]), and three soil properties (phosphorus and nitrogen content, and pH from LUCAS grids[Orgiazzi et al., 2018]). This gave 10 variables for use in the RDA compared to the original work by[START_REF] De Mol | Weed species composition of maize fields in Germany is influenced by site and crop sequence[END_REF] which used 14 variables in their analysis of the weeds of maize crops in Germany.

F

  I G U R E 1 Distribution of the sample plots used in (A) case study FR, (B) case study DE and (C) case study UK. Red dots represent the fields used in the original study; blue dots represent the additional fields from the AWME T A B L E 2 Gross (CCA) and net (pCCA) effect of covariates on weed species composition at the European (n = 4686 fields) and the French level (n = 1396 fields)

  the analysis yielded similar results to those seen in the original publications.The transformation of response variables in step two of our analysis caused little change to the results observed. For example, switching from an analysis based on abundance to one based on presence/ absence data in the FR case study gave a reduction in the explained inertia from 7.2% to 6.6%, but the relative importance of the explanatory variables was almost identical (Table 2, Spearman's rank correlation coefficient, r = 0.830, p = 0.006). Similarly in DE, where the resolution of the species data was reduced from count data to the 6-level Barralis scale, the structure of variation partitioning stayed the same and the values remained similar.In Step 3 of the analysis where we scaled up from national to European scale, we observed several changes in the results of the analyses. There was a gain in explained inertia (FR), a higher rate of explained variance (DE) and narrower confidence intervals on predictions (UK).

F

  I G U R E 2 Ordination diagrams of the canonical correspondence analyses (CCA) at (A) the French scale (CCA1: 31.2% of the variation explained; CCA2: 14.8%) and (B) the European scale (CCA1: 26.8% of the variation explained; CCA2: 15.5%) with sites colour depending on crop type (blue: winter crops, green: spring crops, red: summer crops). W cereals: winter cereals, W OSR: winter oilseed rape. In panel (B), the shapes represent the country. DE, Germany; FR, France; HU, Hungary; IT, Italy; LV, Latvia; PL, Poland T A B L E 3 Gross and net effect (variance partitioning on basis of RDA) of groups of covariates on weed species composition at the German (n = 2593 fields) and European level (n = 3355 fields) in percentage explained variance

F

  I G U R E 4 Predicted (A) weed abundance and (B) species richness (data rescaled to zero mean and unit variance) from a generalised linear mixed effects model. Predictions are classified by position in field, crop type (only three crops are shown here to avoid crowding the graphic), and herbicide treatment (treated/untreated). Results of step two of our analysis are shown in blue (UK) and step three (EU) in red. Error bars show the approximate average standard error of difference.

  Variables are ordered by decreasing values of net effect at the European scale.

		Gross	Net		Gross	Net		Gross	Net
		effect (%)	effect (%)	Order	effect (%)	effect	Order	effect (%)	effect (%)	Order
	Crop type	3.632	2.488	1	3.445	1.850	1	6.022	1.517	1
	Longitude	0.438	0.249	7	0.423	0.200	7	1.522	0.455	2
	Previous crop	1.217	0.845	3	1.187	0.591	2	1.903	0.408	3
	Season	0.633	1.389	2	1.566	0.440	3	3.418	0.333	4
	Temperature	0.656	0.311	5	0.765	0.201	6	1.964	0.291	5
	Year	0.384	0.279	6	0.270	0.169	9	1.135	0.261	6
	Precipitation	0.645	0.230	9	0.804	0.234	5	0.829	0.234	7
	Soil pH	0.630	0.311	4	0.596	0.235	4	0.549	0.225	8
	Latitude	0.687	0.247	8	0.862	0.193	8	1.935	0.195	9
	Field Part	-	-	-	-	-	-	1.174	0.180	10
	Treatment	0.182	0.130	10	0.134	0.139	10	1.532	0.116	11
	Note:

  Note: A separate model was fitted to each dataset for each response variable. N = The number of data points included in each dataset.Term included in model but not significant, *p ≤ 0.05; **p ≤ 0.01; ***p ≤ 0.001, blank cells represent terms that were dropped from the model during the backwards selection process.

						3. Europe
						(rescaled to zero
						mean and unit
						variance)	N = 58 150
		Species richness	Abundance	Species richness	Abundance	Species richness	Abundance
	Position in field (P)	<0.001***	<0.001***	<0.001***	<0.001***	<0.001***	<0.001***
	Crop (C)	<0.001***	<0.001***	<0.001***	<0.001***	<0.001***	<0.001***
	Herbicide treatment (H)	0.903 a	0.949 a	0.994 a	1.000 a	<0.001***	<0.001***
	P Â C			0.004**		<0.001***	<0.001***
	P Â H	0.072 a		0.038*		<0.001***	0.006**
	C Â H	<0.001***	<0.001***	<0.001***	<0.001***	<0.001***	<0.001***
	P Â C Â H

a

13653180, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/wre.12562 by Cochrane France, Wiley Online Library on [29/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

0, from https://onlinelibrary.wiley.com/doi/10.1111/wre.12562 by Cochrane France, Wiley Online Library on [29/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

13653180, 0, from https://onlinelibrary.wiley.com/doi/10.1111/wre.12562 by Cochrane France, Wiley Online Library on [29/12/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

ACKNOWLEDGEMENTS

This work was made possible via the Weeds and Biodiversity working group of the European Weed Research Society. This project was funded under a Rothamsted Research and BBSRC grant number BB/ W510543/1. Helen Metcalfe was partly supported by the Natural Environment Research Council (NERC) and the Biotechnology and Biological Sciences Research Council (BBSRC) research programme NE/N018125/ 1 LTS-M (ASSIST). Jana Bürger's work on this project was supported by Deutsche Forschungsgemeinschaft DFG (grant number BU 3097/1-1).

Grant/Award Number: BU 3097/1-1; Natural Environment Research Council, Grant/Award Number: NE/N018125/1LTS-M(ASSIST); Rothamsted Research

CONFLICT OF INTEREST

The authors have no conflicts of interest to declare.

PEER REVIEW

The peer review history for this article is available at https://publons. com/publon/10.1111/wre.12562.

DATA AVAILABILITY STATEMENT

The data within AWME are available on the submission of a proposal to the coordination group. Data from individual datasets will be released according to their corresponding availability regime with the majority of data accessible for all research needs. Further information is available at https://ewrs.org/en/info/Blog/93/Arable-Weeds-and-Management-in-Europe-AWME-A-database-of-weed-survey-datafrom-across-Europe.

SUPPORTING INFORMATION

Additional supporting information can be found online in the Supporting Information section at the end of this article.


Hélène Tap
email: helene.tap@enseeiht.fr

Brigitte Caussat

Hugues Vergnes

Philippe Arguel

Pierre Trinsoutrot

Véronique Conédéra

François Guerin

Frédéric Gessinn

Jérémie Grisolia

Jérôme Launay

H Tap-Béteille

V Conedera

Graphene in silicon photovoltaic cells

Keywords: graphene, silicon technology, transparent electrode, photovoltaic technology, CVD

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Abstract Text

Graphene is an allotrope of carbon. Its structure is one-atom-thick planar sheets of carbon atoms that are densely packed in a honeycomb crystal lattice [1]. The richness of optical and electronic properties of graphene attracts enormous interest. Its true potential seems to be in photonics and optoelectronics, where the combination of its unique optical and electronic properties can be fully exploited. The optical absorption of graphene layers is proportional to the number of layers, each absorbing A=1-T=πα=2.3% over the visible spectrum [2].The rise of graphene in photonics and optoelectronics is shown by several recent results, ranging from solar cells and light emitting devices, to touch screens, photodetectors and ultrafast lasers. Current photovoltaic (PV) technology is dominated by Si cells, with an energy conversion coefficient  up to 25% [3]. Such an inorganic PV consists in a current transparent conductor (TC) replacing one of the electrodes of a PIN photodiode. The standard material used so far for these electrodes is indium-tinoxide, or ITO. But indium is expensive and relatively rare, so the search has been on for a suitable replacement. A possible substitute made from inexpensive and ubiquitous carbon is graphene. Being only constituted of carbon, it will become cheap and easily recyclable. But at the moment, the major difficulty consists in its fabrication and/or transfer. Our project consists in synthetizing graphene by CVD (Chemical Vapor Deposition) on Cu and in transferring the obtained layer on silicon PV cells, and then in testing their energy conversion efficiency. Graphene was produced in a hot wall tubular APCVD (Atmospheric Pressure CVD) reactor, 5 cm ID and 1m length, from methane diluted in hydrogen and argon. Copper foils (25 m thick, 99,999% Alfa Aesar) of 2x2 cm 2 were used as the catalyst. The operating temperature was fixed at 1000°C. Scanning electron microscopy (SEM), optical microscopy and Raman spectroscopy measurements were carried out to investigate the quality and uniformity of graphene sheets. After synthesis, graphene was transferred classically by a PMMA-assisted wet transfer method directly on the PV cells. Figure 1 presents a characteristic example of APCVD results. As it can be seen on the optical image, the sample shows a good homogeneity on mm 2 scale. On the Raman spectrum obtained before transfer, the low ratio of D/G peaks indicates a low density of defect in the graphene layers. The ratio of 2D/G peaks is slightly lower than 1, which means that the number of graphene layers is between 2 and 4. For this application, a lower number of layers would have been much better and will be one of the keys to increase the PV cell performance.

The photovoltaic (PV) cells are constituted of N + P junctions implemented on silicon <100> P-substrate (fig. 2 left). The solar light used to characterize them is a solar light LS1000 and has a maximal optical power of 22 000 lux. The I(V) measurements are performed by a Keithley 2612 (fig. 2 right). The results obtained for one of the tested cell are presented as an example in fig. 3. One can see a sensitivity increasing. Considering the very low surface of graphene transferred on the PV cell, these first results are encouraging.

[1] Geim, A. K. and Novoselov, K. S. "The rise of graphene". Nature Materials 6 (3), 183-191(2007).

[2] R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K.Geim, "Fine structure constant defines visual transparency of graphene," Science 320, 1308Science 320, (2008)).

[3] M. A. Green, K. Emery, K. Bücher, D. L. King, S. Igari, "Solar cells efficiency tables, version 14", Progress in Photovoltaics 7(4), 321-326 (1999).

  Tap Béteille, Hélène and Caussat, Brigitte and Vergnes, Hugues and Trinsoutrot, Pierre and Conédéra, Véronique andGuerin, François and Gessinn, Frédéric and Grisolia, Jérémie and Launay, Jérôme and Arguel, Philippe Graphene in silicon photovoltaic cells. (2012) In: 38th International conference on Micro and Nano Engineering MNE2012 , 16-20 Sept 2012, Toulouse, France. (Unpublished)

Figure 1 :

 1 Figure 1: Raman spectrum and optical image of graphene synthesized on Cu foil

Figure 3 .

 3 Figure 3. I(V) curves obtained. Yellow: PV cell in obscurity. Dark green: PV cell without graphene under lighting. Light green: PV cell with graphene under lighting.


Nithin Suryadevara

Athanassios K Boudalis
email: bountalis@kit.edu

Jorge Enrique

Olivares Peña

Eufemio Moreno-Pineda

Artem Fediai

Wolfgang Wenzel

Philippe Turek

Mario Ruben
email: mario.ruben@kit.edu

Jorge Enrique Olivares Peña

Molecular-engineered biradicals based on the Y III -phthalocyanine platform

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

Abstract

A mixed-ligand phthalocyanine/porphyrin yttrium(III) radical double-decker complex (DD) was synthesized using the custom-made 5,10,15-tris(4-methoxyphenyl)-20-(4-((trimethylsilyl)ethynyl)phenyl)porphyrin. The trimethylsilyl functionality was then used to couple two such complexes into biradicals through rigid tethers. Glaser coupling was used to synthesize a short-tethered biradical (C1) and Sonogashira coupling to synthesize longer-tethered ones (C2, C3). Field-swept echo-detected (FSED), saturation recovery and spin nutation pulsed EPR experiments revealed marked similarities of the magnetic properties of DD with those of the parent [Y(pc) 2 ]˙ complex, both in the solid state and in CD 2 Cl 2 /CDCl 3 4:1 frozen glasses. FSED experiments on the biradicals C2 and C3 revealed a spectral broadening with respect to the spectra of DD and [Y(pc) 2 ]˙ assigned to the effect of dipolar interactions in solution. Apart from the main resonance, satellite features were also observed, which were simulated with dipoledipole pairs of shortest distances, suggesting spin delocalization on the organic tether. FSED experiments on C1 yielded spectral line shapes that could not be simulated, as the integration of the off-resonance echoes was complicated by field-dependent modulations. While for all dimers the on-resonance spin nutation experiments yielded Rabi oscillations of the same frequencies, off-resonance nutations on C1 yielded Rabi oscillations that could be assigned to a M S = -1 to M S = 0 transition within an S = 1 multiplet. DFT calculations showed that the trans conformation of the complexes was significantly more stable than the cis one and that it induced a marked spin delocalization over the rigid organic tether. This "spin leakage" was most pronounced for the shortest biradical C1.

Tb III by Y III allowed us to use EPR spectroscopy, which is particularly powerful to answer such questions.

As a first step of this project, we carried out EPR studies of pure [Y(pc) 2 ]˙ in the solid state. These demonstrated that magnetically condensed and non-isotopically engineered phases could be coherently manipulated even at room temperatures, as demonstrated by FID-detected Rabi oscillations. Theoretical studies also demonstrated a preponderance of spin densities on carbon atoms of the pc rings, partially explaining the absence of hyperfine interactions. [START_REF] Boudalis | Room-Temperature Spin Nutations in a Magnetically Condensed Phase of [Y(Pc) 2 ]˙[END_REF] In this work, to better understand the spin-density distributions in molecular-engineered quantum systems based on phthalocyanine radicals, we present detailed continuous-wave/pulsed EPR studies of such tailored-designed biradical systems in the solid state and in solution, which we rationalize through DFT calculations. Whenever required, we also present relevant studies on the parent [Y(pc) 2 ]˙ system, reported for the first time in this work, to demonstrate the retention of its properties in the newly reported molecular-engineered systems.

Results

Syntheses

In order to design and build the polynuclear architectures, we require several elements that include the building block, the linker, and the mechanism to couple them. Here, in our case, we chose the porphyrin and phthalocyanine based double-decker as a building block and coupling reactions as a linking strategy. The scheme below shows a clear view of the synthesis, which requires a single sandwich complex and thus can synthesize a family of coupled double-decker complexes, just by varying the linkers and reaction conditions.

The neutral forms of the couple dimeric sandwich complexes (C1-C3) were synthesized using Glaser and Sonogashira coupling from the mononuclear double-decker complex DD, as depicted in Figure 1. In order to obtain the dimeric complex C1, the homo-coupling mechanism was involved in the presence of Pd(PPh 3 ) 2 Cl, AsPPh 3 in aerobic conditions. The oxygen favors the mechanism of the homo-coupling reaction. Whereas in the case of synthesis of complexes C2 and C3, the mono-nuclear complex DD was involved in hetero-coupling with a linker, but with inert conditions for the Sonogashira reaction. Due to the presence of (NBu 4 )F (henceforth TBAF) in the reaction mixture, the crude product was obtained as an anionic complex. The crude product extracted was subsequently subjected to oxidation by sodium-periodate (NaIO 4 ) followed by column chromatography to obtain the pure product in yields of 6-12%. In order to confirm the structure of the product, from spectroscopic methods, NMR is one of the best options available. However, due to the presence of radical it becomes challenging to analyze the spectra. Hence, in order to remove the radical effect, the 1 H-NMR was measured on each sample in 1:1 CD 2 Cl 2 :DMSO-d 6 solution in the presence of 10% (by volume) hydrazine hydrate, acting as reducing agent. Figure 2 shows a clear difference in the spectra in the δ = 7.75-8.00 ppm region (shaded region), which corresponds to the protons on the linker groups (benzene rings). This confirms the coupling of the monomeric complex with the respective linkers. The identity and purity of the compounds was further corroborated by ESI-MS (Figure S1).

Solid-state EPR spectroscopy

CW EPR experiments

Preliminary EPR studies of these complexes were carried out using X-band CW EPR to assess the similarities of the mixed-ligand systems with [Y(pc) 2 ]˙. These experiments mainly focused on the monomer complex DD, while one of the biradical complexes was studied indicatively to fully elucidate this question. C3 was selected mainly due to the available quantity of the powder sample. Room-temperature solid-state spectra of DD and C3 demonstrated a single Lorentzian resonance, typical of homogeneously broadened spectra (Figures S2, andS3, respectively) similar to that recently obtained for the [Y(pc) 2 ]˙ complex. [START_REF] Boudalis | Room-Temperature Spin Nutations in a Magnetically Condensed Phase of [Y(Pc) 2 ]˙[END_REF] Variable-temperature CW EPR spectra collected on powders of DD and C3 revealed broad spectra at 4.2 K (FWHM of 0.83 mT and 0.42 mT, respectively). For DD, the spectra narrowed continuously upon heating to room temperature (0.24 mT), a behavior consistent with that previously observed for [Y(pc) 2 ]˙. [START_REF] Boudalis | Room-Temperature Spin Nutations in a Magnetically Condensed Phase of [Y(Pc) 2 ]˙[END_REF] For C3 the narrowing continued up to 50 K reaching 0.29 mT, before demonstrating additional broadening at room-temperature (0.43 mT).

These linewidths, are the combined result both of the spin-spin relaxation time, T 2 , [START_REF] Weil | Electron Paramagnetic Resonance: Elementary Theory and Practical Applications[END_REF] as well as exchange-narrowing effects known to affect the spectra of identical spins. [START_REF] Abragam | Electron Paramagnetic Resonance of Transition Ions; Oxford classic texts in the physical sciences[END_REF] These solid-state effects are complicated to fully analyze and beyond of the scope of this work, we therefore limit ourselves to our qualitative discussion.

Pulsed EPR experiments in the solid state

The similarities between DD and [Y(pc) 2 ]˙, further extended to pulsed EPR in powders. The powered sample of DD showed FIDs at room temperature, which were used to record FIDdetected nutations (Figure S4), bearing a striking resemblance to the signals previously reported for [Y(pc) 2 ]˙. [START_REF] Boudalis | Room-Temperature Spin Nutations in a Magnetically Condensed Phase of [Y(Pc) 2 ]˙[END_REF] Considering that these studies compellingly demonstrate the similarities between [Y(pc) 2 ]˙ and the mixed-ligand systems, no FID-detected pulsed EPR experiments were carried out on C3.

Frozen solution CW EPR spectroscopy

EPR experiments in frozen solutions were carried out in a CD 2 Cl 2 /CDCl 3 4:1 which showed excellent glassing behavior (Figure S5). Moreover, preliminary studies revealed concentration effects (Figure S6). In particular, 1 mM samples were characterized by double resonances with different saturation profiles, which we attributed to aggregation or to intermolecular dipolar interactions. These persisted even after prolonged sonication of the EPR tubes. In turn, dilution to 0.1 mM removed these artifacts and further descriptions are given for these samples.

The analysis of CW-EPR experiments in frozen solutions was particularly complicated by the observation of absorption-like spectra at relatively low temperatures and moderate microwave powers (Figures S7). E.g., at a 44 dB attenuation (8.4 μW microwave power) such spectra already appeared at 20 K, whereas no available attenuation could produce derivative-like spectra at 4.2 K. Upon heating, this behavior was mitigated, with regular derivative-like spectra reappearing at temperatures between 35-50 K. At low temperatures, however, this behavior was not mitigated even by testing with different cavities with different power saturation profiles. This is a typical case of passage effects associated with a very slow spin-lattice relaxation, [START_REF] Weger | Passage Effects in Paramagnetic Resonance Experiments[END_REF][START_REF] Eaton | Electron Paramagnetic Resonance[END_REF] as confirmed by pulsed EPR experiments (see below).

This hypothesis was confirmed by comparing ascending vs descending field sweeps, at 40 K, a temperature where these effects are still observed (Figures S8 andS9). These spectra revealed inverted spectra for the ascending vs descending sweeps, which persisted even upon reducing the modulation frequency from 100 to 12.5 kHz. This behavior could be partially mitigated by reducing the scan speed, but it still persisted at 40 K, meaning that very long scans would be required at low temperatures. These experiments were therefore not further pursued.

At these concentrations, any half-field signals due to intra-or intermolecular interactions were masked by g ~ 4 impurity signals of our cavities (Figure S10), and were therefore unobservable. We note, however, that this concentration tends to the infinite dilution limit with respect to the intensity of such signals of intermolecular origin. 17

Pulsed EPR spectroscopy in frozen solutions

Spin-lattice relaxation studies

The determination of T 1 times was a prerequisite for subsequent pulsed EPR studies. Variabletemperature determinations were carried out indicatively for DD (Figure 3) to derive the spinlattice relaxation law; for the rest of the complexes such determinations were carried out only at the temperature of further experiments. In all cases these were carried out on the maximum absorption as determined by field-sweep echo-detected (FSED) spectra (see below) using saturation recovery experiments. The magnetization traces were fitted to different models, in particular a monoexponential model

1 ( / ) 0 ( ) (1 ) t T M t M e - = - (1), a stretched exponential model 1 ( / ) 0 ( ) (1 ) t T M t M e β - = - (2
) and a monoexponential law with a spectral diffusion coefficient q,

1 ( / / ) 0 ( ) (1 ) t T t q M t M e -+ = - (3)
. These fits confirmed the initial assumption derived from CW spectra: the T 1 times were very long, increasing from 6.9 ms at 95 K to 849 ms at 10 K. Fits to these results (Figure 3) were carried out to a relaxation model comprising Raman and Direct processes:

1 1 8 ( ) Direct m D R Direct D T T T b J b H T T - Θ   = +   Θ   (4)
where the transport integral ( )

/ 8 8 2 0 1 D T x D x x e J dx T e Θ Θ   =     -
∫ was calculated numerically. [START_REF] Pearson | Octacyanometallate Qubit Candidates[END_REF] We should stress that interpretation of spin-lattice relaxation in frozen solutions benefits from models developed for paramagnetic impurities in crystalline matrices. Magnetic molecules in frozen (glassy) solvents may exhibit relaxation pathways due to local vibrational modes. [START_REF] Eaton | Relaxation Times of Organic Radicals and Transition Metal Ions[END_REF] Attempts, however, to include such processes were unsuccessful. Quite large Debye temperatures were derived from these fits, which we attribute to correlations between fitting variables and to the possibility of different processes contributing differently at different temperatures. At 10 K and below, the T 1 times were too long for the saturation plateau to be attained within the instrumental constrains of our spectrometer, whose PatternJet limited the Shot Repetition Time (SRT) to 2 s, and maximum measurement duration to 1 s. [START_REF] Weber | USER'S MANUAL[END_REF] Thus, T 1 times below ~20 K have a considerable degree of uncertainty and the derived values depend on the relaxation model used for the fits. While these limitations can be overcome by using an external trigger, this was not considered as critical in the context of the current work. Further experiments were carried out at higher temperatures where these constrains were overcome.

To ascertain the source of these long relaxation times, we also carried out pulsed EPR experiments on the parent radical complex [Y(pc) 2 ]˙ (Figure S11). Interestingly, this also revealed similarly long spin-lattice relaxations, which indicates that the magnetic properties of these mixed-ligand complexes may be related to spin delocalization on the phthalocyanine ring. In particular, since spin-orbit coupling is known to be responsible for mediating the communication of the spin with the lattice vibtrations, [START_REF] Blume | Spin-Lattice Relaxation of S -State Ions: Mn 2 + in a Cubic Environment[END_REF][START_REF] Eaton | Relaxation Times of Organic Radicals and Transition Metal Ions[END_REF] delocalization on carbon atoms, with their very low spin-orbit coupling, is expected to be a contributing factor to slow spin-lattice relaxation. Moreover, we carried out such studies on C3 in an attempt to discern an energy Orbach process with an eventual energy barrier assigned to magnetic interactions (Figure S12). However, no such process was revealed, which we assigned to weak intramolecular interactions.

Field-sweep echo-detected (FSED) spectra

Preliminary FSED spectra were conducted to assess the line shapes and central field values. For DD, fits to the 95 and 40 K spectra revealed an almost perfectly Gaussian line shape. Particularly absent from these spectra are any hyperfine features. This is partially explained by DFT calculations which show that most of the spin density is delocalized in C atoms in the phthalocyanines and in the C atoms of the ring of the porphyrin ligand (see section 3.5 and SI). Due to the low natural abundance of magnetic nuclei in carbon we do not expect strong hyperfine couplings which would show up in FSED spectra. As for [START_REF] Abragam | Electron Paramagnetic Resonance of Transition Ions; Oxford classic texts in the physical sciences[END_REF] N nuclei, HYSCORE experiments of C3 showed that such couplings do exist in the "strong" coupling regime (|A| > 2ω 14N , where ω 14N = 1.07 MHz), but they still are too weak to be resolved by FSED experiments. We tentatively suggest that these weak couplings are due to the low spin densities of the N atoms (see Section 3.5 and SI). The lineshapes can very nicely be reproduced either by isotropic convolutional broadenings, or by anisotropic H-strains, that account for unresolved hyperfine couplings.

For comparison, FSED spectra of the parent [Y(pc) 2 ]˙ complex were also recorded and showed Gaussian line shapes of very similar widths, also lacking any hyperfine splittings (Figure S13 and Table 1). In addition, FSED spectra collected for C2 at two different τ delay times demonstrated some modulation-related effects which, nevertheless did not seriously affect the fitted distances (Figure S14). To extract information on inter-radical distances, the symmetric nature of the biradicals prevented us from carrying out DEER experiments, since we could not apply the requisite pump and probe pulses on separate resonances. We also attempted to carry out RIDME experiments. Although these are better suited for distance measurements of asymmetric "AB" systems (such as metal-radical systems) they have, in some cases, also been successfully used in distance measurements of symmetric biradicals [START_REF] Savitsky | High-Field Dipolar Electron Paramagnetic Resonance (EPR) Spectroscopy of Nitroxide Biradicals for Determining Three-Dimensional Structures of Biomacromolecules in Disordered Solids[END_REF][START_REF] Abdullin | Comparison of PELDOR and RIDME for Distance Measurements between Nitroxides and Low-Spin Fe(III) Ions[END_REF] and Gd III dimers. [START_REF] Razzaghi | RIDME Spectroscopy with Gd(III) Centers[END_REF] Unfortunately, attempts at sixpulse RIDME experiments [START_REF] Abdullin | Six-Pulse RIDME Sequence to Avoid Background Artifacts[END_REF] on C3 were unsuccessful as no refocused virtual echo could be detected.

Therefore, we instead carried out fits on the FSED spectra, whose shapes should be affected by the anisotropy induced by dipole-dipole interactions. For these fits, the fitted linewidth values of the mononuclear spectrum were used as fixed variables. Moreover, it was considered that no intermolecular dipolar interactions were operative. Indeed, a Poisson distribution predicts that the vast majority (99.6%) of intermolecular distances at this concentration is above 25 Å (Figure S15).

The first limitation of this approach is that its applicability starts decreasing for distances above ~25 Å, as the line shape of the dipole-coupled dimer starts approaching that of the monomer. E.g., for absorption-type signals with Gaussian peaks of 0.36 mT pp (peak-to-peak) linewidths, the two peaks coalesce into a single one approximately at 16 Å. The effective linewidth of the biradical system decreases and reaches 0.37 mT pp for distances of 30 Å. These are illustrated in Figure 4 and can be compared to the various interspin distances shown in Table 2.

The above means that while we may be able to determine distances between spin densities residing on the proximal atoms of the spin systems, dipole interactions between distal atoms would not yield anisotropies strong enough to be detected by their influence on the EPR line shapes. These distances are shown in Table 2 and for C1-trans in the bottom of Figure 4. With the longer biradicals exhibiting a main peak of effective linewidths of ca. 0.45 mT pp , this approach was applicable for at least a significant part of the spin densities. A second limitation concerns the hypothesis that spin densities reside solely on the pc/por systems. Indeed, theoretical calculations on long-chain bridged biradicals have shown this not always to be the case, [START_REF] Wautelet | Spin Exchange Interaction through Phenylene-Ethynylene Bridge in Diradicals Based on Iminonitroxide and Nitronylnitroxide Radical Derivatives. 1. Experimental Investigation of the Through-Bond Spin Exchange Coupling[END_REF][START_REF] Riplinger | Interaction of Radical Pairs Through-Bond and Through-Space: Scope and Limitations of the Point-Dipole Approximation in Electron Paramagnetic Resonance Spectroscopy[END_REF][START_REF] Tait | Transient EPR Reveals Triplet State Delocalization in a Series of Cyclic and Linear π-Conjugated Porphyrin Oligomers[END_REF] with a "spin leakage" occurring, much more so over conjugated organic tethers than aliphatic ones, in some cases leading to magnetic exchange.

This raises the point of the treatment of eventual superexchange terms. In subsequent analysis superexchange terms (Ĥ exch = J ij Ŝ i Ŝ j ) are not considered for any of the biradicals, for two main reasons.

The first concerns experimental complications arising in their determination by other methods. E.g., due to the expected low values of such couplings, SQUID magnetometry in the solid state might reasonably be dominated by intermolecular interactions which can often be quite significant. [START_REF] Constantinides | Effective Exchange Coupling in Alternating-Chains of a π-Extended 1[END_REF][START_REF] Constantinides | Spin-Triplet Excitons in 1,3-Diphenyl-7-(Fur-2-Yl)-1,4-Dihydro-1,2,4-Benzotriazin-4-Yl[END_REF][START_REF] Paillaud | Radical-Based Ferromagnetic Chain in Yttrium Diphthalocyanine [ YPc 2 ]⋅ CH 2 Cl 2[END_REF] This would require SQUID experiments in solution to unequivocally determine J, in which precise diamagnetic corrections are quite complicated to derive. Alternately, variable-temperature studies of the intensities of half-field signals might be employed, which are also quite demanding and entail significant uncertainties.

The second reason is the lack of relevance of such interactions in the current context. Indeed, these are not expected to be discernible in the field-swept EPR spectra of symmetric biradicals (g 1 = g 2 ), experiencing no hyperfine splittings. Hyperfine-split spectra of asymmetric biradicals are influenced by, and can yield information on, the ratio of J/A, 32 however this is not the case for the systems studied herein. Therefore, in the scope of this work we have disregarded superexchange couplings, if any are operative.

Preliminary fits were carried out to a point-dipole model previously described. [START_REF] Mathivathanan | Origin of Ferromagnetism and Magnetic Anisotropy in a Family of Copper(II) Triangles[END_REF] This model yielded relatively coherent results for C2 and C3 as shown in Figure 5, with the main spectral feature being well reproduced by distances reasonably close to the por-por ones. However, the presence of satellite features prompted us to introduce minor components of smaller interspin distances, a modification constituting an approximation to the distributed-dipole model. [START_REF] Neuman | Transition from Isolated to Interacting Copper( II ) Pairs in Extended Lattices Evaluated by Single Crystal EPR Spectroscopy[END_REF] These features can be rationalized by considering the presence of spin density over the organic tether. This "leaky tether" hypothesis was further tested by DFT calculations (vide infra). It is noteworthy that the satellite features at 40 K were quite weak, making their inclusion in the fits less reliable. These are subsequently not shown. However, these were more pronounced at 95 K allowing us to meaningfully fit their relative intensities.

The above results are summarized in Figure 5 and Table 3. Table 3. Best-fit parameters from fits of the FSED spectra of C2 and C3 to a set of point-dipole pairs. In each case, the relative weight of the central resonance is defined as On the other hand, in the case of the shortest dimer, C1, the line shape of the FSED spectrum was deformed due to modulations of the echo shape when the magnetic field departed from a narrow region (~0.1 mT) off the main resonance (Figure 6). In particular, close to the main peak, the real part of the echo presented the expected form, whereas off the maximum resonance it exhibited strong modulations. This hampered the correct signal integration, consequently, the FSED spectrum could not be reliably fitted. Nevertheless, the off-peak echo was used to draw conclusions about the spin state at that field (see Spin nutation experiments). It is noteworthy that these echo modulations are reminiscent of similar signals detected for a benzene solvate of the α,γ-bisdiphenylene-β-phenylallyl (BDPA) radical, [START_REF] Lenz | Room-Temperature Quantum Memories Based on Molecular Electron Spin Ensembles[END_REF] attributed at that particular case to strong spin-photon coupling with the cavity and to the excitation of polariton modes. Despite this similarities, however, in that work the sample was a 21.5 mg pure BDPA pellet, containing ca. 1.2×10 [START_REF] Eaton | Relaxation Times of Organic Radicals and Transition Metal Ions[END_REF] spins, studied at 7 K in a custom-built Fabry-Pérot resonator. In our case, the sample is a 0.1 mM solution containing ca. 6×10 [START_REF] Weger | Passage Effects in Paramagnetic Resonance Experiments[END_REF] biradicals, studied at 40 K in a standard Bruker dielectric resonator. Overall, that sample was 10 4 times larger than ours and also studied at lower temperatures in a resonator specifically designed to achieve very strong spinphoton couplings.

w = 1 Complex r central (Å) r 1 (Å), w 1 r 2 (Å),
During the review process it was suggested that this is a manifestation of passage through a relatively sharp signal using narrow pulses, with one of the reviewers supplying similar echoes from γ-irradiated silica. Indeed, such signals have also been observed in regular resonators, [START_REF] Bowman | Skew Projection of Echo-Detected EPR Spectra for Increased Sensitivity and Resolution[END_REF] or during electrically-detected magnetic resonance experiments. [START_REF] Lu | High-Resolution Electrical Detection of Free Induction Decay and Hahn Echoes in Phosphorus-Doped Silicon[END_REF] They can be rationalized by the consideration of an echo as two back-to-back FIDs evolving forward and backward in time; [START_REF] Slichter | Principles of Magnetic Resonance[END_REF] when off-resonance, these FIDs will exhibit an oscillatory behavior.

Actually, a method has been proposed for the analysis of echoes to achieve better sensitivities and resolutions with respect to FSED spectra collected by echo integration. [START_REF] Bowman | Skew Projection of Echo-Detected EPR Spectra for Increased Sensitivity and Resolution[END_REF] Based on that method we carried out complex FFT analysis on the real and imaginary parts of the echoes and found that they are characterized by negative and positive frequency offsets for B 0 < B res and B 0 > B res , respectively. The offset was a linear function of the applied magnetic field, with a rate of ~1.8 MHz G -1 (Figure 7). These results highlight the often overlooked importance of the direct dimension in pulse EPR spectroscopy. [START_REF] Bowman | The Direct Dimension in Pulse EPR[END_REF]

Echo-decay experiments

Hahn-echo decay experiments were carried out to assess the phase-memory times, T m , of the various samples. These were carried out at the magnetic field corresponding to each FSED spectrum's maximum, and at a 40 K temperature, at which the T 1 times were short enough to allow a 5T 1 SRT at a reasonable experimental duration, and the T m long-enough to observe sufficiently strong echoes.

The presence of very deep modulations (Figure S16) significantly hampered the quantitative treatment of the echo-decay traces. Attempts to decrease the modulation depth by softer and more selective pulses required 256/512 ns pulses to substantially decrease most of the modulations, though the initial one around 1 μs persisted (Figure S17). We tentatively attribute this modulation to couplings to [START_REF] Abragam | Electron Paramagnetic Resonance of Transition Ions; Oxford classic texts in the physical sciences[END_REF] N nuclei established by HYSCORE experiments. Fits to the latter part of the echo decay trace, which was free of modulations, yielded T M times between 5 and 9 μs (see Supporting Information). It is noteworthy that these results were close matched by echo-decay studies on solution samples of the parent [Y(pc) 2 ]˙ complex.

It should be noted that spin diffusion involving 1 H nuclei could participate in the shortening of the coherence time of these radicals. Indeed, while the experiments were carried out in deuterated solvents, the 1 H nuclei of the undeuterated phtalocyanine/porphyrin ligands, gives an effective 1 H concentration of 4 mM for the monoradicals and 8 mM for the biradicals, which are quite significant. Actually, the larger 1 H concentration of the biradicals is also reflected in theirT-M times, which are approximately half those of monoradicals species. Deuteration of the ligands would be a potential avenue to further increase the coherence time of these systems.

Another factor that may be considered for the shortening of coherence times are molecular motions which can occur even in frozen solvents at low temperatures. Given the quasicylindrical shape of the monoradicals, they may undergo librational motions around their central axis, thereby introducing an additional decoherence pathway. It might therefore be expected that the less symmetric, hence more constrained, biradicals move less freely in the glassy matrix.

If such is the case, then the biradicals constitute a case where one factor that accelerates decoherence, i.e. large 1 H concentration, coexists with a factor that decelerates it, i.e. diminished mobility. It stems therefore that increase of coherence times could be achieved by targeting molecular shapes with small mobility and high rigidity, e.g. by long and rigid side-groups, while taking care to keep the 1 H count low.

Spin nutation experiments

Spin nutation experiments were carried out to assess the ability to coherently drive the spin of the compounds at 40 K. Moreover, these experiments allow us to unequivocally establish the spin multiplet character within which each transition takes place, since the nutation frequency of a transition between states M S and M S +1 within a multiplet S is given by: 40

1 ( 1) ( 1)
B nut S S gB f S S M M µ = + - +  (7)
Initial experiments were carried out at the central resonance with variable MW powers, with the nutation traces of DD (Figure 8) and [Y(pc) 2 ]˙ (Figure S19) being used as calibration standards for the |S T , M S 〉 = |1/2, ±1/2〉 transitions. All experiments revealed oscillations, identified to be Rabi oscillations by the linear dependence of their frequency on B 1 (Figures S18 andS19). Comparison of the frequencies between all complexes confirmed that the nature of the central transition is |1/2, ±1/2〉, while fitting parameters to an exponentially damped oscillation gave comparable results (Table 4). At higher powers we observe a decrease of τ R , which we assign to "driven decoherence", [START_REF] De Raedt | Quantum Simulations and Experiments on Rabi Oscillations of Spin Qubits: Intrinsic vs Extrinsic Damping[END_REF] but also an overall decrease of the signal intensity, which we assign to larger turning angles at higher powers, requiring longer SRT than the ones used at lower MW power experiments. [START_REF] Drew | Spin States of C 60 3and C 120 O n -( n = 2, 3, 4) Anions Using Electron Spin Transient Nutation Spectroscopy[END_REF] However, the particular behavior of C1 prompted us to further assess the satellite resonance. Due to the modulated echo (Figure 6, left inset and Figure 7) a narrow integration window was selected for the detection of the nutation traces. Nutation experiments at this field also yielded oscillations with a frequency dependent on the MW power (Figure S20), thus also confirming these to be Rabi oscillations. Nevertheless, at the same attenuation level (6 dB) the nutation frequency at that field was 23.8 MHz, i.e., higher by a factor of 1.42 ~ √2 than the respective frequency (16.8 MHz) at the center of the resonance and at the same attenuation (Figure 9). Based on Eq. 7, this indicates that this resonance stems from a M S = -1 to M S = 0 transition within a S = 1 spin multiplet. This behavior is reminiscent of that previously observed in a Cu II -nitroxyl radical complex whose spectrum was interpreted in the framework of an exchange-coupled "AB" system. In that system, the appearance of the FSED spectrum depended on the MW power of the pulses, as the external vs internal parts of the spectrum corresponded to different effective S values and, therefore, turning angles for the same MW power. [START_REF] Eaton | Impact of Electron-Electron Spin-Spin Coupling on Electron-Spin Turning Angle in a Spin-Labeled Copper(II) Complex[END_REF] In our case, the two S = 1/2 spins are identical, yet they also give rise to transitions corresponding to different effective spin states.

An additional interpretation was considered for this variance in nutation frequencies, in particular that it is characteristic of an off-resonance FID. Although the signal was indeed from an off-resonant FID, the nutation frequency itself is qualitatively distinct, as it corresponds to the variation of the echo integral as a function of the nutation pulse length. Indeed, the nutation frequency depends on the MW power (see Fig. S20) demonstrating that it is a Rabi oscillation.

Theoretical studies

To get a better understanding of the FSED spectra, we performed ab initio calculations based on density functional theory (DFT) on all the molecules using the quantum package CP2K. [START_REF] Kühne | An Electronic Structure and Molecular Dynamics Software Package -Quickstep: Efficient and Accurate Electronic Structure Calculations[END_REF] In addition to the cis structures we also optimized and simulated the "trans" geometries. The trans structures were those in which one of the two [Y(pc)(por)] molecules was rotated 180° around the organic tethers (see methods' section for details). The stability of each of the cis structures was analyzed in terms of its DFT energy by comparing it to the corresponding trans geometry. The results are displayed in Table 5.

Table 5. Relative energies of the three simulated compounds. The energy differences clearly show that the trans arrangement is more stable than the cis one. All the simulations were carried with identical precision and DFT parameters.

System

ΔE cis-trans (eV) C1 0.257 C2 0.222 C3 0.152

In general, not only are the trans configurations more stable, but the organic linker adopts a straight geometry, in contrast to a more curved one of the cis ones. Moreover, the chain length influences the relative stability of the two conformations, with the shortest chains imposing a greater energetic preference to the trans conformation.

Since the spin localization in similar systems is closely related to phenomena such as magnetic coupling or electronic transport, we also analyzed the spin fingerprints on each of the systems. In contrast to simple double-decker compounds, the spin density is spread across all the carbon atoms of the phthalocyanine ligands as well as in the carbon atoms of the ring in the porphyrin. A substantial difference between the C1-cis and C1-trans is that a larger spin density leakage is observed into the linker in C1-trans, as can be observed in Figure 10b. This behavior seems to diminish as the distance between both double-decker complexes increases (see Figure S21). This observation is in line with that calculated for similar supramolecular multiradical systems. [START_REF] Riplinger | Interaction of Radical Pairs Through-Bond and Through-Space: Scope and Limitations of the Point-Dipole Approximation in Electron Paramagnetic Resonance Spectroscopy[END_REF][START_REF] Tait | Transient EPR Reveals Triplet State Delocalization in a Series of Cyclic and Linear π-Conjugated Porphyrin Oligomers[END_REF] The above findings are in line with the calculations of the singly-occupied molecular orbitals (SOMO) for each spin. These suggest that in the trans conformation of C1 the SOMOs are more extended over to the neighboring double-decker system (Figures S22 vs S23, top). These results are coherent with spin nutation experiments demonstrating the presence of different spin states off the main resonance, presumably due to stronger coupled densities on linker atoms. To further corroborate the above, and also to rationalize the lack of hyperfine couplings in the EPR spectra of these complexes, we performed Hirshfeld analysis to derive the atoms contributing to its total spin magnetization. Indicatively, we selected the two conformations of C1 (Tables S2-S5 and Figures S24,S25). These calculations show that the α-spin density preponderantly resides on C atoms and the β-spin density preponderantly so on N atoms. Moreover, the α-spin density is roughly 8.5 and 8 times greater than the β-spin density, for the cis and trans conformations, respectively, thus explaining the lack of hyperfine signals in EPR spectra.

Moreover, we correlate these results with preliminary HYSCORE studies carried out indicatively on C3 at 95 K (Figure S26). These reveal signals in the (-,+ ) quadrant clearly demonstrating hyperfine couplings with [START_REF] Abragam | Electron Paramagnetic Resonance of Transition Ions; Oxford classic texts in the physical sciences[END_REF] N falling within the "strong" coupling regime (|A| > 2ω 14N , where ω 14N = 1.07 MHz). Indeed, simulations indicate values A xy = -5.61 MHZ, A z = -3.78 MHz, Q x = -0.08 MHz, Q y = -1.52 MHz, Q z = 1.60 MHz. These couplings, remain quite weak to be adequately resolved in FSED experiments. We tentatively assign their weak intensity to the low spin density residing on N atoms.

Discussion

In this work we have proposed a new strategy to design and synthesize stable bis-"double decker" systems, using molecular engineering principles to carefully control their distances and, hence, their magnetic interactions. To do this we used mixed-ligand pc/por double-decker moieties, taking advantage of the synthetic versatility offered by the meso-positions of the por ligands. To the best of our knowledge this is the first such approach to tackle this problem in a rationally designed manner.

Another objective of this work was to compare the magnetic properties of the "parent" [Y(pc) 2 ]˙ radical system with the those of the mixed-ligand [Y(pc)(por)]˙ analogues. Experiments both in the solid state and in solution clearly demonstrated close similarity of these magnetic properties. Indeed, the DD monomer perfectly reproduces the behavior of [Y(pc) 2 ]˙, in both powders and frozen solutions and for several different experiments.

This work has also demonstrated the synthetic feasibility to use the [Ln(pc) 2 ]˙ platform to engineer larger spin systems with predefined architectures and custom-designed magnetic interactions. EPR studies and DFT calculations showed that the rigid supramolecular tether is not an innocent component of the system, as it can become "leaky" due to spin delocalization below a certain length and/or at specific conformations. In that case, significant spin density can leak onto its atoms, introducing new components to the magnetic behavior of the dimers.

Interestingly, we note that studies such as this, entailing: (i) series of carefully engineering biradical systems, studied in detail by a combination of (ii) advanced EPR and (iii) theoretical methods, are quite uncommon. Numerous past studies often focus on one of those aspects or on single biradicals. This combined approach is very rare, and has allowed us to bring forth finer, and previously unobserved, details of the magnetic structures of these systems. These are particularly relevant in regard to surface deposition of such molecules for the construction of molecular devices, a domain in which the [Ln(pc)]˙ platform has been shown to be particularly adapted. [START_REF] Boudalis | Molecular Devices[END_REF] The details of the molecular conformation of such surface-deposited molecules would be a critical parameter in their utility as device components.

A salient point in this respect is the observation made by nutation experiments that resonances away from the main peak can be attributed to S = 1 spin systems, at least in the case of the shortest tethers. This may suggest that the spin leakage and the significantly shortest interspin distances to which it gives rise, create a system with a different spin character.

During these studies, it was also revealed that radical complexes based on the [Y(pc)]˙ moiety exhibit quite long spin-lattice relaxation times in frozen solution. This observation, along with the possibility to design asymmetric biradicals, offers some intriguing perspectives, especially relating to the use of such systems in DNP, where long T 1 times are a particular advantage. In addition, it has been proposed that biradicals with two distinct electronic Larmor frequencies, whose difference is equal to the Larmor frequency of the nucleus under rf excitation should maximize the DNP enhancement. [START_REF] Hu | Dynamic Nuclear Polarization with Biradicals[END_REF] On a parallel track, such asymmetric biradical systems might constitute ideal platforms to implement molecular CNOT gates, whereby the two qubits are weakly coupled due to dipolar interactions, while their different g-values might allow the individual addressing by different microwave frequencies. Recent developments in the design of pulsed EPR experiments render this perspective quite intriguing. [START_REF] Nelson | Gate Operation on a Photogenerated Molecular Electron Spin-Qubit Pair[END_REF] Overall, we have successfully implemented molecular engineering principles to construct biradicals with designed interspin distances, and we have demonstrated their dipole-dipole interactions. Pulsed EPR experiments and DFT calculations showed that while spin delocalization over the rigid organic tether could not be entirely prevented, this "spin leakage" could be minimized by lengthening of the tether. Indeed, fits to a version of a distributed-dipole model showed that roughly 75-80% of the spin densities of the longer-chained biradicals C2 and C3 were based on the pc/por ring systems.

In light of the previously mentioned perspectives of biradical use as DNP polarizing agents and/or CNOT gate elements, we are currently looking into the preparation of asymmetric biradical systems, based on the [Y(pc)]˙ platform.

Figure 1 :

 1 Figure 1: Syntheses and molecular structures of coupled dinuclear sandwich complexes C1-C3

Figure 2 :

 2 Figure 2: 1 H NMR spectra of yttrium analogs of dimeric complexes in CD 2 Cl 2 -DMSO-d6 (1:1) in the presence of ca. 10% (by volume) hydrazine.

Figure 3 .

 3 Figure 3. Left: Saturation recovery traces for a 0.1 mM CD 2 Cl 2 :CDCl 3 4:1 frozen solution of DD at various temperatures and fits to a monoexponential model comprising spectra diffusion (black lines). Right: T 1 times as a function of temperatures and fit to a relaxation model comprising Raman and Direct processes. Best-fit were Θ D = 244 K, b Raman = 1.0×10 5 s -1 , m Direct = 2.0, b Direct = 0.94 s -1 T -2.0 . The vertical error bars indicate the 95% confidence intervals.

Figure 4 .

 4 Figure 4. Top: Line shapes of simulated FSED spectra of symmetric dipole-dipole coupled species. Bottom: Distances between different atoms of the delocalized system C1-trans, derived from a calculated structure.

Figure 5 .

 5 Figure 5. Left. FSED spectrum for a 0.1 mM CD 2 Cl 2 :CDCl 3 4:1 frozen solution of DD and fit to a single resonance, with best-fit parameters shown in Table 1. The linewidths of these spectra were then used as a fixed variables to fit the spectra of dimers. Middle. FSED spectrum for a 0.1 mM CD 2 Cl 2 :CDCl 3 4:1 frozen solution of C2 at 40 K and fit to two subcomponents. Right. Fit to FSED spectra of C3. The 40 K spectrum was fitted to only one dipole-dipole distance. The 95 K spectrum was fitted to three subcomponents. Best-fit parameters for the spectra of C2 and C3 are shown in Table 3. Experimental conditions:. f MW = 9.81456 GHz (DD, 40 K), 9.7575 GHz (DD, 95 K), 9.75515 GHz (C2), 9.81331 GHz (C3, 40 K), 9.75577 GHz (C3, 95 K); τ = 1170 ns (DD, C1), 1150 ns (C2, C3), π/2 = 16 ns, 150 ns integrator gate.

Figure 6 .

 6 Figure 6. FSED spectrum for a 0.1 mM CD 2 Cl 2 :CDCl 3 4:1 frozen solution of C1 at 40 K (τ = 1.19 μs, f = 9.81315 GHz, π/2 = 16 ns, 150 ns integrator gate). The insets show indicative Hahn echo traces at two magnetic fields near and further away from the maximum.

Figure 7 .

 7 Figure 7. Real (left) and imaginary (center) components of Hahn echoes for a 0.1 mM CD 2 Cl 2 :CDCl 3 4:1 frozen solution of C1 (T = 40 K, τ = 1.19 μs, f = 9.81315 GHz) as a function of the magnetic field. The FFT on the complex signal (right) shows frequency offset as a function of the magnetic field (shown in the plot inset).

Figure 8 .

 8 Figure 8. Left: Spin nutation for a 0.1 mM CD 2 Cl 2 :CDCl 3 4:1 frozen solution of DD at various microwave powers at 40 K. Right: Fourier transform spectra of the nutation traces.

Figure 9 .

 9 Figure 9. FSED spectrum for a 0.1 mM CD 2 Cl 2 :CDCl 3 4:1 frozen solution of C1 with the Rabi oscillations at the different magnetic fields as insets.

Figure 10 :

 10 Figure 10: Spin density of C1-cis and C1-trans in a) in b) respectively. Red/blue correspond to α/β spins, respectively. It can be seen that in C1-cis, most of the density is delocalized over the carbon atoms in both of the ligands. Nevertheless, C1-trans presents spin leakage into some of the carbons in the organic tethers.

Table 1 .

 1 Best-fit parameters to FSED spectra of monomer DD and [Y(pc) 2 ]˙.

	Isotropic convolutional	Anisotropic
	broadening	broadening

Table 2 .

 2 Calculated interatomic distances for the trans conformations of C1-C3. Distance r por-por refers to the porphyrin carbon atoms on which the tether is grafted.

	Conformation	r por-por (Å)	r pc-pc-prox (Å)	r pc-pc-dist (Å)
	C1-trans	14.98	18.29	28.80
	C2-trans	19.26	22.20	34.30
	C3-trans	23.62	26.20	38.54

Table 4 .

 4 Dependence of the Rabi damping times on the MW power attenuation

	Complex

Acknowledgments

Financial support from the CNRS research infrastructure INFRANALYTICS (FR2054) for conducting the research is gratefully acknowledged. AKB thanks the Baden-Württemberg Stiftung for financial support through the MOLTRIQUSENS project. EMP thanks the Panamanian National System of Investigators (SNI, SENACYT) for support. JEOP thanks DFG grants FE 1776/2-1 and WE 1863/34-1. We thank Prof. Joris van Slageren and Dr. David Hunger (University of Stuttgart), for helpful discussions.

Supporting Information

PDF file with supporting information contains: (i) synthetic procedures and characterization, (ii) materials and methods for physical studies and theoretical calculations, (iii) additional CW and pulse EPR experiments on powders and frozen solutions, (iv) additional results of theoretical calculations and spin density analysis.

(1) Vincent, R.; Klyatskaya, S.; Ruben, M.; Wernsdorfer, W.; Balestro, F. Electronic Read-out of a Single Nuclear Spin Using a Molecular Spin Transistor. Nature 2012, 488 (7411), 357-360. https://doi.org/10.1038/nature11341.

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