Xuhong Li

Franck Davoine

Yves Grandvalet

A Simple Weight Recall for Semantic Segmentation: Application to Urban Scenes

In many learning tasks, including semantic image segmentation, performance can be effectively improved through the fine-tuning of a pre-trained convolutional network, instead of training from scratch. With fine-tuning, the underlying assumption is that the pre-trained model extracts generic features, which are at least partially relevant for solving a segmentation task, but that would be difficult to extract from the smaller amount of data that is available for training in urban driving scenes segmentation. However, besides the initialization with the pre-trained model and the early stopping, there is no mechanism in classical fine-tuning approaches for keeping the generic features. Even worse, the standard weight decay drives the parameters towards the origin and affects the learned features. In this paper, we show that a simple regularization that uses the pre-trained model as a reference consistently improves the performance when applied to semantic urban driving scene segmentation. Experiments are done on the Cityscapes dataset, with four different architectures of convolutional networks.

I. INTRODUCTION

Recent years have seen an increasing interest in driving scene understanding and semantic image segmentation is one of the important tools that can help to distinguish the different objets in the surrounding neighborhood of a vehicle as well as their complex relationships.

Image segmentation, i.e. the partitioning of an image into sets of pixels that correspond to parts that are coherent in terms of low-level cues such as colors, textures and smoothness of boundaries, has been widely explored in the 90s. Nowadays, semantic image segmentation, i.e. the labeling of each pixel of an image with the category of the object it belongs to, is still a fundamental topic, at the interface of deep learning and computer vision. This research is of broad interest for various applications such as autonomous driving, human-machine interaction or medical image computing to name a few. Contemporary deep networks used for semantic image segmentation (FCN [START_REF] Long | Fully convolutional networks for semantic segmentation[END_REF], DeepLab [START_REF] Chen | Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected CRFs[END_REF], PSPNet [START_REF] Zhao | Pyramid scene parsing network[END_REF]) are variants of networks initially proposed for image classification (AlexNet, VGG net [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF], GoogLeNet [START_REF] Szegedy | Going deeper with convolutions[END_REF], ResNet [START_REF] He | Deep residual learning for image recognition[END_REF]). Most of them are pre-trained for a source task on a largescale database like ImageNet [START_REF] Russakovsky | Imagenet large scale visual recognition challenge[END_REF] and then fine-tuned on a smaller database for a more specific target task like object detection, or specialization like driving scene segmentation. Some form of knowledge is believed to be extracted by learning from large-scale databases of the source task and this knowledge is then transferred to the target task by initializing the network with the pre-trained parameters. However, after fine-tuning, some of the parameters may

The authors are with Sorbonne universités, Université de technologie de Compiègne, CNRS, Heudiasyc Lab., UMR 7253, Compiègne, France.

be quite different from their initial values, resulting in possible losses of general knowledge that may be relevant for the targeted problem. In particular, during fine-tuning, L 2 regularization drives the parameters towards the origin and thereby encourages large deviations of the parameters from their initial values.

In order to help preserve the acquired knowledge embedded in the initial network, we consider using another parameter regularization method during fine-tuning. We argue that the standard L 2 regularization, which drives the parameters towards the origin, is not adequate in the framework of transfer learning where the initial values provide a more sensible reference point than the origin. This simple modification keeps the original control of overfitting, by constraining the effective search space around the initial solution, while encouraging committing to the acquired knowledge. In this paper, we investigate a variant of L 2 penalties using the pretrained model as reference, which we name L 2 -SP because the pre-trained parameters represent the starting point (-SP) of the fine-tuning process. We show that this simple and easy to implement method produces consistent improvement with noticeable effects in segmentation tasks. We present comprehensive experiments using four different deep networks, i.e. FCN, ResNet, and two ResNet-based networks, DeepLab and PSPNet, pre-trained on ImageNet [START_REF] Russakovsky | Imagenet large scale visual recognition challenge[END_REF] and on COCO [START_REF] Lin | Microsoft COCO: Common objects in context[END_REF] for two of them, and fine-tuned on Cityscapes [START_REF] Cordts | The cityscapes dataset for semantic urban scene understanding[END_REF].

II. RELATED WORK

In this section, we recall the existing works dedicated to the improvements of convolutional networks for image semantic segmentation and the existence of similar regularization techniques that were previously applied in different domains.

A. Convolutional networks for segmentation

Besides the success in image classification, convolutional networks have also achieved impressive progress in object detection, e.g. [START_REF] He | Mask r-cnn[END_REF], and segmentation, e.g. [START_REF] Long | Fully convolutional networks for semantic segmentation[END_REF]- [START_REF] Zhao | Pyramid scene parsing network[END_REF], relying on fine-tuning to improve the performance over training from scratch.

Fully convolutional network (FCN) [START_REF] Long | Fully convolutional networks for semantic segmentation[END_REF], based on VGG-16 [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF], is the first end-to-end convolutional network for segmentation. FCN convolutionalizes the fully-connected layers, exploits the spatial information from convolution operations and compensates the loss of information in pooling layers by adding skips from intermediate layers and bilinear interpolations. Residual Network (ResNet) [START_REF] He | Deep residual learning for image recognition[END_REF] is one of the most popular architectures for image classification, and can be lightly modified for segmentation tasks. DeepLab [START_REF] Chen | Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected CRFs[END_REF], constructed on ResNet, integrates dilated convolutional layers (also called as atrous) into the standard ResNet structure, with a fully connected Conditional Random Fields (CRFs) as a post-processing method to improve the segmentation performance. Besides that, DeepLab collects multi-scale features extracted by atrous layers with different scales, to classify pixels in consideration of pixels in a large neighborhood. Similarly, PSPNet [START_REF] Zhao | Pyramid scene parsing network[END_REF] gathers pooled feature maps in different scales, and concatenates them with local feature maps to combine local, global and intermediate-scale information.

All these convolutional networks for segmentation are fine-tuned from the pre-trained weights instead of training from scratch. Fine-tuning is the most popular method for transfer learning tasks, including segmentation tasks, when using deep convolutional networks. The success of transfer learning with convolutional networks relies on the generality of the learned representations that have been constructed from a large open database like ImageNet. Yosinski et al. [START_REF] Yosinski | How transferable are features in deep neural networks?[END_REF] quantified the transferability of these pieces of information in different layers, e.g. the first layers learn general features, the middle layers learn high-level semantic features and the last layers learn the features that are very specific to a particular task. That can be also noticed by the visualization of features [START_REF] Zeiler | Visualizing and understanding convolutional networks[END_REF]. Overall, the learned representations can be conveyed to related but different domains and the parameters in the network are reusable for different tasks.

B. Parameter regularization

Parameter regularization can take different forms in deep learning. L 2 regularization has been used for a long time as a very simple method for preventing overfitting by penalizing the L 2 norm of the parameter vector. It is the usual regularization used in deep learning, including for fine-tuning.

In lifelong learning, where a series of tasks is learned sequentially with a single model with the objective to achieve a good performance on all tasks, and domain adaptation, where the target task is identical to the source task and no (or a small quantity of) target data is labeled, several works attempt to improve the performance by using parameter regularization approaches to preserve pre-trained parameters from source tasks. Li et al. [START_REF] Li | Learning without forgetting[END_REF] proposed to use the outputs of the target examples, computed by the original network on the source task, to define a learning scheme preserving the memory of the source tasks when training on the target task. They also tried to preserve the pre-trained parameters instead of the outputs of examples but without significant effectiveness. Kirkpatrick et al. [START_REF] Kirkpatrick | Overcoming catastrophic forgetting in neural networks[END_REF] developed a similar approach with success, getting sensible improvements by measuring the sensitivity of the parameters of the network learned on the source data thanks to the Fisher information. However, their regularization scheme is designed for lifelong learning tasks and may be thought as being inadequate for inductive transfer learning, where performance is only measured on the target task. Rozantsev et al. [START_REF] Rozantsev | Beyond sharing weights for deep domain adaptation[END_REF] introduced a parameter regularization for keeping the similarity between the pre-trained and the fine-tuned models.

Regularization has been a means to build shrinkage estimators for decades. Shrinking towards zero is the most common form of shrinkage, but shrinking towards adaptively chosen targets has been around for some time, starting with Stein shrinkage (see e.g. [16, chapter 5]), where it can be related to empirical Bayes arguments. In transfer learning, it has been used in maximum entropy models [START_REF] Chelba | Adaptation of maximum entropy capitalizer: Little data can help a lot[END_REF] or SVM [START_REF] Yang | Adapting svm classifiers to data with shifted distributions[END_REF]- [START_REF] Tommasi | Learning categories from few examples with multi model knowledge transfer[END_REF]. These approaches were shown to outperform standard L 2 regularization with limited labeled data in the target task [START_REF] Aytar | Tabula rasa: Model transfer for object category detection[END_REF], [START_REF] Tommasi | Learning categories from few examples with multi model knowledge transfer[END_REF]. These relatives differ from the application to deep networks in several respects, the more important one being that they consider a fixed representation, where transfer learning aims at producing similar classification parameters in that space, that is similar classification rules. For deep networks, transfer aims at learning similar representations upon which classification parameters will be learned from scratch. Hence, even though the techniques we discuss here are very similar regarding the analytical form of the regularizers, they operate on very different objects.

Thus, to the best of our knowledge, we present the first results on segmentation with convolutional networks that are based on the L 2 -SP regularization term described in the following section.

III. REGULARIZERS FOR FINE-TUNING

In this section, we detail the penalties we consider for fine-tuning. When learning from scratch, regularization is aimed at facilitating optimization and avoiding overfitting, by implicitly restricting the capacity of the network, that is, the effective size of the search space. In transfer learning, the role of regularization is similar, but the starting point of the finetuning process conveys knowledge that pertains to the source problem (domain and task). Hence, the network capacity has not to be restricted blindly: the pre-trained model sets a reference that can be used to define the functional space effectively explored during fine-tuning.

Since we are using early stopping, fine-tuning a pre-trained model is an implicit form of inductive bias towards the initial solution. We explore here how a coherent explicit induction bias, encoded by a regularization term, affects the training process. Section IV shows that this such scheme gets an edge over the standard approaches.

Let w ∈ R n be the parameter vector containing all the network parameters that are to be adapted to the target task. The regularized objective function J that is to be optimized is the sum of the standard objective function J and the regularizer Ω(w). In our experiments, J is the negative log-likelihood, so that the criterion J could be interpreted in terms of maximum a posteriori estimation, where the regularizer Ω(w) would act as the log prior of w. More generally, the minimizer of J is a trade-off between the datafitting term and the regularization term.

L 2 penalty: Our baseline penalty for transfer learning is the usual L 2 penalty, also known as weight decay, since it drives the weights of the network to zero:

Ω(w) = α 2 w 2 2 , (1)
where α is the regularization parameter setting the strength of the penalty and • p is the p-norm of a vector. L 2 -SP penalty: Let w 0 be the parameter vector of the model pre-trained on the source problem, acting as the starting point (-SP) in fine-tuning. Using this initial vector as the reference in the L 2 penalty, we get:

Ω(w) = α 2 w -w 0 2 2 . (2)
Typically, the transfer to a target task requires slight modifications of the network architecture used for the source task, such as on the last layer used for predicting the outputs. Then, there is no one-to-one mapping between w and w 0 , and we use two penalties: one for the part of the target network that shares the architecture of the source network, denoted w S , the other one for the novel part, denoted w S . The compound penalty then becomes:

Ω(w) = α 2 w S -w 0 S 2 2 + β 2 w S 2 2 . (3)
We have tested several different forms of regularization approaches on classification tasks [START_REF] Li | Explicit inductive bias for transfer learning with convolutional networks[END_REF] and conclude that for target tasks, L 2 -SP is the most efficient among those regularization approaches that preserve the learned knowledge from source domains (at par with a more complex penalty based on Fisher information). In this article, we prove that on segmentation tasks L 2 -SP also behaves better than the standard L 2 that is currently used.

IV. EXPERIMENTS

We evaluate the L 2 and L 2 -SP penalties on Cityscapes [START_REF] Cordts | The cityscapes dataset for semantic urban scene understanding[END_REF] with several different networks. L 2 -SP can be applied to all layers except new layers, and parameters in new layers are regularized by L 2 penalty as described in Section III.

A. Databases and networks

Source Databases: ImageNet [START_REF] Russakovsky | Imagenet large scale visual recognition challenge[END_REF] and Microsoft COCO [START_REF] Lin | Microsoft COCO: Common objects in context[END_REF] are used as sources. Both of them are large-scale databases: ImageNet for image classification; Microsoft COCO for object detection and semantic image segmentation. Pre-training on ImageNet can largely increase the performance for most transfer learning tasks, moreover pretraining on ImageNet and then on COCO can further raise percentages in segmentation performance. In our experiments, we compare L 2 -SP with the standard L 2 regularization approach using these two pre-training schemes.

Target Database: Cityscapes [START_REF] Cordts | The cityscapes dataset for semantic urban scene understanding[END_REF] is a database of realworld urban driving scenes for segmentation. The database splits 5000 finely labeled images into a training set (2975 images), validation set (500 images) and test set (1525 images). The ground truth of test set is not available on public so in our experiments we train our networks on the training set and evaluate the performance on the validation set. Meanwhile, we have also submitted some of our results on the Cityscapes benchmark to evaluate our method on the TABLE I: Mean IoU scores on Cityscapes. The second column recalls the results obtained in previous works and the two last columns show our results with L 2 and L 2 -SP fine-tuning. Note that the initial models for DeepLab-COCO and PSPNet-COCO are pretrained on ImageNet and then on Microsoft COCO, the other four are only pre-trained on ImageNet. The reported mIoU scores are on the Cityscapes validation set, except for the two scores marked (test set) that have been computed on the Cityscapes test set. Convolutional Networks for Semantic Image Segmentation: FCN [START_REF] Long | Fully convolutional networks for semantic segmentation[END_REF] is one of the most classical structures for segmentation. Deeplab [START_REF] Chen | Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected CRFs[END_REF] and PSPNet [START_REF] Zhao | Pyramid scene parsing network[END_REF] stayed for some time on the top of the Cityscapes benchmark and are two favored structures. Unfortunately, we do not have enough GPU resources to perfectly reproduce the performance of PSPNet, as explained in the training details. Nonetheless, our experimental work here focuses on four quite diverse structures of networks, FCN, the standard ResNet-101, DeepLab, and PSPNet for demonstrating the consistency of L 2 -SP.

L 2 in [2], [3], [9] L 2 L 2 -

B. Training details

All images in Cityscapes are color images. All training examples are pre-processed as follows: we subtract the mean activity computed over the training set from each channel, then we adopt random blur, random mirror and random crop for data augmentation. The network parameters are regularized using the two techniques as described in Section III. We have also separated all weights to w S and w S for L 2 , using α and β respectively as regularization hyperparameters. According to experiments in [START_REF] Li | Explicit inductive bias for transfer learning with convolutional networks[END_REF], we tried {10 -2 , 10 -3 , 10 -4 } for α and {10 -3 , 10 -4 } for β. Regarding testing, we compute the mean intersection-over-union metric (mIoU) score [START_REF] Cordts | The cityscapes dataset for semantic urban scene understanding[END_REF] over 19 classes in Cityscapes and we do not make use of further post-processing methods to improve the performance. Stochastic gradient descent with momentum 0.9 is used for optimization. We set the learning rate as large as possible, provided the loss can decrease in the first iterations. For FCN, we do not decrease the learning rate as suggested in [START_REF] Long | Fully convolutional networks for semantic segmentation[END_REF]. For ResNet based networks, we use the polynomial learning rate policy as in [START_REF] Chen | Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected CRFs[END_REF], [START_REF] Zhao | Pyramid scene parsing network[END_REF]. The batch size is 2 and image crops have the size of 800×800 except for PSPNet. In order to stabilize the statistics of batch normalization layers, for PSPNet, we use 16 examples in a mini-batch with image crops of 624×624 pixels. All experiments are performed with Tensorflow [START_REF] Abadi | TensorFlow: Largescale machine learning on heterogeneous systems[END_REF].

C. Results

We reproduce the experiments of [START_REF] Chen | Deeplab: Semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected CRFs[END_REF], [START_REF] Zhao | Pyramid scene parsing network[END_REF], [START_REF] Cordts | The cityscapes dataset for semantic urban scene understanding[END_REF] that use the standard L 2 fine-tuning, and compare with L 2 -SP fine-Fig. 1: Comparisons of L 2 -SP and L 2 on three images from the Cityscapes validation set. The first column shows the original image above its ground truth segmentation (overlayed colors encode semantic classes [START_REF] Cordts | The cityscapes dataset for semantic urban scene understanding[END_REF], the black color is not included in any evaluation and is treated as void). Columns 2 -5 present four different networks: FCN, DeepLab-COCO, PSPNet, PSPNet-COCO. On the first line, segmentation results with L 2 , and on the second line with L 2 -SP. Pixels that are correctly classified keep their ground truth color. Pixels that are incorrectly classified are set to white (a 100% accuracy segmentation result should not contain any white pixel).

Ground Truth

FCN DeepLab-COCO PSPNet PSPNet-COCO L 2 L 2 -SP L 2 L 2 -SP L 2 L 2 -SP
tuning, all other setup parameters being unchanged. The results, computed on the validation set of Cityscapes, are reported in Table I. PSPNet is the only network we could not perfectly reproduce because we had to use smaller input images compared to [START_REF] Zhao | Pyramid scene parsing network[END_REF], due to our limited computational ressources. We readily observe that fine-tuning with L 2 -SP in place of L 2 consistently improves the performance in mean IoU score, for all networks. Several examples are shown in Figure 1. The three images displayed in Figure 1 belong to the validation set. They were chosen so as to display the dissimilarity between the two regularization approaches for the best performing model. More precisely, they have large difference in mean IoU score between PSPNet-COCO-L 2 and PSPNet-COCO-L 2 -SP. We also include the segmentations obtained for three other models for comparison purposes.

Table II show the per-class results and we can see that fine-tuning with L 2 -SP maintains the scores in easy classes like road, building, vegetation, sky etc, but also improves the performance in those difficult but important classes, like people and vehicles. Some image details centered on certain objects are shown in Figure 2. Images in Figure 2 are chosen in the same way as Figure 1.

Table I and II report the results evaluated on the validation set. Table III shows the results on the test set. The numerical results in Table III have been submitted to the Cityscapes evaluation server, and will be made public on the official website.

D. Analysis and discussion

1) Theoretical insights: Analytical analyses are very difficult in the deep learning framework. Under some (highly) simplifying assumptions, the effect of L 2 regularization can be analyzed by doing a quadratic approximation of the objective function around the optimum [23, Section 7.1.1]. This analysis shows that L 2 regularization rescales the parameters along the directions defined by the eigenvectors of the Hessian matrix. This scaling is equal to λ i /(λ i + α) for the i-th eigenvector of eigenvalue λ i . A similar analysis can be used for the L 2 -SP regularization.

We recall that J(w) is the unregularized objective function, and J(w) = J(w) + α ww 0 2 2 is the regularized objective function. Let w * = argmin w J(w) and w = argmin w J be their respective minima. The quadratic approximation of J(w * ) gives

H( w -w * ) + α( w -w 0 ) = 0 , (4)
where H is the Hessian matrix of J w.r.t. w, evaluated at w * . Since H is positive semidefinite, it can be decomposed as H = QΛQ T . Applying the decomposition to Equation (4), we obtain the following relationship between w and w * :

Q T w = (Λ + αI) -1 ΛQ T w * + α(Λ + αI) -1 Q T w 0 . (5)
We can see that with L 2 -SP regularization, in the direction defined by the i-th eigenvector of H, w is a convex combination of w * and w 0 in that direction since λ i /(λ i + α) and This contrasts with L 2 that leads to a compromise between w * and the origin. Clearly, searching a solution around the pre-trained parameter vector is intuitively much more appealing, since it is the actual motivation for using the pre-trained parameters as the starting point of the fine-tuning process. Hence, the regularization procedures resulting in the compromise with the pre-trained parameter encode a penalty that is coherent with the original motivation.

2) Coherent motivation from shrinkage estimation: Using L 2 -SP instead of L 2 can also be motivated by an analogy with shrinkage estimation see e.g. [16, chapter 5]. Although it is known that shrinking toward any reference is better than raw fitting, it is also known that shrinking towards a value that is close to the "true parameters" is more effective. The notion of "true parameter" is not applicable to deep networks, but the connection with Stein shrinking effect may be inspiring by surveying the literature considering shrinkage towards other references, such as linear subspaces. In particular, it is likely that manifolds of parameters defined from the pretrained network would provide a better reference than the single parameter value provided by the pre-trained network.

3) Computational efficiency: L 2 -SP penalty introduces no extra parameters, and only increases slightly the computational burden, by less than 1% of the number of floating point operations of ResNet-101. At little computational cost, we can thus obtain 1∼2% improvements in mIoU score, and no additional cost is experienced at test time.

4) Proportion of new parameters: Most layers of the network used for segmentation were pre-trained on a classification task, but for solving the segmentation tasks, some changes in the network are necessary. All the networks evaluated in this paper require new layers and thereby new parameters for solving the Cityscapes segmentation task. However, the ratio of new parameters is quite different among the four networks: FCN has less than 0.1% new parameters, ResNet-101 has 0.1%, DeepLab 3.4% and PSPNet 37.5%. Since new parameters are penalized with L 2 , the proportion of new parameters reduces the relative effect of L 2 -SP. This is visible with PSPNet: the scores of several classes are degraded despite one percent improvement in average. As for PSPNet-COCO, only five classes are moderately degraded. We argue that most new parameters in the PSPNet model were trained on Microsoft COCO and can be used as reference when training on Cityscapes, so the effect of L 2 -SP remains. Note that DeepLab models are different from PSPNet in architecture, and training on COCO does not reduce the proportion of new parameters. So when using the two DeepLab models, the trends of L 2 -SP, compared with L 2 , are both positive.

V. CONCLUSION

In this paper, we described and tested a variant of the L 2 penalty, L 2 -SP, that uses pre-trained model parameters as a reference to encode an explicit bias towards the solution learned on a source task. The L 2 -SP penalty has been already used for other purposes but we demonstrate here its relevance in segmentation tasks with different deep convolutional networks, through an evaluation on the Cityscapes database. This penalty is very simple to implement and quite more effective than the standard L 2 penalty that is currently used in fine-tuning. We also provide theoretical hints motivating L 2 -SP by the effective hypothesis space explored during optimization and shrinkage estimation. We recommend this simple L 2 -SP scheme as the legitimate baseline fine-tuning strategy for segmentation tasks.

  98.4 84.6 92.1 45.6 53.1 63.2 71.2 75.3 93.0 71.5 95.1 84.1 65.9 95.0 61.0 74.3 62.8 64.0 73.9 74.9 PSPNet.L 2 -SP 98.3 83.8 92.0 50.7 53.5 61.0 68.5 73.5 92.9 71.5 94.9 83.3 65.8 95.0 66.2 73.9 66.3 63.0 72.8 75.1 PSPNet-COCO.L 2 98.5 85.5 92.7 53.5 57.5 65.7 74.2 77.9 93.4 73.1 95.4 86.0 69.4 95.7 59.2 73.5 63.6 69.7 76.2 76.9 PSPNet-COCO.L 2 -SP 98.5 85.0 92.7 53.3 58.0 64.4 73.0 77.3 93.4 72.2 95.3 85.7 69.2 95.5 63.7 73.6 69.9 68.9 75.8 77.1

Fig. 2 : 2 L 2

 222 Fig. 2: Comparisons of L 2 -SP and L 2 : zoom on some object classes like rider, person, and different kinds of vehicles. Images are from the validation set and pixels are colored in the same way as in Figure 1. Ground Truth FCN DeepLab-COCO PSPNet PSPNet-COCO

TABLE II :

 II IoU scores for each object class of the Cityscapes Validation set. *-COCO means that the model is first pre-trained on ImageNet and then on Microsoft COCO. road sidew. build. wall fence pole t.light t.sign veg. ter. sky pers. rider car truck bus train m.bike bike mIoU FCN.L 2 97.1 79.1 89.2 36.6 48.7 51.9 57.5 69.5 90.7 58.1 92.4 75.1 51.5 91.8 46.8 69.5 48.3 47.5 70.5 66.9 FCN.L 2 -SP 97.1 79.0 89.4 42.8 49.4 55.0 59.9 71.1 90.8 56.8 90.6 75.3 51.0 92.2 49.1 70.2 50.6 48.6 71.3 67.9 ResNet-101.L 2 97.4 79.9 90.3 44.8 48.7 52.8 58.9 68.6 91.3 58.5 92.7 76.4 52.0 92.3 49.0 66.1 48.9 52.4 72.6 68.1 ResNet-101.L 2 -SP 97.5 80.7 90.6 45.4 50.2 54.0 61.9 70.8 91.4 58.8 93.2 77.0 52.8 92.7 49.9 66.4 45.8 53.9 73.3 68.7 PSPNet-COCO.L 2 -SP 98.2 85.5 92.5 52.0 61.5 65.2 72.1 80.0 92.6 65.6 94.7 83.9 65.8 95.5 82.6 89.0 78.9 67.2 78.7 79.0

	DeepLab.L 2	97.3 79.7 90.3 49.0 50.4 51.8 55.1 66.2 90.8 57.9 93.1 75.3 51.2 92.1 52.7 70.8 56.4 53.4 70.2 68.6
	DeepLab.L 2 -SP	97.4 80.2 90.7 48.7 52.5 53.4 58.4 68.2 91.0 59.0 93.5 76.3 54.0 92.5 58.4 74.5 62.7 53.4 71.5 70.3
	DeepLab-COCO.L 2	97.6 81.5 90.9 46.8 50.4 54.4 61.2 71.6 91.2 59.7 93.4 78.0 56.5 93.3 67.8 81.3 62.8 56.5 73.0 72.0
	DeepLab-COCO.L 2 -SP 97.6 81.2 90.9 48.0 51.4 54.2 60.8 70.9 91.2 60.3 93.3 78.3 57.5 93.6 71.9 84.1 72.4 59.3 73.5 73.2
	PSPNet.L 2	98.0 84.0 92.0 46.3 57.8 64.0 71.0 78.1 92.3 64.2 94.6 81.7 61.7 94.8 68.7 80.3 54.2 65.0 77.6 75.1
	PSPNet.L 2 -SP	97.9 83.4 91.8 50.5 55.2 61.9 68.3 76.8 92.3 65.0 94.3 80.7 61.7 94.8 74.6 84.2 70.1 65.6 76.7 76.1
	PSPNet-COCO.L 2	98.2 85.3 92.4 46.2 58.7 65.8 72.7 80.5 92.4 64.8 94.7 83.7 64.0 95.5 81.3 87.2 71.7 67.8 78.8 78.0

TABLE III :

 III IoU scores for each object class of the Cityscapes Test set. *-COCO means that the model is first pre-trained on ImageNet and then on Microsoft COCO. road sidew. build. wall fence pole t.light t.sign veg. ter. sky pers. rider car truck bus train m.bike bike mIoU DeepLab-COCO.L 2 97.9 81.1 90.6 42.0 45.8 53.1 61.3 68.0 91.8 68.6 94.1 80.2 58.3 93.8 54.4 64.3 59.6 58.9 69.2 70.2 DeepLab-COCO.L 2 -SP 97.9 81.2 90.6 42.8 47.2 53.1 60.8 67.9 91.8 68.7 94.2 80.5 59.9 94.0 56.4 66.1 61.9 60.2 69.6 70.8

	PSPNet.L 2

Acknowledgements: This work was carried out within SIVALab, a joint laboratory between Renault and Heudiadyc CNRS/UTC Lab., with the support of the China Scholarship Council. We acknowledge the support of NVIDIA Corporation with the donation of the GPUs used for this research.


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DFT investigation of methane metathesis with L 2 AnCH 3 actinide complexes catalysts (L = Cl, Cp

Keywords: C-H bond activation, Actinide complexes, DFT calculations, Reaction mechanism

In order to understand the catalytic activity of the actinide complexes L 2 AnCH 3 (An = Ac, Th, Pa, U, Np and Pu; L = Cl, Cp and Cp*) towards the activation of the C-H bond of methane, relativistic ZORA/DFT investigations have been carried out. The results obtained from Linear Transit (LT) and Intrinsic Reaction Coordinate (IRC) calculations show that the mechanism involved in these reactions starts with a proton transfer from methane to the methyl group of the complex leading to the formation of a four center transition state characteristic of a bond metathesis process. The U(III) and Np(III) complexes exhibit a high ability to activate the methane C-H bond, the activation energies being respectively equal to 10.5, 17.1 and 21.0 kcal/mol for Cl 2 NpCH 3 , Cp 2 NpCH 3 and Cp* 2 UCH 3 respectively whereas the Th(III) complexes exhibit the highest activation energy, 34.9 kcal/mol for Cp* 2 ThCH 3 . Since the initial step of the reaction is viewed as a proton transfer, the analysis of the charges evolution and frontier molecular orbitals of the complexes and the transition states, shows that a facile polarization of the bonds involved in the reaction has the effect of reducing the activation energy. The role of the metallic 5f orbitals in the reactivity of the L 2 AnCH 3 compounds towards CH 4 is analyzed and discussed. More important the 5f actinide orbital contribution, less important is the activation energy.

Introduction

The potential catalytic reactivity of metallic compounds leading to the functionalization of alkane C-H bonds [START_REF] Labinger | Understanding and exploiting C-H bond activation[END_REF][START_REF] Jia | Conversion of alkanes to linear alkylsilanes using an iridiumiron-catalyzed tandem dehydrogenation-isomerization-hydrosilylation[END_REF] presents important applications in the chemical industry with financial and environmental benefits. It allows the conversion of saturated hydrocarbons into value-added chemicals products. Thus, such bonds activation by organometallic compounds has been an attracting and fascinating subject for a long time since the discovery of the role of the transition metal mediation in the activation of the C-H [3-7] as well as C-F [START_REF] Aizenberg | Catalytic Activation of Carbon-Fluorine Bonds by a Soluble Transition Metal Complex[END_REF][9], C-C, and H-H [START_REF] Kubas | Molecular hydrogen complexes: coordination of a sigma bond to transition metals[END_REF] strong bonds reminding their high bonding energy, about 100 kcal/mol for C-H. Among the pioneers in this area, Janowicz and Bergman [START_REF] Janowicz | Activation of carbon-hydrogen bonds in saturated hydrocarbons on photolysis of (ɳ 5 -C 5 Me 5 )(PMe 3 )IrH 2[END_REF] reported in 1982 the C-H additive-oxidative activation by the iridium complex (Cp*)(PMe 3 )IrH 2 in a high yield photolysis of a saturated hydrocarbon (R-H) solution at room temperature leading to the formation of the hydrido alkyl complex (Cp*)(PMe 3 )Ir(R)(H). Since then, investigations were carried out, not only on the reactivity of the transition metal ions/complexes toward C-H bonds [START_REF] Stahl | Homogeneous Oxidation of Alkanes by Electrophilic Late Transition Metals[END_REF][START_REF] Niu | Inter-and Intramolecular C-H Activation by a Cationic Iridium(III) Center via Oxidative-Addition Reductive-Elimination and σ-Bond Metathesis Pathways[END_REF][START_REF] Bromberg | The Mechanism of a C-H Bond Activation Reaction in Room-Temperature Alkane Solution[END_REF][START_REF] Rothwell | Carbon-hydrogen bond activation in early transition metal systems[END_REF][START_REF] Balcells | C-H Bond Activation in Transition Metal Species from a Computational Perspective[END_REF] but also on those involving f-block metal ones [17]. Thus, in 1983, Watson et al [START_REF] Watson | Facile C-H activation by lutetium-methyl and lutetium-hydride complexes[END_REF] showed the role of the Lu(Cp*) 2 R (R = CH 3 , H) complex mediation in the activation of various sp 2 and sp 3 C-H bonds as well as the sp 3 C-H bond of methane.

Activation of these inert bonds by organometallic complexes occurs via different modes like oxidative addition, 1,2-addition, σ-complex-assisted mechanism (σ-CAM) and electrophilic processes [19][START_REF] Gretz | Carbon-hydrogen bond activation by electrophilic transition-metal compounds. Palladium(II)-mediated oxidation of arenes and alkanes including methane[END_REF][START_REF] Bergman | A physical organic road to organometallic C-H oxidative addition reactions[END_REF]. The mainly known and most common mode especially for C-H bond activation by lanthanide and actinide complexes is the sigma-bond metathesis which involves a four centers transition state without change of the metal oxidation state [START_REF] Perrin | Lanthanide complexes: electronic structure and H-H, C-H and Si-H bond activation from a DFT perspective[END_REF]. Indeed, using DFT/B3PW91 calculations for the study of the CH 4 activation by the (Cp 2 ) * LnMe complex where Cp * is modeled by Cl and Ln is a lanthanide atom, Maron and coworkers [START_REF] Maron | DFT study of CH 4 activation by d 0 Cl 2 LnZ (Z = H, CH 3 ) complexes[END_REF] demonstrated that the overall reaction was sigma-bond metathesis which proceeds via proton transfer between two anionic groups near the lanthanide center [START_REF] Waterman | σ-Bond Metathesis: A 30-Year Retrospective[END_REF].

Regarding actinide complexes, few experimental studies [START_REF] Siladke | Actinide Metallocene Hydride Chemistry: C-H Activation in Tetramethylcyclopentadienyl Ligands to Form [μ-η 5 -C 5 Me 3 H(CH 2 ) -κC] 2-Tuck-over Ligands in a Tetrathorium Octahydride Complex[END_REF][START_REF] Peters | C-H Bond Activation with Actinides: The First Example of Intramolecular Ring Bite of a Pentamethylcyclopentadienyl Methyl Group[END_REF] and less theoretical studies related to the activation of C-H bonds have been reported [27]. The experimental investigation performed by Kiplinger and coworkers [START_REF] Kiplinger | sp 3 versus sp 2 C-H bond activation chemistry of 2-picoline by Th(IV) and U(IV) metallocene complexes[END_REF] highlighted the sp 3 and sp 2 C-H bonds activation by Th(IV) and U(IV) metallocene complexes respectively which were rationalized theoretically using DFT (B3LYP) computations by Yang et al [START_REF] Yang | Theoretical Studies of the sp 2 versus sp 3 C-H Bond Activation Chemistry of 2-Picoline by (C 5 Me 5 ) 2 An(CH 3 ) 2 Complexes (An = Th, U)[END_REF]. Otherwise, the study of the reactivity of Ac + -Pu + actinide cations toward methane C-H bond in gas phase, using a DFT approach, has been reported by Almeida et al [START_REF] De Almeida | Gas phase methane activation by the Ac + -Pu + ions: theoretical insights into the role of 5f electrons/orbitals in early actinide chemistry[END_REF].

In order to clarify the potential catalytic activity of different actinide complexes towards CH 4 C-H bond activation and the role of the various ligands, we have undertaken a DFT study of the reaction L 2 AnCH 3 + CH 4 (L = Cl (chlorine), Cp (cyclopentadienyl), Cp* (pentamethylcyclopentadienyl); An = Ac, Th, Pa, U, Np, Pu). The analysis of the obtained results and the comparison with those involving lanthanide complexes should provide an understanding of the reaction process, the ability of the actinide complexes to activate the methane C-H bond as well as the role of the ligand (Cl, Cp et Cp*) on these reactions. The role of the 5f electrons of the actinide ions in the reaction will be also investigated.

Computational details

For all the studied complexes, the calculations were performed using Density Functional Theory (DFT) [START_REF] Hohenberg | Inhomogeneous electron gas[END_REF][START_REF] Kohn | Self-consistent equations including exchange and correlation effects[END_REF][START_REF] Parr | Density-Functional Theory of Atoms and Molecules[END_REF], scalar relativistic corrections being introduced via the zeroth-order regular approximation (ZORA) [START_REF] Van Lenthe | Relativistic regular two-component Hamiltonians[END_REF][START_REF] Van Lenthe | Relativistic total energy using regular approximations[END_REF][START_REF] Van Lenthe | Geometry optimizations in the zero order regular approximation for relativistic effects[END_REF] to the Dirac equation. Solvent effects (tetrahydrofuran, THF) have been accounted using the conductor-like screening model (COSMO) [37], as implemented in the employed Amsterdam Density Functional (ADF2014.01) program package, which is well suited for the study of the electronic structure and reactivity of actinide molecular systems [START_REF] Fonseca | Towards an order-N DFT method[END_REF][START_REF] Velde | Chemistry with ADF[END_REF][START_REF] Adf | SCM, Theoretical Chemistry[END_REF]. The Vosko-Wilk-Nusair functional (VWN) [START_REF] Vosko | Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis[END_REF] for the local density approximation and the gradient corrections for the exchange and correlation of Becke and Perdew, respectively, i.e., the BP86 functional [42-43] have been used. Geometry optimizations which have been carried out at the scalar relativistic level were followed by single point computations including spin-orbit coupling. In this work, we used for all atoms a triple-ζ Slater-type valence orbitals augmented by one set of polarization functions, i.e. the triple-zeta polarized (TZP) basis set, taken from the ADF/ZORA/TZP database directory. The spin unrestricted DFT formalism is used for the open-shell systems.

The frozen-core approximation, where the core density is obtained from four component Dirac-Slater calculations, has been applied for all atoms; the electronic cores 1s and 1s/2s/2p were frozen for the elements carbon (C.1s) and chlorine (Cl.2p) respectively. The atomic basis sets of the heavy element An, include the valence 5f/6s/6p/6d/7s/7p shells, were considered according to the "medium core" approximation (An.5d). Numerous theoretical studies have shown that the ZORA/BP86/TZP approach reproduces the experimental geometries and ground-state properties of f-element complexes with a satisfying accuracy [START_REF] Ricciardi | Electronic structure, chemical bond, and optical spectra of metal bis (porphyrin) complexes: a DFT/TDDFT study of the bis (porphyrin) M (IV) (M= Zr, Ce, Th) series[END_REF][START_REF] Kaltsoyannis | Recent developments in computational actinide chemistry[END_REF][46][47].

In this study, we carried out first the full geometry optimizations of the species under consideration, in the gas phase, at the spin unrestricted level. Next, the geometries were re-optimized in the solvent (THF) using the COSMO model. We used the non-default Delley type of cavity [37b], the solvent being considered with its relative dielectric constant of 7.58 and its effective cavity radius of 3.18 Å. Then, our complexes being f-element species, where spin-orbit corrections are expected to be important, single-point calculations including spinorbit coupling were done using the previously optimized geometries, for both the gas phase and the solution.

Through an harmonic vibrational frequency analysis, the stationary points on the potential energy surface (PES) identified via linear transit (LT) calculations performed for all L 2 AnCH 3 + CH 4 reactions, were confirmed to be equilibrium structures (all normal modes have real frequencies, NIMAG = 0), or transition states (TSs) characterized by one normal mode with an imaginary frequency (NIMAG = 1). The character of the normal mode associated with the imaginary frequency was analyzed to ensure that the correct transition state was found. The connectivity between the stationary points was established by intrinsic reaction coordinate (IRC) calculations [START_REF] Gonzalez | An improved algorithm for reaction path following[END_REF] to check the connections of the first-order saddle points with the local minima found on the PES. The zero-point vibration energy (ZPVE) contributions have been included in the computed free energies at T = 298.15 K. The activation energies ∆G # are then calculated as the free energy differences between the transition state and the reactant (∆G # = ∆G(TS) -∆G(reactants)), whereas the enthalpy barriers represent the enthalpy differences between the transition state and the reactant (∆H # = ∆H(TS) -∆H(reactants)), and the electronic activation energies ∆E # corresponds to the total bonding energies (TBEs) differences (∆E # = TBE(TS) -TBE(reactants)) between the transition state and the reactants, reminding that the ADF program computes TBEs of the considered species instead of their energies.

Finally, the Mulliken populations and Hirshfeld analyses were carried out to follow the charge transfers during the chemical reactions.

The computational exploration of f-block element compounds reactivity is a difficult task owing to the fact that it often involves open shell systems, with spin contamination and SCF convergence problems. It should be noted that in our case, we checked that all species occurring during the L 2 AnCH 3 + CH 4 reaction process (reactants, TSs and products) exhibit a negligible spin contamination (deviation less than 3% between the computed values <S 2 > of the squared spin operator and the exact ones).

Results and discussion

Preliminary calculations

In order to verify the reliability of the methodology used in the present work, the C-H bond activation by actinide complexes (Cp) 2 An(Me) 2 with An = U and Np have been explored in order to compare our results to the previous studies involving the same complexes and the same reactions [START_REF] Castro | Are 5f Electrons Really Active in Organoactinide Reactivity? Some Insights from DFT Studies[END_REF]. In these studies, Castro et al. used a DFT approach with the B3PW91 functional validated by CASSCF (complete active space SCF) computations. The same methodology was used by Barros et al. [START_REF] Barros | Single but stronger UO, double but weaker UNMe Bonds: The tale told by Cp 2 UO and Cp 2 UNR[END_REF] to the study of the reaction of Cp 2 UNMe and Cp 2 UO with MeC≡CMe and H 3 Si-Cl. By comparing the results obtained with the multireference calculations (CAS (2,7) for U and CAS (3,7) for Np) to those obtained by DFT approach, the authors observed that these systems do not exhibit significant multireference character, only one configuration is dominant with a weight practically equal to 100 % The obtained results using our (ZORA/BP86) approach on (Cp) 2 An(Me) 2 complexes are reported on Figure 1 where the structures of the reactants and TSs are displayed. Concerning the reactivity of (Cp) 2 U(Me) 2 with methane as well as the reaction involving (Cp) 2 Np(Me) 2 , the geometrical parameters of the reactant and the TS are in good agreement with those obtained by Castro et al. (Geometrical coordinates are given in SI 1). As it can be seen, the calculated U-C2 bond lengths in the reactant and TS are 2.40 and 2.60 Å respectively, close to those of Castro and coworkers, respectively 2.40 and 2.65 Å. The activation energies ∆G # of the Cp 2 AnMe 2 + CH 4 reaction with An = U and Np are found to be equal to 34.8 kcal/mol and 32.6 kcal/mol respectively whereas the previous study of Castro estimates these activation energies around 41.7 kcal/mol and 39.6 kcal/mol respectively, noting that the energy difference between the two actinide complexes is the same in both calculations.

To conclude, our ZORA/BP86 approach leads to very similar results to those previously published, and can then be used in the study of the reactivity of L 2 AnCH 3 (L = Cl, Cp and Cp*) complexes toward the methane molecule. + CH 4 . Distances in angstroms (Å) and angles in degrees (°). Values of reference [START_REF] Castro | Are 5f Electrons Really Active in Organoactinide Reactivity? Some Insights from DFT Studies[END_REF] between parentheses.

L 2 AnCH 3 complexes

Optimized geometries

The geometries of the L 2 AnCH 3 complexes where An = Ac, Th, Pa, U, Np, and Pu and L = Cl, Cp, and Cp* have been fully optimized in the gas phase and in the solvent THF, at the spin-unrestricted level of theory. All compounds were considered without any symmetry constraints. We have considered different possible spin states for each complex. The optimized geometries determined in both the gas phase and THF solvent have been verified as minima by vibration frequencies calculation.

The overall symmetry of the optimized structures has been found similar for all actinide complexes. As an example we display on Figure 2 the optimized geometries of the uranium complexes. The ground state optimized geometrical parameters of the Cl 2 AnCH 3 and Cp 2 AnCH 3 (with An = Ac, Th, Pa, U, Np and Pu) complexes are reported in Table 1. 2 In this series of complexes, the results show that the variation of the An-Cl distance is not equal to the contraction of the An(III) ionic radius. Indeed, the M-Cl distance decreases from Ac to U by 0.156 Ǻ for an ionic contraction equal to 0.090 Å; the U-Cl, Np-Cl and Pu-Cl distances are calculated to be very close. The observed differences do not exceed 6.10 -3 Ǻ for a contraction of the ionic radius equal to 0.033 Ǻ. A slightly different trend is observed in the case of the An-C distance with the exception of the Cl 2 PaCH 3 complex which has the smallest An-C bond (2.349 Ǻ). A bond length shortening of 0.179 Ǻ is observed going from Ac to Pu for a contraction of the ionic radius equal to 0.125 Ǻ. However, like the An-Cl distances, the U-C, Np-C and Pu-C distances are very close; the calculated differences do not exceed 5.10 -3 Ǻ. This trend is in accordance with the Nalewajski-Mrozek (NM) bond orders [51] where the values of the An-Cl and An-C bond indices, increase from 1.023 to 1.303 and from 0.870 to 1.039 respectively, in accordance with the decrease of the corresponding distances from Ac to Pa, then these values decrease insignificantly until Np (1.234 and 0.999). Pu complex presents the lowest bond indices (0.648 and 0.738 respectively) (Full NM bond orders are in SI.6).

The structures of Cl 2 AnCH 3 complexes have more or less pyramidal geometries as indicated by the sum of the bond angles An-Cl and An-C, except the complex Cl 2 ThCH 3 which has a planar triangular geometry as indicated by the value of the sum of its bonding angles (equal to 360 °).

In the case of Cp When the Cp ligand is substituted by the Cp* ligand, we note a very slight increase in the An-C distances. Its variation throughout the series of complexes remains unchanged. On the other hand, the Cp*-An-Cp* angle is greater than the Cp-An-Cp one with a maximum deviation equal to 23.9° in the case of the Pa complex. This is probably due to the steric hindrance effect due the methyl groups of the Cp*. The effect of the solvent on these neutral complexes is not important. There is only a slight decrease of the An-C (Cp*) distances. Indeed, with the exception of the Ac complex, the distance An-C(CH 3 ) increases by 0.02 Å. The angle Cp*-An-Cp* is almost invariant, the whole geometric parameters are given in SI.3. Generally, the total bonding energies (TBEs) of Cl 2 AnCH 3 complexes in their high spin ground states are of the same order of magnitude, although they decrease from the Ac complex (-31.521 eV) to the Np one (-34.640 eV) in accordance with the number of unpaired electrons, in other words with the number of 5f electrons. When the Cl ligand is substituted by the Cp or Cp* ligand, the TBE variation still remain the same in the two series of complexes.

The TBEs of all complexes, including the solvent effects and spin-orbit corrections are given in Table SI.5 as well as the discussion of these values.

Charge and frontier molecular orbital (FMO) analysis

In order to investigate the electronic structure of the L 2 AnCH 3 complexes, in particular the metal-ligand interactions, Mulliken populations (MPA) and Hirshfeld [START_REF] Hirshfeld | Bonded-atom fragments for describing molecular charge densities[END_REF] charges analyses were carried out. For example, in Table 2 are given the net charges of the metal, the CH 3 group and Cl ligand of Cl 2 AnCH 3 complexes as well as the metal spin population (MSP) which is given by the difference between the total spin populations α and β of the metal, for the Ac, Th, Pa, U, Np and Pu complexes. The ligand-to-metal donation is evidenced by the net MPA charge of the metal, varying from 0.92 for Pa complex to 1.29 for Ac complex, which is much lower than its ionic charge +3. As indicated by the negative charge of the CH 3 fragments the metal-methyl bond exhibits some ionic character. A detailed charge analysis is reported in SI.6. Moreover, Hirshfeld analysis leads to lower net charges compared to MPA ones.

In order to highlight the role of the orbitals of the actinide atom, particularly that of the valence shell in the studied complexes, a frontier molecular orbital (FMO) analysis was undertaken. In particular, we will focus on the highest single occupied molecular orbital (SOMO or HOMO) and the lowest unoccupied molecular orbital (LUMO).

The FMO diagram of Cl 2 AnCH 3 is displayed in Figure 3 (the full diagrams of all complexes with different ligands are given in SI.7). The energies of these FMOs are given with the percentages d/f/An/L representing the percentage weights of the d and f orbitals, as well as those of actinide atoms and all ligands L (L 2 + CH 3 ). All the FMOs of the Pa, U, Np and Pu complexes are of predominantly 5f metallic character with a minor contribution of the ligands An +3 Spin population Mulliken - (Hirshfeld) in the first three complexes (less than or equal to 3.7%) and a significant contribution (10%)

to the LUMO in the last complex.

The FMOs of Th complex are mainly localized on the metal atom. The contribution of the 5f orbitals is negligible in the SOMO (1.9%) and is important in the LUMO (52.4%).

In the Cl 2 AcCH 3 complex, the SOMO is delocalized on the metal center and the carbon of the methyl group with a greater participation of the latter (61.4%). The LUMO has a majority metallic character (92.3%).

Methane C-H bond activation by L 2 AnCH 3 complexes

The activation reaction of the C-H bond of methane CH 4 by the actinide complexes was studied in the gas phase and in THF solution at the same level of theory, namely using DFT/ZORA/BP86/TZP calculations. The balance equations are given in scheme 1:

Scheme 1 (the bold blue color to indicate the transferred methyl group from methane to the complex).

This reaction, also called Watson exchange, was observed for the first time with the complex (Cp*) 2 Lu(III)Me [START_REF] Watson | Facile C-H activation by lutetium-methyl and lutetium-hydride complexes[END_REF].

Transition state geometries

The linear transit (LT) approach was performed in order to identify the transition states on the PES for all reactions between

Energy profiles

These reactions correspond to a methyl exchange so that the difference in free energies between the reactants and the product is equal to zero (∆G° = 0 kcal/mol). Activation energies ∆G # were calculated as the free energy difference between the transition state and the The results show that the highest value of activation energy relative to a given series of complexes is obtained for the Th complex regardless the ligand. The The comparison between the two series of complexes Cl 2 AnCH 3 and (Cp*) 2 AnCH 3 shows that the difference between the activation energies increases with the decrease of the ionic metal radius and it varies between 4.4 kcal/mol for Ac and 7.5 kcal/mol for Pu. For the two series of complexes Cp 2 AnCH 3 and (Cp*) 2 AnCH 3 , this difference oscillates around the value of 3.9 kcal/mol for Ac, Pa, U and Pu and it takes the limit value of 6.1 kcal/mol in the case of Th. Methyl groups of the cyclopentadienyl rings have a more or less steric influence.

However, the L 2 NpCH 3 complexes (L = Cl, Cp and Cp*) remain the exception with the highest differences (6.62, 14.65 and 8.03 kcal/mol respectively).

Concerning the (Cp*) 2 AnCH 3 + CH 4 reaction, the influence of the solvent on the activation energies is rather weak except for the (Cp*) 2 UCH 3 complex which exhibits an increase of the order of 3.8 kcal/mol of the activation energy compared to the gas phase. Not surprisingly the activation energies are unaffected by the spin-orbit corrections (SOCs). In fact, according to Table 5 where the SOC energies of the different species (reactants and transition states) related to (Cp*) 2 AnCH 3 complexes as well as the activation energy with and without SOC (values within parentheses) are reported, the activation energies still have the same magnitude compared to those without SOC because both the reactants and the transition states are affected in the same way by SOC. The influence of the oxidation state of the L 2 AnCH 3 (L = Cl, Cp and An = Th, Pa, U, Np and Pu) reactants on their reactivity toward methane has also been studied considering the oxidation state IV which is also common to the actinides (the detailed calculations are displayed in SI.8 and SI.9). In the Cl 2 AnCH 3 series of complexes, the Th and the Pa complexes still remain the less reactive but with lower barrier values, 17.4 and 14.2 kcal/mol respectively, than those with oxidation number III whereas the U, Pu and Np complexes are the more reactive with activation energies of 7.4, 10.6 and 11.8 kcal/mol respectively. In Cp 2 AnCH 3 series of complexes, the trend is comparable to that of oxidation state III, the U and Np complexes are the more reactive with close activation energies (18.9 and 19.2 kcal/mol respectively) which increase slightly for Pu (19.4 kcal/mol) to Th (21.5 kcal/mol) complexes.

Charge and FMO analysis

Although the steric effects and the ionic radius of the metal cannot be neglected, these factors are not the only ones which determine the activation energies of the reaction. So, we undertook other analyses related to the transition states, the first one related to the charge distribution and transfer during the reaction process. The atomic net charges and the metal spin density, according to the Hirshfeld analysis, in the four centers transition state involved in the reaction are given in Table 6. The results of Table 6 show alternating positive and negative charges on the four centers involved in reactions, i.e. L 2 An, CH 3 , CH 3 ' and H, as depicted on Figure 8. This distribution of charges is likely to stabilize such transition state. During the reaction process the charges distribution changes; the An-C(CH 3 ) bonds become less polarized than in the reactive state and charge transfer from the methyl group to the L 2 An fragment occurs. To evaluate the influence of this evolution on the activation energies, we calculated the variations of charge Δq (TSreactant) of the L 2 An fragment as the difference between its charges in the TS and in the reactant (as given in Table 7). Within each series of complexes, the U and Np complexes which are characterized by high charge transfer whatever the ligands (0.13 and 0.15 respectively for the Cl ligand) exhibit also the lowest activation energies contrarily to the Th complexes which exhibit a low charge transfer (0.04 for Cl ligand) and present high activation energy.

However, according to the Figure 9 where the correlation between the activation energy and the charge transferred from the methyl group to the L 2 An fragment (with L = Cl, Cp) is displayed, a better linear correlation is noted for the reactions involving the Cl 2 AnCH 3 complexes compared to those involving the Cp 2 AnCH 3. In the case of (Cp*) 2 AnCH 3 complexes the correlation is less good even if the Np and U complexes still remain the most reactive. This is probably due the steric hindrance effect on the activation energies. As suggested by Bursten and Burns [START_REF] Burns | Covalency in f-element organoletallic complexes: Theory and experiment[END_REF] discussing the covalent character of An-ligand bonds for the early actinides, the actinide 6d orbitals, which are more diffuse, are involved in the covalent nature of the An-CH 3 bond. In addition, it is known that An 5f orbitals are less contracted compared to those of lanthanide 4f and they are also involved in the formation of covalent bonds.

Moreover, in the early actinides, the 5f orbitals are very close in energy to the 6d orbitals (more than the 4f and 5d lanthanide orbitals) and can therefore be involved with the latter orbitals and the 7s orbitals to form metal-ligand bonds. Noting that even if the contribution of 6d and 7s orbitals to the FMOs is low for the almost complexes understudy, the calculation shows that these atomic orbital contribute to the other inner molecular orbitals lower in energy; indeed, in the case of Cl 2 PaCH 3 , the percentage contributions to SOMO-1 of 7s and 6d orbitals are respectively 34.9% and 11.6% in the transition state, and of 43.3% and 24.51% in the reactant.

For the transition states of Cl 2 AnCH 3 + CH 4 (An = Pa, U, Np and P) reactions, as one can see on Figure 10, the contribution of 5f orbitals to the SOMO are identical with a difference not more than 3.03%. The weight of these same orbitals in the LUMO is however different. It increases from Pa (78.4%) to Np (94.7%) and then decreases slightly from Np to Pu (87.7%).

Here, we find that the activation energy decreases in parallel with the increase of the contribution of 5f orbitals to the LUMO. Thus, the transition state structures as well as the reactant complexes with mainly 5f orbitals contribution in the FMOs exhibit less important activation energies which make them more efficient to activate the methane C-H bond. In fact, the reactions involving Cl 2 UCH 3 Cl 2 NpCH 3 complexes with low activation energies (13.68 and 10.48 kcal/mol respectively) correspond to the structures with an important 5f orbitals average contribution (92.9 and 94.3 % respectively) contrarily to the less reactive Cl 2 ThCH 3 complex which exhibits the lowest average 5f contribution (37.7 %) in this series of complexes. The same trend is observed for the Cp 2 AnCH 3 series but less pronounced in the (Cp*) 2 AnCH 3 series because of the steric hindrance effect which is not negligible in this case.

Conclusion

The present work was devoted to the study of the reactivity of L 2 AnCH 3 (An = Ac, Th, Pa, U, Np and Pu; L= Cl, Cp and Cp*) complexes toward methane C-H bond activation using relativistic DFT calculations, taking into account the solvent effect and spin-orbit coupling.

The computational results show that the ground state of these complexes corresponds to the

Fig. 1 .

 1 Fig. 1. Optimized geometries of the reactant and transition state for the reaction Cp 2 U(CH 3 ) 2

Fig. 2 .

 2 Fig. 2. Optimized geometries of L 2 UCH 3 complexes (with L = Cl, Cp and Cp*). Distances are in angstroms (Å) and angles in degrees (°).

2

 2 AnCH 3 complexes like their Cl 2 AnCH 3 counterparts, the An-C distance decreases by 0.160 Ǻ (against 0.179 Ǻ in the Cl 2 AnCH 3 complexes) going from Ac (2.620 Ǻ) to Pu (2.460 Ǻ), with the exception of Cp 2 PaCH 3 complex which has the shortest distance An-C like its Cl 2 PaCH 3 counterpart. It is noteworthy that this An-C distance is longer in the Cp 2 AnCH 3 complexes compared to the Cl 2 AnCH 3 complexes because of the steric hindrance of the Cp groups. The variation of the distances An-(Cp) and An-(Cp') where (Cp) indicates the center of the ring, does not follow also the contraction of the metallic ionic radius. Although they are both very close for all complexes, they do not vary exactly in the same way. The mean distance An-(Cp) decreases significantly from Ac to Pa by about 0.245 Å and then increases slightly to Pu by 0.024 Å. The (Cp)-An-(Cp') angle in Pa and Pu complexes is smaller; this is probably due to a steric repulsion effect between the two cyclopentadienyl ligands which is less important when the An-(Cp) distance is shorter, as in the case of Pa complex.

Fig. 3 .Fig. 3 .

 33 Fig. 3. Frontier Molecular Orbitals diagram of Cl 2 AnCH 3 complexes at ZORA/BP86/TZP level.

L 2 1 )Cp 2 Fig. 4 .

 2124 Fig.4. L 2 AnCH 3 + CH 4 methyl exchange reaction

Fig. 5 .

 5 Fig. 5. Optimized transition states of L 2 UCH 3 + CH 4 reactions. a) L = Cl b) L = Cp c) L = Cp*. Distances are in angstroms (Å) and angles in degrees (°).

  Figure 6.

Fig. 6 .

 6 Fig. 6. Energy profiles of L 2 AnCH 3 + CH 4 reactions in gas phase: a) L = Cl, An = U. b) L = Cp, An = U. c) L = Cp*, An = U. d) L = Cl, An = Pa[1] singlet and Pa[3] triplet states.

  Cl 2 ThCH 3 and Cp 2 ThCH 3 complexes have close activation energy values, i.e. 29.9 kcal/mol and 28.8 kcal/mol respectively. The activation energy of the complex (Cp*) 2 ThCH 3 is equal to 34.9 kcal/mol. These values show that the Th(III) complexes are the less reactive. The activation energies decrease to the lowest value by going from Th to Np in the case of Cl 2 AnCH 3 and Cp 2 AnCH 3 and going from Th to U in the case of the (Cp*) 2 AnCH 3 series of complexes. The (Cp*) 2 UCH 3 complex exhibits the lowest activation energy (21.04 kcal/mol) making it the most reactive among the (Cp*) 2 AnCH 3 series whereas Cl 2 NpCH 3 and Cp 2 NpCH 3 are the more reactive complexes in their corresponding series with activation energies of 10.48 and 17.10 kcal/mol respectively. Two possible spin states have been explored for the Pa complexes i.e. a triplet and a singlet one which exhibit practically identical activation energy 21.36 kcal/mol and 21.52 kcal/mol respectively for the triplet and the singlet, even if the singlet ground state of the complex is less stable by 8.43 kcal/mol relatively to the triplet one as indicated in Figure 6d.

Figure 7

 7 Figure7shows that the two plots representing the two series of complexes Cl 2 AnCH 3 and Cp 2 AnCH 3 behave qualitatively in a similar way. As expected, the complexes carrying the Cp* ligands exhibit the highest activation energies due to the larger steric hindrance they create making access of the CH 4 molecule to the An-C bond difficult.

Fig. 7 .

 7 Fig. 7. Computed activation energies of the L 2 AnCH 3 + CH 4 reactions in the gas phase

Fig. 8 .

 8 Fig. 8. Hirshfeld charge distribution in the TS structure of the L 2 UCH 3 + CH 4 reaction (L= Cl, Cp and Cp *).

H

  Since this is a mechanism for a proton transfer between two methyl groups, it is interesting to follow and analyze the evolution and redistribution of the electronic charges during the reaction. In the reaction whatever the ligand, the H 3 C-H bond approaches the An-C bond with the CH 3 group closer to the metal. The strong polarity of An-C bond induces the polarization of the H 3 C-H bond required for this reaction. It seems that there is no direct correlation between the charge polarity (charge separation) of the An-C(CH 3 ) bond and the values of the calculated activation energies along each series. Moreover, a large polarity (charge separation) in the case of the Cp 2 AnCH 3 and (Cp*) 2 AnCH 3 complexes does not necessarily lead to low activation energies.

Fig. 9 .

 9 Fig. 9. Activation energy versus the transferred charges from the methyl group to the L 2 An fragment ∆q (L 2 An) for actinide complexes. a) L = Cl; b) L = Cp.

Fig. 10 .

 10 Fig. 10. Frontier Molecular Orbitals diagram of Cl 2 AnCH 3 + CH 4 transition states at ZORA/BP86/TZP level(L% =Cl 2 +CH 3 ).

Fig. 11 .

 11 Fig. 11. Correlation between the activation energy and the contribution of 5f orbitals in LUMO (for L 2 AnCH 3 + CH 4 reactions, L = Cl).

SI. 1 :SI. 2 : 8 :

 128 to the LUMO (%) higher spin state with mainly 5f orbital contribution to the FMO(s) in the case of Pa, U, Np and Pu complexes whatever the ligand. All the transition states found and confirmed thanks to LT and IRC calculations exhibit identical structure, four center cycles, characteristic of σmetathesis reaction where a proton is transferred between the two methyl groups. In the two series of Cl 2 AnCH 3 and Cp 2 AnCH 3 complexes, the Np complex seems to be the more reactive regarding the C-H bond activation, whereas in the Cp* 2 AnCH 3 case, the U complex is found to be the more reactive with an activation energy of 21.04 kcal/mol; moreover, in all cases the activation energy of Np and U complexes are close. Finally, there is only a small influence of the metal oxidation state (III or IV) on the activation energies. The U(IV) and Np(IV) complexes appear to be the most reactive ones.Charge and FMOs analyses highlight correlations between activation energies and the transferred charge from the methyl group to L 2 An fragment on one hand and the weight of 5f orbitals in FMO on the other one. Globally, more important the charge transferred from the reactant CH 4 to the L 2 An fragment lower is the activation energy. More important the 5f actinide orbital contribution, less important is the activation energy. Although the 6d metal orbital contribution to the metal-ligand bonding is important, the participation of the 5f electrons in bonding is evidenced particularly in the case of the two series of L 2 AnCH 3 (L = Cl and Cp) complexes. This participation is also highlighted by the important 5f orbitals contribution in the FMOs. In the case of Cp* complexes, the activation energy is not only governed only by the nature of bonding but also by the steric hindrance of the Cp* ligands.Supporting InformationOptimized coordinates of reactants and Transition State in gas phase for: (a) L 2 AnCH 3 + CH 4 (An = Ac, Th, Pa, U, Np, Pu) reactions; (b) Cp 2 An(Me) 2 + CH 4 (An = U, Np) reactions. Optimized structures of L 2 AnCH 3 + CH 4 systems SI.3: Geometrical parameters of the all species (Reactants and TS) in gas phase and in THF SI.4: Vibrational frequencies of the Transition States SI.5: Total Bonding Energies SI.6: Mulliken Populations, Hirshfeld Charges and Nalewajski-Mrozek bond orders Analyses SI.7: Energies and compositions of the frontier molecular orbitals SI.Optimized coordinates of L 2 AnCH 3 + + CH 4 systems SI. 9: Total bonding energy of L 2 AnCH 3 + + CH 4 systems

Table 1 :

 1 Main geometrical parameters a (distances (Ǻ) and angles (°)) of An(III) L 2 AnCH 3 complexes (L = Cl and Cp) at the ZORA/BP86/TZP level in gas phase.

	Cl 2 AnCH 3	Ac	Th	Pa	U	Np	Pu
	An-Cl	2.685	2.590	2.544	2.529	2.531	2.535
	An-C	2.538	2.404	2.349	2.364	2.363	2.359
	Cl-An-Cl'	114.4	131.9	124.0	111.7	114.2	118.4
	Sum of angles	324.0	358.7	341.8	312.7	312.2	315.2
	Cp 2 AnCH 3	Ac	Th	Pa	U	Np	Pu
	An-Cp	2.688	2.554	2.447	2.431	2.465	2.471
	An-Cp'	2.688	2.552	2.439	2.466	2.461	2.462
	An-C	2.620	2.500	2.453	2.478	2.464	2.460
	Cp-An-Cp'	138.6	137.6	126.7	140.8	134.1	127.7

a Distances and angles are defined in Fig.

Table 2 :

 2 MPA, Hirshfeld atomic charges (values in parentheses) of Cl 2 AnCH 3 in the gas phase.

Table 3 :

 3 Main geometrical parameters (distances (Ǻ) and angles (°)) of the transition states of the Cp* 2 AnCH 3 + CH 4 reaction at the ZORA/BP86/TZP level in the gas phase to 0.07Å. On the other hand, the angle C(Cp)-U-C'(Cp') is somewhat affected by this reaction since it decreases by 13.5 °. In all the studied complexes, the proton is bridged almost halfway between the two carbons of the two methyl groups and forms an

	TS (Cp*) 2 AnCH 3 +CH 4	An-Cp* An-C	An-H	C-H	C-H-C' C-An-C' Cp*-An-Cp*'
	Ac	2.675	2.770	2.305	1.456	175.7	63.3	140.2
	Th	2.554	2.713	2.234	1.444	174.8	64.2	141.0
	Pa	2.473	2.644	2.185	1.443	177.2	65.9	152.6
	U	2.462	2.617	2.159	1.446	178.4	67.2	145.5
	Np	2.473	2.607	2.141	1.451	177.0	67.8	139.4
	Pu	2.486	2.634	2.153	1.447	176.3	66.6	134.2

It should be noted that in the Cp 2 UCH 3 complex, the CH 4 approach leads to a noticeable lengthening of the U-C(Cp) bond equal to approximately 0.16 Å whereas the other U-C'(Cp) elongates only up eliminated because it involves the π-bond participation and thus requires the presence of metal-element multiple bond. The σ-CAM involves the formation of a stable σ-complex (though not always isolable) prior to C-H cleavage which is not observed in the reactions under study.

It is also noted that the An-C and An-H distances are shorter in the Cl 2 AnCH 3 + CH 4 transition state compared to its Cp and Cp* systems counterparts. In all complexes, there is a significant decrease of the An-H distance from Ac to U and U to Pu where this decrease becomes less important. On the other hand, the values of this distance in the Cp 2 AnCH 3 and (Cp*) 2 AnCH 3 complexes are very close, as in the case of (Cp) 2 PuCH 3 and (Cp*) 2 PuCH 3 where the An-H distances are 2.148 and 2.153 Å respectively whereas in Cl 2 PuCH 3 this distance was found equal to 2.100 Å.

Table 4 :

 4 Activation energy ∆G

			∆G # (kcal/mol)
	An	L = Cl	L = Cp	L = Cp* (gas) L = Cp* (THF)
	Ac	22.92	23.42	27.32	26.93
	Th	29.88	28.83	34.91	34.08
	Pa	21.36	23.40	27.30	26.78
	U	13.68	17.25	21.04	24.87
	Np	10.48	17.10	25.13	25.25
	Pu	17.51	21.11	25.03	25.79

# (kcal/mol) of the reaction L 2 AnCH 3 + CH 4 (L = Cl, Cp and Cp*) in gas phase and in THF solution (only for Cp*).

Table 5 :

 5 Spin-orbit correction energies E SOC (of reactants and transitions states) and activation energies ∆E # of (Cp*) 2 AnCH 3 + CH 4 reactions. (Values of ∆E # given within parentheses correspond to the activation energies without SOC); all energies are in kcal/mol.

	An		Ac	Th	Pa	U	Np	Pu
	Reactants	-63.88	-68.77	-86.67	102.83	-114.23	-126.59
	E SOC	TS	-63.93	-68.83	-86.61 -103.09 -114.52	-126.95
	∆E #		16.98	24.05	20.31	12.29	15.60	15.57
			(16.91)	(24.16)	(19.76)	(12.54)	(15.85)	(15.81)

Table 6 :

 6 Hirshfeld charges of TSs of the L 2 AnCH 3 + CH 4 reaction at the ZORA/BP86/TZP level in gas phase: L = Cl (L = Cp, within parentheses).

	L 2 AnCH 3	Spin		Hirshfeld net charges L = Cl ( L = Cp)
		population	An	Cp 2	AnCp 2	CH 3	CH 3 '	H
	Ac	0.00 (0.00)	0.84 (0.74)	-0.67 (-0.46)	0.17 (0.28)	-0.09 (-0.15)	-0.10 (-0.15)	0.01 (0.01)
	Th	0.91 (1.05)	0.57 (0.56)	-0.45 (-0.33)	0.12 (0.23)	-0.07 (-0.12)	-0.07 (-0.12)	0.02 (0.02)
	Pa	1.79 (2.14)	0.62 (0.66)	-0.51 (-0.46)	0.10 (0.20)	-0.06 (-0.11)	-0.06 (-0.11)	0.02 (0.01)
	U	2.96 (3.19)	0.61 (0.61)	-0.54 (-0.43)	0.07 (0.19)	-0.04 (-0.10)	-0.05 (-0.10)	0.02 (0.02)
	Np	4.18 (4.22)	0.60 (0.57)	-0.56 (-0.38)	0.05 (0.19)	-0.03 (-0.10)	-0.04 (-0.11)	0.02 (0.02)
	Pu	5.31 (5.30)	0.74 (0.71)	-0.65 (-0.47)	0.09 (0.24)	-0.05 (-0.12)	-0.05 (-0.13)	0.01 (0.01)

Table 7 :

 7 Hirshfeld Charge difference of the L 2 An fragment between the reactant and the corresponding TS. An) are negative thus indicating an electron density transfer from the methyl groups to the L 2 An fragment. By comparing the three series of complexes with each other, we observe a decrease in the transferred charge from the Cl ligand to the Cp* one, as seen for example in Pa complexes, where the charge transfer is 0.09, 0.07 and 0.04 with Cl, Cp and Cp* ligands respectively, thus causing the increase of activation energies when passing from Cl, Cp to Cp* ligands for each actinide.

	Cl 2 AnCH 3	Ac	Th	Pa	U	Np	Pu
	∆q (Cl 2 An)	-0.10	-0.06	-0.09	-0.13	-0.15	-0.12
	Cp 2 AnCH 3	Ac	Th	Pa	U	Np	Pu
	∆q (Cp 2 An)	-0.06	-0.04	-0.07	-0.12	-0.10	-0.08
	Cp* 2 AnCH 3	Ac	Th	Pa	U	Np	Pu
	∆q (Cp* 2 An)	-0.05	-0.03	-0.04	-0.09	-0.10	-0.07
	The charge difference ∆q(Cl 2

Acknowledgements

The authors acknowledge the financial support from the Algerian Project CNEPRU n° B00L0 1501 20130025. Computing facilities were provided by ASELKAM Computer Center (UMMTO, Algeria). The authors are grateful to GENCI-IDRIS and GENCI-CINES for an allocation of computing time (Grant No. 2016-2017-080649).

Author Information

-Corresponding Authors * E-mail:azizelkechai@yahoo.fr ; (aziz.elkechai@ummto.dz) * E-mail: abdou.boucekkine@univ-rennes1.fr -ORCID Aziz Elkechai:0000-0003-0808-6120 Abdou Boucekkine: 0000-0002-3714-7191 -Notes

The authors declare no competing financial interest.

Highlights

 Activation of C-H bond methane by actinide complexes viewed as one-proton transfer process between the two methyl's of reactants.  Computations shows a Transition state characteristic of σ-metathesis reaction.  High ability of uranium and neptunium complexes to activate C-H bond of methane.  Crucial role of the 5f actinide orbitals in the lowering of the activation barriers


Henry Dominique

Rifai Ayoub

Pons Patrick

Aubert Hervé
email: aubert@laas.fr

Millimetre-wave Scanning Radar for the Detection and Remote Reading of Passive Electromagnetic Sensors

Keywords:

This communication reports the latest developments in Frequency-Modulated Continuous-Wave (FMCW) radar interrogation technique for chipless and wireless sensors. For the first time a millimetre-wave scanning radar is used for detecting and reading passive and chipless electromagnetic sensors. Measurement results show that, with a 24 cm depth resolution and a 2 degrees angular resolution, it is possible to localize and distinguish two passive sensors separated by 5 cm at a distance of 3 meters from a FMCW radar operating at 30GHz. Sensing modes visualization derived from the millimetre-wave radar scanning of a scene makes possible the separation length measurement with an accuracy of 1cm.

INTRODUCTION

In the last decade, environmental, industrial, and military monitoring applications have motivated an enormous amount of research activity related to wireless sensing. Some of these applications require continuous and stable measurements for an long period of time [START_REF] Weller | A wireless interrogator -passive sensor approach for deeply embedded sensing applications[END_REF] [START_REF] Cao; Fesehaye | Virtual Battery: An Energy Reserve Abstraction for Embedded Sensor Networks[END_REF]. For such applications, it is desirable that the sensing device has a long operating lifetime. Therefore, active and semi-passive (battery-assisted) sensors are not good candidates due to their high cost and the short life time of the onboard battery. The passive sensors research activity on RFID-based or chipless sensors offers promising solutions.The RFID-based sensors incorporate an integrated circuit (IC) which enables sophisticated features such as rewritable memory and communication protocols. The power rectifier that generates the required power for activating the IC limits the maximum reading range to few meters [START_REF] Feldengut | A Passive Long-Range UHF Transponder with Integrated Temperature Sensor[END_REF] [START_REF] Vaz | Long range, low power UHF RFID analog front-end suitable for batteryless wireless sensors[END_REF]. To the best knowledge of the authors, the achieved reading range with RFID-based sensors is typically lower than 10 meters [START_REF] Donelli | Design of long-range, powerless RFID sensor at 10 GHz[END_REF]. Surface Acoustic Wave (SAW) tags offer longer reading distance due to the absence of ICs (22 meters was recently reported [START_REF] Li | A SAW passive wireless sensor system for monitoring temperature of an electric cord connector at long distance[END_REF]). However, the highest operation frequency of this sensor is typically limited to a few GHz. Recently harmonic and intermodulation radars were used for sensing applications. A reading range of 21 meters was obtained using harmonic radar [START_REF] Song; Pesonen | On the use of the intermodulation communication towards zero power sensor nodes[END_REF] while 55 meters may be reached by using a harmonic radar [START_REF] Nassar | A Compact 3-D Harmonic Repeater for Passive Wireless Sensing[END_REF]. The limiting factor of harmonic interrogation is the high frequency offset between the transmitted and received signals which makes difficult the fulfilment of the frequency regulations. The conversion loss of intermodulation tags limits the efficiency of this approach.

The technique based on the measurement of the RADAR Cross Section (RCS) variability of passive millimetre-wave sensors was proposed for the first time by the authors in 2008 [START_REF] Jatlaoui | Pressure Sensing Approach Based on Electromagnetic Transduction Principle[END_REF] while the proof-of-concept was demonstrated in 2010 [START_REF] Chebila | Pressure Measurement from the RADAR Interrogation of Passive Sensors[END_REF]. Compared with lower frequencies, millimetre-waves improve the sensor immunity to objects located at its vicinity by increasing the electrical length separation distance to them. Moreover they allow reducing the sensor and antenna sizes and designing directional (high gain) antennas for beamforming, multi-beam or beam-steering RADAR reader.

The wireless sensing technique based on RCS-variability measurement has been successfully applied to the remote estimation of many physical quantities (see an overview in [START_REF] Aubert | Wireless Sensing and Identification based on RADAR Cross Sections Variability Measurement of Passive Electromagnetic Sensors[END_REF]). A reading range of at least 30 meters was measured with a spatial resolution of few centimetres. Until now this technique was applied to the remote reading of passive sensors of known positions and consequently, the main lobe of the reader high-gain antenna could be pointed in the direction of the sensor. In case of the sensors occupying unknown positions, we show here that the scanning of the scene by this lobe could be performed to detect the presence of the passive and chipless sensors and to derive their locations.

In this communication and for the first time, a millimetrewave scanning radar is proposed for detecting and reading passive and chipless electromagnetic sensors. The sensors are here passive scatterers composed of an antenna, a length of transmission line and a sensing device (variable impedance in the millimetre-wave frequency range). After a brief reminder of the beat frequency spectrum definition, a wireless technique to distinguish and get the positions of two sensors separated by a short distance is reported. This technique keeps unchanged the measurement sensitivity, measurement resolution and full-scale measurement range.

II. MILLIMETRE-WAVE FMCW RADAR INTERROGATION

FOR PASSIVE ELECTROMAGNETIC SENSORS: THEORY

A. Wireless interrogation of passive sensors using FMCW Radar

A physical model for the calculation of RCS of a loaded antenna is reported by Harrington in [START_REF] Harrington | Theory of loaded scatterers[END_REF]. It includes backscattering of the incident electromagnetic wave by the antenna structure and the back-scattering due to the antenna loading impedance. Assuming a delay line of length l between the load and the antenna, the beat frequency spectrum of the loaded antenna can be obtained from the use of a homodyne FMCW radar. Considering a transmitted chirp with a radial frequency bandwidth Δω, the resulting beat frequency spectrum b(ω) measured by the radar at a given radial frequency ω is found to be:

∑ (1)
where ω 0 is the carrier radial frequency, R the radar-to-sensor distance, T R and ω R denote respectively the period and radial frequency of the modulation signal, t 0 the round-trip duration from the radar to the antenna structure, t 1 the delay generated by the line, δ represents the Dirac function and S 11 (ω 0 ) the reflection coefficient on the sensing device at the carrier radial frequency. In Eq.( 1) the constant B is derived from the radar characteristics and A(ω 0 ) depends on antenna geometry. Eq.( 1) shows that the beat frequency spectrum combines two cardinal-sine functions. The first sine function corresponds to the contribution of the structural scattering mode with:

(

while the second term is relative to the sensing mode contribution with:

(3)

These functions are centred at the two following beat radial frequencies:

(4-a) (4-b)
with c designate the vacuum celerity of light and v φ the phase velocity in the delay line. According to Eqs.( 1) and (4-b), if the delay line is long enough to avoid overlapping of the two modes, the contribution of the sensing mode can be given as follows:

(5) which leads to a magnitude:

| | | | (6-a) where | | (6-b)
According to (6-a), the contribution of the sensing mode is proportional to the reflection coefficient on the sensing device. Fig. 1 shows the measured level of the spectral component at beat radial frequency ω 2 associated to the sensing mode for various reflection coefficients. This experimental result validates the convenient linearity predicted by Eq.(6-a).

B. Wireless identification of passive sensors using FMCW radar

The length of the delay line is an additional parameter which is used for passive sensors identification. It controls the beat frequency of sensing modes and multiple configurations can be imagined to create specific beat frequency spectrum signatures. An example of delay lines and load configurations for passive sensors identification can be found in [START_REF] Jatlaoui | Original identification technique of passive EM sensors using loaded transmission delay lines[END_REF].

III. BEAM SCANNING FOR DETECTING AND READING PASSIVE SENSORS: FIRST EXPERIMENTAL RESULTS

In our previous works based on the use of millimetre-wave FMCW Radar for reading and identifying passive electromagnetic sensor, the location of the sensor was known and the radar Tx-antenna pointed its main lobe in a unique direction. In this section, positions of passive sensors are considered as unknown and a wireless technique is proposed to detect, localize, read and identify passive sensors. The millimetre-wave scanning radar used in this experiment is a FMCW Radar with a bandwidth of Δf = 620 MHz and operating at 30 GHz. The depth resolution is then given by [14]:

According to Eq.( 7) the depth resolution is expected to be d=24 cm. A parabolic antenna having a 2 degrees beamwidth and a gain of 35 dB is used as the transmitting radar antenna (Tx-antenna). The beamwidth leads to an angular resolution φ=2 degrees. A beam scanning is performed with a rotational sweep of 0,5 degree step. The receiving antenna (Rx-antenna) of the radar is a motionless rectangular horn having a beamwidth of 60 degrees. The chirp transmitted by the Tx-antenna is back-scattered by passive sen experiment the sensors are passive scatterer horn antenna (beamwidth: 60 degrees; gain of coaxial line and a resistance R device = 0Ω R device =50Ω (matched load). These correspond respectively to the minimal values taken by of the sensing device millimetre-wave frequency range. . The len line is used for separating in the beat frequ structural scattering mode and the sensing must be at least half of the resolution d measurement and for each rotational step o Fast-Fourier Transform (FFT) is applied to t in order to display the beat frequency sp minimum measurable separation distance be sensors is then given by the radar c oversampling is applied to the beat spectru results with the maximal depth reso accomplished when having a sampling freq the beat frequency resolution T R =1 kH frequency of T R /10=100 Hz is then chosen h FFT. This sampling is followed by a sm consider a distance between the passive sen of 3 meters and an electrical length of the c m. ). The t spots are in the same direction and at dista 1,3m of their respective structural scattering is reduced to 20 cm, the two spots associate scattering modes are more difficult to dis 6.a). However, by restricting the spots to 20dBm of back-scattered power, a distance derived between spots centres. When R device of the passive sensors are located between of their structural scattering modes (see Fig Fig . 7, by reducing W to 5cm the two detectable but the echo level does not allow the two sensors. A solution is to give signature to one of the two sensing modes. transmission line length L 2 to 2m40 it is po the two sensing modes while the two str modes are still merged (see Fig 8). Assum mode locations are at spot centres and that on the same direction than structural scatter obtain an estimation of the distance betwee sensors by measuring the angle between the sensing mode spots ( IV. BEAM SCANNING FOR DETECTING AND READING PASSIVE SENSORS: MULTI-SENSORS APPROACH From the previous measurement results the maximum number of passive sensors which can be simultaneously detectable, identifiable and readable may be estimated. Hence it is possible to calculate the maximal density of detectable sensors at a given read range. Assuming that delay lines are properly chosen to avoid sensing modes overlapping, the resolution area a in which only one passive sensor can be detected is given by: a

and the maximal density S of detectable sensors is given by: s

With an angular resolution of 2 degrees and a depth resolution of 24cm (see section III and Fig. 10), the maximal density of detectable sensors at 3 meters is then 39 sensors per meter square. V. CONCLUSION A 30GHz scanning FMCW radar is used for detecting and reading passive and chipless electromagnetic sensors. Measurement results show that it is possible to detect two sensors separated by 5cm at a 3m read range. The separation is calculated with an error of 1cm with 24 cm of depth resolution and 2 degrees of angular resolution.

Fig 1 .

 1 Fig 1. Measured amplitude of the spectral component at the beat frequency associated to the sensing mode for various reflection coefficients on the sensing device.

Fig 2 .

 2 Fig 2. Measured beat frequ passive sensor when the Tx-a the direction of the sensor.

Fig 3 .

 3 Fig 3. Radar image for a singl = 50Ω and (b) when R device = 0 Two passive sensors are n They are located at D = 3 mete from each other by a distance minimum distance W Min to dis from the angular resolution and φ = 2 degrees one foun sensors are connected to a coa and L 2 respectively and, are order to estimate the angular re are performed with various va W.

Fig 4 .

 4 Fig 4. Experiment configuratio

Fig 5 .Fig 6 .Fig 7 .Fig 8 .

 5678 Fig 5. Radar image obtained for two passiv 50 cm and L 1 =L 2 =1,20m when (a) R device = 5 R device = 0. (a)

Fig

  Fig 9. Geometric construction separation length W from the k measurement of the sensing mo

Fig 10 .

 10 Fig 10. Illustration of the beam scanning technique for a maximum number of passive sensors at a given read range (3m). 39 sensors per meter square are detectable.