Youness Moukafih
email: youness.moukafih@uir.ac.ma

Abdelghani Ghanem
email: abdelghani.ghanem@uir.ac.ma

Karima Abidi
email: karima.abidi@loria.fr

Nada Sbihi
email: nada.sbihi@uir.ac.ma

Mounir Ghogho
email: mounir.ghogho@uir.ac.ma

Kamel Smaïli

Kamel Smaili
email: kamel.smaili@loria.fr

A Simple fully-Supervised Contrastive Learning Framework for Text Representation

Keywords: Natural Language Processing, Contrastive Learning, Neural Network, Supervised Learning

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

Introduction

Over the last few years, deep supervised learning models have achieved tremendous success in a variety of applications across many disciplines varying from Computer Vision (CV) and Automatic Speech Recognition (ASR) to Natural Language Processing (NLP). These models are usually trained by minimizing the commonly-used cross-entropy (CE) objective function. The basic concept of CE is simple and intuitive: each class is assigned a target (usually 1-hot) vector.

Equal contribution

Despite its popularity, the CE objective loss -the KL-divergence between onehot vectors of labels and the distribution of the model's output logits -suffers from major robustness issues, which limits its use. In fact, CE suffers from adversarial robustness, as was shown in [START_REF] Xu | GRethinking softmax cross-entropy loss for adversarial robustness[END_REF], which demonstrated empirically that training with a CE loss can cause the representations to spread sparsely over the representation space during training. Additionally, introducing noisy data seams to reduce the performance substantially, due to the fact that the cross entropy loss supposes that all the training labels are true, and neglects the fuzziness of noisy labels [START_REF] Zhang | Revisiting few-sample BERT fine-tuning[END_REF].

To overcome the above-mentioned challenges, many successful alternatives have been proposed to adjust the reference label distribution problems through label smoothing [START_REF] Szegedy | Rethinking the inception architecture for computer vision[END_REF][START_REF] Smüller | When does label smoothing help?[END_REF], Mixup [START_REF] Szhang | mixup: Beyond empirical risk minimization[END_REF], and knowledge distillation [START_REF] Hinton | Distilling the knowledge in a neural network[END_REF]. Recently, contrastive learning (CL) algorithms that were developed as estimators of mutual information, has led to major advances in self-supervised representation learning. Inspired by the recent works on contrastive representation learning strategy, we introduce SimSCL, a simple supervised contrastive learning framework that uses a novel contrastive loss for binary classification task by leveraging label information more effectively. In this work, we consider many positives per an-chor, unlike previous works on self-supervised contrastive learning which uses only a single positive example per anchor, and many negatives. In other words, the positive points are sampled from the same class as the anchor, instead of being augmented views of the same anchor, as done in self-supervised learning. In figure 2, we show how we select positive examples and negative examples for each class. The use of many positives and many negatives for each anchor in our framework allows the encoder function to better maximize the inter-class and minimize the intra-class similarities (learn effective generalizable features) than the standard framework which relies on the cross-entropy loss using the same model architecture. In figure 1 we can clearly see that our proposed objective function enforces more compact clustering of examples within the same class.

The empirical results show that our proposed framework consistently outperforms the standard cross-entropy loss using the same model architecture on three publicly available benchmark SA datasets, namely, Yelp-2, SST-2, and Amazon-2. Further experiments on Moroccan and Algerian dialects demonstrate that our framework also works well for under-resource languages.

Related Work

Our research builds upon previous works in self-supervised representation learning, contrastive learning, and supervised learning. Here, we shed light on the most pertinent papers.

Cross entropy is the de facto choice for the loss function in classification tasks. This prominence is due to many reasons. First, CE has good theoretical grounding in information theory, which makes it useful for theoretical analysis of systems [START_REF] Andreieva | Generalization of Cross-Entropy Loss Function for Image Classification[END_REF]. Second, CE loss has been proven to rival many loss function in large data-sets. However, a number of works have analyzed the shortcomings of the commonly adapted cross-entropy objective function, showing that it leads to poor generalization performance due to poor margins, and sensitivity to noisy labels. Classification models are theoretically evaluated by their ability the separate classes in the representation space. Separability is also of practical use, since large margins can make models robust to small perturbations of the input space and hence, more robust to noise. [START_REF] Xu | GRethinking softmax cross-entropy loss for adversarial robustness[END_REF] showed that CE does not maximize the separating margins between classes, and proposed an alternative that solves this problem. This phenomenon can be attributed to the leniency of the penalties of the cross entropy when close to the ground truth label (i.e. CE is eager for the model to be right), and can lead to poor generalization.

Recently, there has been several investigations for the use of contrastive loss for self-supervised learning. Primarily in the computer vision (CV) field, deep Contrastive learning has been use to great effect for learning image representations . For instance, in [START_REF] Chen | A simple framework for contrastive learning of visual representations[END_REF] Hinton and his colleagues propose SimCLR a simple framework, for learning visual representations without specialized architectures or a memory bank, that generates anchor positive pairs by randomly augmenting the same image (e.g. random cropping and Rotation) while anchor-negative pairs are, from augmented views of different images within the same batch and minimizing a contrastive loss shown in Eq 1 that makes augmented views of the same example agree, which were shown to considerably outperform previous methods for self-supervised and semi-supervised learning on various benchmark datasets.

L self i = - i∈I log exp(z i .z j(i) /τ ) a∈A(i) exp(z i .z a /τ ) (1)
Where i ∈ I ≡ {1...2N } is the index of an arbitrary augmented sample, j(i) is the index of the other augmented sample originating from the same source sample. A(i) ≡ I {i} is the set of all batch samples except the anchor. P (i) ≡ {p ∈ A(i) : ỹp = ỹi } the set of indices of all positives in the multiviewed batch distinct from i. We can rewrite the set A(i) as A(i) ≡ P (i) ∪ N (i), where

N (i) ≡ {p ∈ A(i) : ỹp = ỹi }.
Most similar to our method is the work done by [START_REF] Khosla | Supervised contrastive learning[END_REF], in that paper the authors proposed two variants of a contrastive supervised loss named SupCon (see E 2andEq3). SupCon outperforms cross entropy loss and produces state-ofthe-art results on ImageNet using ResNet architecture [START_REF] Zhang | Deep residual learning for image recognition[END_REF] with four different implementations of data augmentation.

L sup out,i = i∈I - 1 |P (i)| p∈P (i) log exp(z i .z p /τ ) a∈A(i) exp(z i .z a /τ ) (2)
L sup in,i = i∈I -log    1 |P (i)| p∈P (i) exp(z i .z p /τ ) a∈A(i) exp(z i .z a /τ )    (3)
Other researchers have extended these methods to learn representations of graph structured data [START_REF] Hassani | Contrastive multi-view representation learning on graphs[END_REF][START_REF] Zhu | Deep graph contrastive representation learning[END_REF][START_REF] Veličković | Deep graph infomax[END_REF][START_REF] Qiu | Gcc: Graph contrastive coding for graph neural network pre-training[END_REF][START_REF] Hafidi | Graphcl: Contrastive self-supervised learning of graph representations[END_REF]. For instance, in [START_REF] Hafidi | Graphcl: Contrastive self-supervised learning of graph representations[END_REF] the authors proposed GraphCL a general framework for learning node representations in a self supervised manner using a contrastive loss that aims at maximizing the similarity between the representations of two transformations of the same node's local sub-graph. In the context of NLP, in [START_REF] Mikolov | Efficient estimation of word representations in vector space[END_REF] Mikolov and his colleagues proposed the first contrastive-based framework for learning word-level embeddings by using co-occurring words as positive pairs and k randomly chosen negative samples words form the corpus as negative pairs. More recently, contrastive learning was used for sentence-level representations. [START_REF] Nitski | Declutr: Deep contrastive learning for unsupervised textual representations[END_REF] proposes a self-supervised contrastive objective by performing both masked language modeling and contrastive learning to learn a universal sentence representations by training a transformer-based encoder to minimize the distance between the embeddings of textual segments randomly sampled from nearby in the same document. More recently, in [START_REF] Gunel | Supervised contrastive learning for pre-trained language model fine-tuning[END_REF] the authors proposed a novel loss for fine-tuning that includes a supervised contrastive learning term [(1 -λ)L CE + λL sup out ] novel loss that a supervised contrastive learning objective for fine-tuning transformer-based pre-trained language models that improve performance over a strong RoBERTa-Large baseline on multiple datasets of the GLUE benchmark in the few-shot learning settings.

The proposed method

The main goal of the proposed framework is to learn representations by training an encoder network via a novel fully-supervised contrastive loss for classification task. The objective function is meant to capture the similarities between sentences of the same class while distancing the representations of sentences belonging to different classes.

First, we tackle one of the most crucial steps in any contrastive learning framework, namely, creating positive samples. In self-supervised, the common way for creating these positive samples is using various data augmentation strategies such as rotations and cropping in computer vision domain. Nevertheless, directly grafting the way of generating augmented views from the image domain is infeasible, since arbitrarily altering a sentence may change its semantics and thus its sentiment. To address this issue, we consider that sentences of the same sentiment are positive examples of each other. In figure 2, we show how we select positive examples and negative examples for each class.

Inter-class and Intra-class Distances

We first set up notation and describe the proposed framework for classification tasks that will be essential for the analysis. Let D = {(x i , y i )} i be the dataset, where x i represent the i th sentence of the dataset and y i is its label. Let S k l = {(x ki , y ki )|y ki = y kj , ∀i = j; 0 ≤ i ≤ l} denote the set of all sentences belonging to the same class within the corpus with l being the max-length of the sentences. Let B k ∼ S k l be a mini-batch of randomly sampled examples from the same class. Let f w (.) denotes the encoder operator where the sub-index w refers to the weights of the encoders to be learnt. Let H k = f w (B k ) ∈ R N ×d be the highest level l 2 normalized representation of the encoder where N is the batch size and d is the dimension of the embedding vector. The j th row of H k corresponds to the embedding h (l) j of sentence k. Mathematically, this can be presented as

H k =      h 1 h 2 . . . h |B k |      ∈ R N ×d

Contrastive objective function

Now that we have all the mathematical notions needed, we proceed with the formulation of the objective function of the proposed contrastive learning framework:

V (C1,C1) = H 1 H 1 = f w (B 1 ) × f w (B 1 ) ∈ R N1×N1 (4)
V (C2,C2) = H 2 H 2 = f w (B 2 ) × f w (B 2 ) ∈ R N2×N 2 (5)
U (C1,C2) = H 1 H 2 = f w (B 1 ) × f w (B 2 ) ∈ R N1×N2 (6)
U (C2,C1) = H 2 H 1 = f w (B 2 ) × f w (B 1 ) ∈ R N2×N1 (7)
Where, B 1 ∼ S 1 l and B 2 ∼ S 2 l . V (C1,C1) and V (C2,C2) are the distances between the positive examples, which should be minimized by the objective (interclass similarity), and V (C1,C2) and V (C2,C1) are the distance between the representation of each batch and the representation of the other batch, which should be maximized (intra-class similarity).

Finally, we concatenate the V (C1,C1) with V (C2,C2) inter-class matrices, and U (C1,C2) with U (C2,C1) intra-class:

V = V (C1,C1) V (C2,C2) U = U (C1,C2) U (C2,C1)
In order to overcame the mismatching dimension of V (C1,C1) with V (C2,C2) and that of U (C1,C2) with U (C2,C1) we adjust the matrix of the lowest dimension (column space) to be equal to that of the highest one by adding zeros.

given the previous calculations, we formulate our supervised contrastive objective that we call L sup concat as follows:

L sup concat = - 1 N N i=1 log      1 N C(i) -1 N C(i) j=1,j =i exp(V ij /τ ) 1 N C(i) -1 N C(i) j=1,j =i exp(V ij /τ ) + 1 N C(i) N C(i) j=1 exp(U ij /τ )      (8)
where, N = N C(i) + N C(i) , N C(i) is the number of elements of the same class as example i and N (i) the number of the elements of the other class, τ ∈ R + is a scalar temperature parameter, V i and U i are the i th elements of V and U respectively.

Note that, by minimizing the proposed supervised contrastive loss L sup concat , the encoder operator adjust its weights so that representation of sentences with same class label are close to each other (high values for [V i ] i=1,2... ), while representation of sentences belonging to different classes are far from each other (low values for [U i ] i=1,2... ). Moreover, in contrast to self-supervised learning, our objective function trains the model by exploiting multiple positive examples, resulting in more compact clustering of the embedding space.

It is worth pointing out that our loss is generic, i.e, it can be used for any binary classification problem. In this paper, we only use it for text binary classification task, leaving its exploration for other classification tasks as future work.

Main Results

Datasets

We evaluate the effectiveness of the proposed losses on three popular datasets namely, SST-2, Yelp-2, and Amazon-2, used for benchmarking state-of-the-art sentiment classification learning methods. We also tested our proposed objective function for two other low-resource languages datasets namely, the Moroccan Sentiment Analysis Corpus (MSAC) and the Algerian Sentiment Analysis Corpus (ASAC). MSAC is a multi-domain dataset containing sentences from sport, social and politics domains. ASAC is an Algerian Sentiment Analysis Corpus, it is our own dataset that we collected and annotated taking advantage of the data available on Youtube video comments. The problem was how to extract from Youtube, only the comments concerning the Algerian dialect. As there is no standard method for this problem, we opted for the approach we had proposed in a previous work [START_REF] Abidi | CALYOU: A comparable spoken Algerian corpus harvested from youtube[END_REF]. We collected data on YouTube, by selecting several hashtags or keywords used mainly by Algerians. Subsequently, all the data collected was checked and filtered and those which were not Algerian, they were excluded from the corpus. Then, we manually annotated all the comments by assigning each sentence its polarity (we didn't take into consideration neutral sentences). The constructed corpus, written in Arabic and Latin characters, is made up of 3976 positive comments and 4443 negative comments 3 . We summarize each dataset in Table 1.

Training Details

Our framework allows various choices of the network architecture without any constraints. However, since the aim of this work is to compare different loss functions on the same model architecture, we opt for simplicity and adopt the commonly used BiLSTM-based encoder.

For SST-2, Yelp-2, and Amazon-2 datsets, L sup concat was trained for 60 epochs using Adam optimizer with learning rate of 0.001 [START_REF] Kingma | Adam: A method for stochastic optimization[END_REF]. We initialize the input layer of the encoder with Glove pre-trained word representations of size 300 [START_REF] Pennington | Glove: Global vectors for word representation[END_REF]. we use an encoder function of 3 hidden layers, a hidden units of 512, and a batch size of 800. We apply dropout of 0.5 on each layer. Note that the CE loss is evaluated by increasing the mini-batch size up to 1000. However, the best results are obtained using a batch size of 500.

For ASAC and MSAC datsets, similarly, the supervised L sup concat was trained for 15 epochs using Adam optimized with a learning rate of 0.003. However, for these datasets, we use an encoder with 1 hidden layer due to the number of examples that we have in the datasets, a hidden units of 128, and a batch size of 200. We apply dropout of 0.1. Similarly, we the CE is trained for a batch size up to 400, but the best results are obtained using a batch size of 64.

Following common practice, we opt for a linear evaluation of the learned sentence representations. More precisely, we use the learnt representations to train a logistic regression model to solve the text classification task. In practice, the evaluation process was performed using both a linear, and non-linear (ReLU activation) classifier. However, better results were obtained by the latter, achieving an average performance gain of 2% across all datasets.

Classification Accuracy

Here, we report the obtained results using L sup concat in different settings on 5 benchmark datasets, and those obtained by the CE and SupCon [START_REF] Khosla | Supervised contrastive learning[END_REF] losses. The results are given in terms of accuracy score measured on the same balanced test set. Following common practice, we first study the importance of adding a projection head that maps representations to the space where supervised contrastive loss is applied. Similar to we tested three different MLP architecture: (1) identity mapping; (2) linear projection z = g(h) = W (1) h ∈ R 512 ; (3) non-linear projection with one additional hidden layer as used by several previous approaches z = g(h) = W (2) ReLU (W (1) h) ∈ R 512 . Similar to what have found in previous works, we observe that a non-linear is better than linear and identity functions for projection head (See table 2). Note that, the projection head network is used only in the contrastive training phase, however, we discard it at the fine-tuning and inference phases.

For the evaluation performance, we tested our supervised representation for transfer learning in two settings: (1) the (non-linear) classifier is trained on top of the frozen representation (transfer learning); (2) we train the classifier, where we allow all weights to be adjusted during training (fine-tuned). It is clear from the table 3 that the learnt representations by our loss function are useful for the downstream tasks without adjusting them. In this paper, we provide the results that we obtained with the transfer learning strategy. Table 4 shows the obtained results of biLSTM-based model using our L sup concat objective function on the previously described datasets; and those obtained by the cross-entropy and SupCon losses. The results are given in terms of accuracy score measured on the same balanced test set. It is clear that in all cases, our framework provides better performance; the gain in performance is significant. Indeed, SimSCL leads to a 4.7% improvement of accuracy on SST-2, 3.6% improvement on Yelp-2, 5% improvement on Amazon, 3.9% improvement on ASAC, and 7.6% improvement on MSAC compared to CE loss. The large performance gap for MSAC dataset demonstrates that cross-entropy struggles with separating classes when dealing with small datasets. Furthermore, the results for MSAC and ASAC prove that our framework is very promising for under-resourced languages, which makes it advantageous over more sophisticated models such as transform-based models (e.g, BERT, RoBERT), which cannot be used for these languages due to the large amount of data needed for pre-training. Moreover, our experiments showed that CE overfits the MSAC dataset very quickly, with a training accuracy of 96% and only 72% accuracy on test. The overfitting problem cannot be explained by the large number of parameters of the biLTSM, since SimSCL-Obj also uses biLTSM (i.e, the same number of parameters as CE). Indeed, the problem can be explained by the fact that CE learns very poor margins between the two classes. Finally, it is worth pointing out that, similar to the cross-entropy loss, our loss function is robust to weights initialization.

Conclusion & future work

In this paper, we presented SimSCL, a simple supervised contrastive learning framework for training deep neural network for the binary classification task using a novel loss function. The latter is based on inter-class similarities (to be maximized), and intra-class similarities (to be minimized). We demonstrated, empirically, that SimSCL separates the two classes better than the encoder based on the classical cross-entropy and the SupCon losses. In the future, we plan to extend our method to other domains, such as computer vision, and graph neural network.

  These methods explicitly aim at training an encoder to learn latent representations of data instances to learn by pulling together representations of augmented views of the same data example (positive pairs), and pushing away representations of augmented views of different data examples (negative examples).

Fig. 1 :

 1 Fig. 1: T-SNE plots of the learned sentence representations using SimSCL and Cross-entropy on the SST-2 test set.

Fig. 2 :

 2 Fig. 2: Overview of the positive and negative examples construction process

Table 1 :

 1 dataset statistics

	Dataset	#Train	#Dev	#Test	#Classes
	SST-2	60k	3.5k	3.5k	2
	Yelp-P	600k	50k	38k	2
	Amazon-P	3M	600k	400k	2
	MSAC	1.6k	0.2k	0.2k	2
	ASAC	6.8k	0.8k	0.8	2

Table 2 :

 2 Linear evaluation of representations with different projection heads g(•) (Accuracy). The representation h (before projection) is 512-dimensional (%).

	Dataset \Projection	Identity	Linear	Non-linear
	SST-2	93.40	93.60	94.15
	Yelp-2	95.13	95.31	95.45
	Amazone-2	93.23	93.61	94.71
	MSAC	78.48	79.33	80.10
	ASAC	79.73	80.91	82.63

Table 3 :

 3 Comparison of transfer learning and fine-tuning performance (Accuracy).

	Dataset	Transfer learning	Fine-tuned
	SST-2	94.05	94.15
	Yelp-2	95.53	95.45
	Amazone-2	94.71	94.58
	MSAC	80.10	78.21
	ASAC	82.63	82.16

Table 4 :

 4 Performance Results (%)

			Classification Accuracy Results
	Dataset	CE	SupCon (L sup out )	SimSCL (L sup concat )
	SST-2	91.28	93.53	94.15
	Yelp-2	92.12	94.84	95.45
	Amazon-2	92.94	93.98	94.71
	MSAC	72.51	78.33	80.10
	ASAC	78.70	82.11	82.63


Rinaldo Poli
email: rinaldo.poli@u-bourgogne.fr

Kevin M Smith

Peter Legzdins

Metal-based chirality and spin state change in 16-electron CpML 2 systems: a computational study of CpW(NO)(PH 3 )

published or not. The documents may come

Metal-based chirality and spin state change in 16-electron CpML2 systems: a computational study of CpW(NO)(PH3)

Several highly reactive Cp*W(NO)L intermediates (L = PMe 3 , 1 PPh 3 , 2 NCHCMe 3 , 3 HCCPh [4][5][6] ) have previously been shown to be generated by reductive elimination of CMe 4 or SiMe 4 . † These proposed 16 electron, d 6 Cp*W(NO)L species are not observed as they proceed to activate C-H bonds, [1][2][3][4] coordinate weak p-acceptor ligands, 7 or engage in coupling and rearrangement reactions 5,6 with available trapping reagents. Previous theoretical studies [8][9][10] have demonstrated that the geometries and orbital energies of 16e, d 6 CpML 2 species are influenced by the bonding properties of their ligands. For example, p-donor ligands enforce a planar-at-metal conformation (i.e. the metal sits on the plane defined by the two ligands L and the Cp center of gravity), while pyramidal geometries are preferred for complexes containing either s-donor (p-neutral) or p-acceptor ligands. However, these studies were carried out using semiempirical methods and so were confined to the spin singlet energy hypersurface. The computational studies that we report here for the CpW(NO)(PH 3 ) model system indicate that the spin state can play a previously unsuspected yet critical role in 16e, d 6 CpML 2 species.

The optimised geometries and relative energies of the singlet and triplet CpW(NO)(PH 3 ) complexes are shown in Table 1 and Fig. 1. ‡ The singlet is pyramidal at W, as expected for a CpML 2 species containing p-acceptor and s-donor ligands. 9,10 However, triplet CpW(NO)(PH 3 ) is calculated to possess a planar geometry at W, and to be 3.3 kcal mol 21 (1 cal = 4.184 J) more stable than the pyramidal singlet species. No significant variation in W-NO bond distance is observed between the two different spin configurations since the W-NO p-bonding orbitals are fully occupied in both cases. 17 There is, however, the expected 18,19 slight overall extension of all bond lengths in the triplet, as well as an increase in CNT-W-P angle.

While triplet Cp*W(NO)(PR 3 ) complexes have yet to be detected spectroscopically, the intermediacy of such a species where R = Ph is consistent with kinetic measurements of the reaction between Cp*W(NO)(h 2 -PPh 2 C 6 H 4 )H and CNCMe 3 . 7,20 Replacing the Cp and PH 3 ligands of the model complex with bulkier Cp* and PR 3 groups would be expected to enforce a larger CNT-W-P angle and a planar-at-W geometry, thereby further destabilising the singlet state. The steric shielding of the metal centre coupled with the expected reduced reactivity 21 of the high-spin configuration should impart additional stability, making triplet Cp*W(NO)(PR 3 ) compounds reasonable synthetic targets. §

In order to explore the role of the triplet spin state in the inversion of pyramidal, diamagnetic CpML 2 species, further calculations were performed at various values of f for both spin states (Fig. 1). The highest energy singlet conformation is the planar geometry (f = 180°), leading to an inversion barrier of 7.7 kcal mol 21 along the singlet spin surface, which compares well with previous studies on other 16-electron systems. 10 The energy of triplet CpW(NO)(PH 3 ) increases relatively gradually as the geometry is distorted away from the planar-at-W conformation. As a result, the f angle at which both spin states are equal in energy corresponds to a high degree of pyramidalization (f ≈ 130°), only 0.8 kcal mol 21 higher in energy than the singlet ground state.

The one-dimensional energetic situation illustrated in Fig. 1 would suggest a low-energy inversion mechanism for diamagnetic, pyramidal CpW(NO)(PH 3 ) via the spin triplet surface. ¶ However, the two geometries at the spin-crossover point are significantly different (Table 1). According to the Franck-Condon principle, both the geometries and the energies must be very similar for the spin flip process to occur. At the crossover point (f = 130°), the vertical excitation energies of singlet and triplet geometries (energy of the triplet configuration at the singlet geometry and of the singlet configuration at the triplet geometry) are 6.9 and 8.2 kcal mol 21 , respectively. These numbers give an estimate of the upper bound of the spin flip barrier.∑ The energetic proximity of these vertical excitation energies and the inversion barrier along the singlet surface (within ca. 1 kcal mol 21 ) prohibits the definitive identification of the inversion mechanism (two-state vs. one-state) for the CpW(NO)(PH 3 ) species. It is readily apparent, however, that the involvement of the triplet spin state represents a distinct and realistic alternative to a process restricted to the singlet spin surface, the only mechanism which has hitherto been considered for this class of compounds. Further experimental and theoretical work is unquestionably required to explore this possibility for Cp*W(NO)L species, as well as for CpML 2 compounds in general.

Several 16e, d 6 Cp*M(PR 3 )X species have been invoked in intra-and inter-molecular C-H bond activation reactions (M = Ir, X = CH 3 + ; 25 M = Os, X = CH 2 SiMe 3 ; 26 M = Ru, X = CH 2 CMe 3 ; 27 M = Re, X = CO, PMe 3 ; 28-30 M = W, X = NO 1 ). In particular, much recent theoretical, synthetic, and mechanistic work has been focused on the low-temperature alkane C-H bond activation reactions of the Cp*Ir(P-Me 3 )(CH 3 ) + complex, [31][32][33][34] but to the best of our knowledge, only one study has addressed the possible involvement of triplet species in this system. 19 The role of the spin state in the reactivity of unsaturated Cp*W(NO)L species is currently under theoretical investigation. 35 R. P. thanks the Région Bourgogne for supporting this research, and K. M. S. is grateful for a TMR Marie Curie Postdoctoral Fellowship.

Notes and References † Cp = h 5 -C 5 H 5 ; Cp* = h 5 -C 5 Me 5 ; CNT = Cp ring centroid. ‡ Calculations were performed using Gaussian 94. [START_REF] Frisch | Gaussian 94[END_REF] The LanL2DZ basis set was employed to perform geometry optimisations with a density functional theory (DFT) approach. The three-parameter form of the Becke, Lee, Yang and Parr functional (B3LYP) [START_REF] Becke | [END_REF] was employed. The LanL2DZ basis set includes both Dunning and Hay's D95 sets for H and C [START_REF] Dunning | Modern Theoretical Chemistry[END_REF] and the relativistic electron core potential (ECP) sets of Hay and Wadt for the heavy atoms. [START_REF] Hay | [END_REF][15][16] Electrons outside the core were all those for H, C, N and O, the 5s, 5p, 5d and 6s electrons for W and the 3s and 3p electrons for P. The mean value of the first-order electronic wavefunction, which is not an exact eigenstate of S 2 for unrestricted calculations on open shell systems, was considered suitable for the unambiguous identification of the spin state. Ground state energies are based on complete geometry optimisations. The singlet geometry for f = 180° was optimised with an imposed mirror plane. For all other values of f, the C 5 ring of the Cp ligand was fixed as a regular pentagon, the degree of pyramidalisation was set at a specific N-W-CNT-P dihedral angle (f), and the geometry was optimised with no other constrained parameters.

§ For the use of steric bulky ligands in stabilising Cp*Ru(PR

Fig. 1

 1 B3LYP/LANL2DZ energies of optimized singlet (-) and triplet (8) CpW(NO)(PH 3 ) at various fixed dihedral N-W-CNT-P (f) angles

Table 1

 1 DFT-B3LYP optimized geometries and energies for CpW(NO)(PH 3 )

		Energy minima	Spin-crossover point
	Parameter	Singlet	Triplet	Singlet	Triplet
	f (N-W-CNT-P)	125.0	180.0	130.0	130.0
	W-CNT	2.018	2.093	2.023	2.107
	W-P	2.482	2.522	2.481	2.528
	W-N	1.791	1.794	1.792	1.795
	N-O	1.251	1.252	1.251	1.253
	CNT-W-P	121.38	132.82	122.37	129.37
	CNT-W-N	128.55	133.55	128.35	133.48
	P-W-N	93.33	93.63	95.36	85.64
	W-N-O	175.34	176.71	175.37	176.90
	Relative energy/kcal mol	0	23.3	+0.8	+0.8

  3 )X species, see refs. 9, 22 and 23. ¶ For discussion of similar examples of 'two-state reactivity' see ref. 24 and references therein. ∑ For a discussion of the problems inherent in estimating spin-crossover energies, see refs. 18, 21 and 24.


Li-Sheng Wang

James C Fettinger

Rinaldo Poli

Rita Meunier-Prest

†

    Cyclopentadienylmolybdenum(II) and -(III) Complexes Containing Diene and Allyl Ligands. 3. Reactivity Studies of the Bis(butadiene) Complex [CpMo( s-cis-supine -η-C 4 H 6 )( s-trans -η-C 4 H 6 )][BF 4 ]

Introduction

In the course of our recent studies of cyclopentadienylmolybdenum(II) and -(III) complexes containing allyl and diene ligands, 2,3 we have established that the electron-rich isomeric complexes CpMo(η 3 -C 3 H 5 )(η 4 -C 4 H 6 ) (1a-c; see Scheme 1) are not susceptible to nucleophilic attack, while the electrophilic attack by protons easily takes place. The position of attack and nature of the ultimate products depend on the coordination mode of the allyl and diene ligands in the starting compound and on the reaction conditions (especially the nature of the solvent) (see Scheme 1). It is particularly intriguing to observe that, in MeCN, the s-trans diene in 1c is more susceptible to proton attack than the allyl ligand, whereas the allyl is always selectively attacked in 1a or 1b, where the diene ligand has the s-cis configuration. Calculations of charge distribution in 1a-c by DFT methods have provided a rationalization of this difference, as well as details on the Mo-allyl and Mo-butadiene bonding as a function of the ligand conformation. 3 The protonation of 1a with HBF 4 in the presence of excess butadiene has led to the selective preparation of isomerically pure [CpMo(s-cis-supine-C 4 H 6 )(s-trans-C 4 H 6 )]BF 4 (2), isoelectronic with complexes 1. There are few reported complexes containing a coordinated s-trans diene ligand, [4][5][6][7][8][9][10][11][12] and fewer still are those where both an s-cis and an s-trans diene are coordinated to the same metal center. The only such example known to us is CpNb(η 4 -C 4 H 6 ) 2 , reported by Nakamura et al., but this is unfortunately obtained in admixture with the bis-scis isomer. 5 We expected that the positive charge in 2, relative to the precursor complexes 1, would change the electronic properties of the coordinated diene ligand in favor of the reactivity toward nucleophiles. Nucleophilic additions to coordinated diene ligands have been extensively used in regiocontrolled organic synthetic applications, especially when the diene is functionalized by the [CpMo(CO) 2 ] + template. [START_REF] Pearson | Comprehensive Organometallic Chemistry II[END_REF] However, this reaction has been mostly investigated for cyclic diene ligands. For acyclic dienes, studies have mostly been limited to the addition of nucleophiles such as hydride, vinylcuprates, and cyanide to s-cis-coordinated ligands. [START_REF] Pearson | Comprehensive Organometallic Chemistry II[END_REF] There is only one reported study, to the best of our knowledge, of nucleophilic additions to a coordinated s-trans ligand, namely in the complexes [CpMo(CO) 2 (s-trans-CH 2 dCH-CHdCHR)] + (R ) H, Me). 11 In many cases, studies of this nature are rendered difficult by the rapid transformation of the s-trans diene to the s-cis isomer. 8,11 The comparative reactivity of s-cis and s-trans diene ligands in the same coordination environment does not appear to have ever been investigated. Therefore, we have seen a unique opportunity to carry out such a study for complex 2. The results of these investigations are the subject of the present contribution.

Experimental Section

General Procedures. All reactions were conducted by standard Schlenk-line techniques under a dinitrogen atmosphere. Solvents were dried by conventional methods (THF and Et2O on Na/benzophenone, toluene and heptane on Na, CH2Cl2 on P4O10) and distilled directly from the drying agent under dinitrogen. All routine NMR experiments were carried out on Bruker AM400 and WF 200 spectrometers, while 2D NMR spectra were recorded on a Bruker AMX500 spectrometer. The 1 H and [START_REF] Pearson | Comprehensive Organometallic Chemistry II[END_REF] C NMR data of all new compounds are given in Table 1. EPR spectra were recorded on a Bruker ER200 spectrometer and IR spectra on a Perkin-Elmer FTIR 1600 spectrophotometer. Cyclic voltammograms were recorded with a PRT 30 Tacussel potentiostat equipped with a home-built amplifier, a Hewlett-Packard 3314A function generator, and a Nicolet 450 digital oscilloscope or an X-Y Sefram plotter. The electrochemical cell was fitted with an SCE reference electrode and Pt working and counter electrodes. The supporting electrolyte used was 0.1 M Bu n 4NPF6. All potentials are reported vs the Cp2Fe/Cp2Fe + couple, which has an E1/2 value of +0.50 V relative to SCE under conditions identical with those of the other experiments. Mass spectra were measured with a VG 7070E mass spectrometer. Elemental analyses were performed by Atlantic Microlab, Inc., or the analytical service at the LSEO, Dijon, France. [CpMo(s-cissupine-η-C4H6)(s-trans-η-C4H6)][BF4] (2) was prepared according to the literature procedure. 3 Reactions of 2 with Bu t NC. Formation of [CpMo-(CNBu t )2(supine-C4H6)][BF4] (3). To a CD3COCD3 suspension of complex 2 (10 mg, 28 µmol in 0.5 mL) was added 2 equiv of tert-butyl isocyanide (6.3 µL, 56 µmol), followed by vigorous shaking. The suspension remained unchanged and no reaction was detected by 1 H NMR within 0.5 h. After it stood for 24 h at room temperature, most of the solid had dissolved and the 1 H NMR showed new resonances at δ 5.71 (2Ha, m), 5.33 (5H, Cp, s), 2.36 (2Hb, d, 3 JHH a ) 7 Hz), 1.50 (18H, CNBu t , s), and 1.20 (2Hc, d, 3 JHH a ) 7.5 Hz), which are assigned to [CpMo(CNBu t )2(supine-C4H6)][BF4] (3) by comparison with the literature, 3 accompanied by the resonances at δ 6.35 (multiplet, 2H), 5.21 (doublet of multiplet, 2H), and 5.08 (doublet of multiplet, 2H) for free butadiene. Integration of the resonances shows the formation of 3 and C4H6 in a 1:1 ratio.

Reaction of 2 with PMe3. Preparation of [CpMo(syn-Me3PCH2-prone-η-C3H4)(s-cis-supine-η-C4H6)][BF4] (4). (i)

NMR Monitoring. Compound 2 (10 mg, 0.028 mmol) was suspended in 0.5 mL of acetone-d6 in an NMR tube. PMe3 (5.8 µL, 0.056 mmol) was added by microsyringe, causing the formation of a yellow-brown solution. Monitoring by 1 H NMR spectroscopy showed the quantitative conversion of compound 2 to [CpMo(syn-Me3PCH2-prone-η-C3H5)(s-cis-supine-η-C4H6)]-[BF4] (4), without the formation of significant amounts of other NMR-active byproducts.

(ii) Preparative Scale. To a suspension of compound 2 in acetone (200 mg, 0.56 mmol in 10 mL) was added PMe3 (116 µL, 1.12 mmol). The suspension turned to a yellow-brown solution within 10 min. Stirring was continued for an additional 0.5 h at room temperature, yielding a green-yellow precipitate. The solution was filtered, the solvent was removed under reduced pressure, and the solid was washed with 5 mL of THF, giving a green-yellow solid (yield, 215 mg, 89%). 31 P-{ 1 H} NMR: 18.9 ppm (doublet of doublets of doublets, 2 JH gP ) 15 Hz, 2 JH hP ) 15 Hz, 3 JH f′P ) 8 Hz). Anal. Calcd for C16H26-BF4MoP: C, 44.5; H, 6.1. Found: C, 44.2; H, 6.1. A single crystal for the X-ray analysis was obtained by vapor diffusion of diethyl ether into an acetone solution.

Reaction of 2 with MeLi. Preparation of CpMo(syn-Et-prone-η-C3H4)(s-cis-supine-η-C4H6) (5). (i) NMR Monitoring. To a suspension of complex 2 (5 mg, 0.014 mmol) in 0.5 mL of THF was added 10 µL of a MeLi solution (1.4 M in diethyl ether, 1 equiv) causing the dissolution of the yellow starting material and formation of an orange solution. All solvent was removed by rapid dinitrogen flow, followed by evaporation under reduced pressure for 5 min. C6D6 (0.5 mL) was subsequently added, and the solution was investigated by 1 H NMR. The entire operation took ca. 15 min from the mixing of the reagents. The NMR showed the formation of isomerically pure CpMo(syn-Et-prone-η-C3H4)(s-cis-supine-η-C4H6) (5).

(ii) Preparative Scale. To a suspension of complex 2 (200 mg, 0.562 mmol) in THF (20 mL) was added 1 equiv of MeLi (1.4 M in Et2O, 0.4 mL, 0.56 mmol), resulting in the immediate formation of an orange solution. After 0.5 h of stirring at room temperature, all solvent was removed under reduced pressure. The product was extracted with 2 × 20 mL of heptane, followed by filtration and solvent removal under reduced pressure, to yield an yellow oil (yield 310 mg). Low-resolution mass spectrum (FAB+): m/z 286 [CpMo(Et-C3H4)(C4H6)] + , 38%. The experimental isotopic envelope is in excellent agreement with the simulation. Cyclic voltammetry (THF, room temperature): ECE process with electrochemical oxidation for 5 at E1/2 ) -0.50 V (∆Ep ) 60 mV), followed by chemical transformation to 7/7 + (see Results).

Reaction of 5 with HBF4. Formation of trans-2-Pentene. Complex 5 (5 mg, 17.6 µmol) was dissolved in 0.5 mL of C6D6. HBF4'Et2O (3 µL) was added by microsyringe, causing the precipitation of a gray solid. 1 H and [START_REF] Pearson | Comprehensive Organometallic Chemistry II[END_REF] C NMR showed the formation of trans-2-pentene. 1 H NMR (C6D6, δ): 5.39 (m, 2H), 1.93 (m, 2H), 1.58 (d, 3H), 0.91 (t, 3H). [START_REF] Pearson | Comprehensive Organometallic Chemistry II[END_REF] C{ 1 H} NMR (C6D6, δ): 133.3 (1C), 123 (1C), 25.9 (1C), 18.0 (1C), 12.4 (1C).

Reaction of 2 with C3H5MgBr. Formation of CpMo-(syn-CH2dCHCH2CH2-prone-η-C3H4)(s-cis-supine-η-C4H6) (6). To a suspension of complex 2 (400 mg, 1.12 mmol) in THF (20 mL) was added allylmagnesium bromide (1 M in Et2O, 1.1 mL, 1.1 mmol) by syringe, causing the immediate formation of a yellow-brown solution. The solution was stirred overnight, followed by solvent removal under reduced pressure. The product was extracted with heptane (40 + 20 mL), followed by filtration. Evaporation of the solvent under reduced pressure gave an oily residue. Investigation of this residue by 1 H NMR showed the formation of the new complex CpMo(syn-CH 2dCHCH2CH2-prone-η-C3H4)(s-cis-supine-η- C4H6) (6) and CpMo(prone-η-C3H5)(s-cis-supine-η-C4H6) (1a). The latter was recognized by comparison of its NMR properties with those reported previously. 2 Integration of the 1 H NMR resonance gave a 6/1a ratio of 90:10. Low-resolution mass spectrum (FAB+): m/z 312 [CpMo(CH2dCHCH2CH2C3H4)-(C4H6)] + , 17%. The experimental isotopic envelope is in excellent agreement with the simulation.

Oxidation of 5 by FcPF6. Preparation of [CpMo(syn-Et-supine-η-C3H4)(s-cis-supine-η-C4H6)][PF6] ([7]PF6). (i)

Preparative Scale. A solution of compound 5 in heptane (190 mg, 0.669 mmol in 1 mL) was added to a solution of ferrocenium hexafluorophosphate (221 mg, 0.668 mmol) in acetone (30 mL). The purple-violet solution initially turned green and then changed to dark brown within seconds. After filtration, the volume of the solution was reduced to 5 mL under reduced pressure. Upon addition of 20 mL of THF, black needle-shaped crystals formed. The mother liquor was filtered off, and the solid was washed with 5 mL of THF and dried under vacuum for 1 h (yield 100 mg, 35% (ii) Spectroscopic EPR Monitoring. An EPR tube was charged with complex 5 (1 mg, 3 µmol) and Cp2FePF6 (1 mg, 3 µmol). Acetone (200 µL) was added at -196 °C. The mixture was thawed to -80 °C only immediately before the introduction into the EPR probe. The reaction was monitored by EPR, with gradual elevation of the temperature from -80 to 25 °C in increments of 20 °C. At -80 °C, the green mixture showed a major EPR signal at g ) 2.039 (a4H ) 8 G, aMo ) 28 G), which was assigned to [5] + , and a minor signal at g ) 2.034. The intensity of the two species remained unchanged 20 min. As the temperature was increased to -20 °C, the original major species disappeared over 20 min, while the original minor species gained intensity. At 25 °C this species showed a signal at g ) 2.029 (a5H ) 7 G, aMo ) 33 G), corresponding to [7] + (see previous section).

) 3 JHH f ) 3 JHH f ′ ) 10 Hz), 1.68 (1Hg, m), 1.49 (1He, 3 JHH d ) 9 Hz, 2 JHH f ) 3 Hz), 1.44 (1Hh, m), 1.33 (1Hf ′, ddd, 3 JHH d ) 10 Hz, 3 JHH g ) 3 JHH h ) 7 Hz), 1.08 (3Hi, dd, 3 JHH g ) 3 JHH h ) 7
) 3 JHH f ) 3 JHH f ′ ) 10 Hz), 2.20 (2Hi, ddd, 3 JHH j ) 6.5 Hz, 3 JHH g ) 3 JHH h ) 7 Hz), 1.62 (1Hg and 1Hh, m), 1.47 (1He, 3 JHH d ) 9 Hz, 2 JHH f ) 3.5 Hz), 1.34 (1H f ′, ddd, 3 JHH d ) 10 Hz, 3 JHH g ) 8 Hz, 3 JHH h ) 6. 5
CpMo(syn-Et-supine-η-C3H4) (s-cis-supine-η-C4H6) (7) a 4.49 (1Ha′, ddd, 3 JHH a ) 3 JHH b′ ) 7 Hz, 3 JHH c′ ) 9. 5
Reduction of [7]PF 6 by Cp2Co. Formation of CpMo-(syn-Et-supine-η-C3H4)(s-cis-supine-η-C4H6) (7). [7]PF6 (5 mg, 7.8 µmol) and Cp2Co (1.5 mg) were placed in an NMR tube, to which 0.5 mL of acetone-d6 was subsequently added. An instant reaction took place with the formation of a violet solution and precipitate. Monitoring by 1 H NMR revealed the selective formation of complex 7, followed by its slow conversion to 5 with the half-life t1/2 ) 95 min.

X-ray Crystallography for Compound 4. A yellow crystal with dimensions 0.500 × 0.213 × 0.100 mm was placed and optically centered on the Enraf-Nonius CAD-4 diffractometer. The cell parameters and crystal orientation matrix were determined from 25 reflections in the range 17.7 < θ < 19.58°and confirmed with axial photographs. Data collection (3783 reflections in the -h,k,l and -h,k,l and h,-k,-l octants) and reduction were routine. A decay correction was not necessary, whereas an absorption correction based upon crystal faces was applied (T in the 0.8442-0.9229 range). Averaging of equivalent data gave 3311 unique intensities (R(int) ) 0.0206). Systematic absences from the data uniquely determined the space group as P212121 (No. 19). Direct methods resulted in the successful location of the Mo and P atoms and several C atoms. The remaining non-hydrogen atoms were located from two subsequent difference Fourier maps, alternating with full-matrix least-squares refinement cycles. Hydrogen atoms attached to carbon atoms were placed in calculated positions and continually updated but not refined. All of the non-hydrogen atoms were refined anisotropically. As the refinement converged, the absolute structure parameter, Flack(x), was refined to 0.40. The structure was inverted with the Flack(x) parameter refined to 0.37. At this point, a racemic twinning model was used, leading to refinement of the BASF parameter, equivalent to the Flack(x) parameter, at a value of 0.52 (6). This indicates that the correct structure is composed of both enantiomorphs. The structure was refined to convergence (∆/σ e 0.001) with R(F) ) 5.03, Rw(F 2 ) ) 7.83%, and GOF ) 1.055 for all 3311 unique reflections [R(F) ) 3.41%, Rw(F 2 ) ) 7.13% for those 2749 data with Fo > 4σ(Fo)]. A final difference Fourier map was featureless with |∆F| e 0.43 e Å -3 , indicating that the structure is both correct and complete. Relevant crystal and refinement parameters are collected in Table 2, and selected bond distances and angles are given in Table 3.

Theoretical Calculations. The geometry of the [CpMo-(s-cis-supine-C4H6)(s-trans-C4H6)] + cation was optimized at the DFT-B3LYP level. [START_REF] Becke | [END_REF] The calculations were run using GAUSS-IAN 94 15 on the SGI Power Challenge at the Universite ´de Bourgogne. The LanL2DZ basis set used includes both Dunning and Hayı ´s D95 sets for H and C [START_REF] Dunning | Modern Theoretical Chemistry[END_REF] and the relativistic electron core potential (ECP) sets of Hay and Wadt for the Mo atom. [START_REF] Hay | [END_REF][18][19] Electrons outside the core were all those of H and C atoms and the 4s, 4p, 4d, and 5s electrons for Mo. Molecular orbital calculations were also carried out by the Fenske-Hall method 20 on the B3LYP-optimized geometry, using version 5.1 of the program for the Macintosh. [START_REF] Hall | Hall Molecular Orbital Program[END_REF] The default basis functions used by the program are generated by the numerical XR atomic orbital program of Herman and 2) readily reacts with a variety of nucleophilic reagents, i.e., MeCN, t BuNC, PMe 3 , and Grignard reagents. The reaction path followed, however, differs depending on the reagent chosen. We have already reported that dissolution of compound 2 in MeCN leads to the substitution of the s-trans butadiene ligand with two molecules of the solvent. 3 An analogous exchange process occurs upon treatment of 2 with 2 equiv of tert-butyl isocyanide, to quantitatively yield the substitution product [CpMo-(supine-C 4 H 6 )(CNBu t ) 2 ][BF 4 ] (3) and 1 equiv of butadiene (see eq 1). Compound 3 was previously obtained from the addition of t BuNC to [CpMo(supine-C 4 H 6 )(η 2µ-F 2 BF 2 )] x . These substitution reactions are indicative of the greater lability of the s-trans butadiene ligand.

Reaction of 2 with PMe 3 leads instead to the selective nucleophilic attack at the endo terminal position of the s-trans butadiene ligand to form a substituted allyl ligand (see eq 2). Due to the low symmetry of the product [CpMo(syn-prone-η-C 3 H 4 -1-CH 2 PMe 3 )(s-cis-supine-η-C 4 H 6 )][BF 4 ] (4), all butadiene and allyl protons have different chemical shifts. The complete assignment of the 1 H NMR spectrum (Table 1) was assisted by a 1 H homonuclear selective decoupling experiment (see I for the proton nomenclature).

The determination of the conformation of the butadiene and allyl ligands is based on the chemical shifts and geminal coupling constants of corresponding protons, following the same analysis described in detail earlier for compound 1c. 2 The diastereotopic protons H g and H h of the methylene group resonate at δ 2.91 and 2.45, both as doublets of doublets of doublets because of geminal coupling with each other, with the adjacent allyl proton, and with the phosphorus nucleus. While the phosphorus couplings are identical (15 Hz), the coupling constants with H f ′ are quite different (3 Hz vs 12 Hz), reflecting a preferential conformation of the CH 2 PMe 3 group with substantially distinct H f ′ CCH g and H f ′ CCH h dihedral angles. The phosphorus nucleus also exhibits an observable (8 Hz) three-bond coupling to the allyl anti proton H f ′ , which is evidenced both in the 1 H and in the 31 P NMR spectrum. The structure of compound 4 is further confirmed by a single-crystal X-ray analysis (vide infra).

Treatment of 2 with 1 equiv of methyllithium immediately yields a yellow-brown solution of CpMo(syn-Et-prone-η-C 3 H 4 )(s-cis-supine-η-C 4 H 6 ) (5) (see eq 3). No trace of compound 7 (vide infra) is observed in this reaction. As shown in Table 1, the spectroscopic properties of 5 are similar to those of compound 4; thus, an identical structure (i.e. I) is proposed. Again, all allyl and diene hydrogen atoms are chemically inequivalent because of the low symmetry. The diastereotopic methylene protons (located at 1.68 and 1.44 ppm) show in this case identical coupling with proton H f ′ . The relative upfield shift of these protons, as well as of the Cp, butadiene, and allyl protons, relative to those of complex 4 can be rationalized by the inductive effect of the methyl vs the phosphonium group. A positive NOE effect between H a and H f and between H a′ and H f ′ can be taken as further evidence that the ethyl group occupies a syn position. A positive NOE effect was also observed between H a and H f in the symmetric compound CpMo(prone-η-C 3 H 5 )(s-cis-supine-η-C 4 H 6 ) (1a). 2 Treatment of 2 with allylmagnesium bromide yields a mixture of CpMo(syn-CH 2 dCH(CH 2 ) 2 -prone-η-C 3 H 4 )-(s-cis-supine-η-C 4 H 6 ) (6) and CpMo(prone-η-C 3 H 5 )(s-cissupine-η-C 4 H 6 ) (1a) in a 90:10 ratio. The two products may be rationalized by a competition of the two established reaction pathways: 90% of nucleophilic attack at the s-trans diene terminal carbon according to eq 3, and 10% of substitution of the s-trans diene ligand according to eq 1. The diastereotopic methylene protons in compound 6 overlap at ca. 1.62 ppm. The proton signals of the terminal vinyl group (-CH j dCH k H l ) are found in the typical range, indicating that this group is not coordinated to the metal center. The chemical shifts of other protons of 6 are close to the same protons of 5, indicating that similar geometries and conformations are adopted by both complexes.

X-ray Structure of Compound 4. The nature of the PMe 3 addition product as the proposed [CpMo(synprone-η-C 3 H 4 -1-CH 2 PMe 3 )(s-cis-supine-η-C 4 H 6 )][BF 4 ] has been confirmed by an X-ray structural study. A view of the cation is shown in Figure 1. The overall geometry, conformation of the allyl and diene ligands, and (22) This behavior is identical with that of the previously reported parent complex 1a, where oxidation to green [1a] + is followed by a rapid isomerization to violet [1b] + . 2 The EPR spectrum of green [5] + can only be observed by carrying out the oxidation reaction directly in the EPR tube at -80 °C, although extensive isomerization to the violet isomer has already taken place. Subtraction of the equilibrium spectrum (mostly due to [7] + , vide infra) from the intial spectrum of the mixture yields a binomial pentet (g ) 2.039, a Mo ) 27 G, a 4H ) 8 G, THF, -80 °C) for [5] + (see Figure 2a), which is essentially identical with the EPR spectrum previously reported for [1a] + (g ) 2.039, a Mo ) 28 G, a 4H ) 8.5 G, acetone, -80 °C). 2 This comparison is consistent with our previous conclusion that the electron couples to the four terminal butadiene hydrogen nuclei and not to those of the allyl ligand. 2 The EPR spectrum of [7] + , on the other hand, exhibits a sextet at g ) 2.034 in the EPR spectrum, due to the coupling to five protons (a 5H ) 7 G) (see Figure 2b). In view of the septet patternobserved for [1b] + and assigned to the coupling to the four terminal butadiene protons and two syn allyl protons, 2 the EPR data of [7] + are easily interpreted as deriving from the coupling to the four terminal butadiene protons and one syn allyl proton, because one syn position is occupied by the ethyl group. The EPR data are thus consistent with the NMR assignment of the syn structure for the allyl ligand in the precursor 5. The spectrum in Figure 2b does not exclude the presence of a small amount of [5] + at equilibrium.

Reduction of the 17-electron complex [7] + by cobaltocene gives the diamagnetic [CpMo(syn-supine-η-C 3 H 4 -1-Et)(s-cis-supine-η-C 4 H 6 )] ( 7), which quantitatively transforms to compound 5 as shown by the NMR monitoring. Again, this behavior parallels that reported for the allyl complex [1b] + , 2 whose reduction afforded 1b followed by the slow (t 1/2 ) 6.5 h) isomerization to the thermodynamically more stable 1a. The kinetic analysis of the conversion of 7 to 5 (see Figure 3) yields the rate constant k ) 7.3 × 10 -3 min -1 , corresponding to a halflife of 95 min, and an extrapolated initial 7:5 ratio of 94.3:5.7. We assume that this also corresponds to the equilibrium ratio of [7] + : [5] + before the cobaltocene reduction.

The cyclic voltammetric study of complexes 5 and [7] + are fully consistent with the results of the chemical investigation. At high sweep rates (v > 0.2 V s -1 ) compound 5 exhibits an electrochemically reversible one-electron oxidation wave in THF at E 1/2 ) -0.50 V. However, at lower sweep rates the return reduction wave has a smaller intensity and is followed by a new reduction wave at E 1/2 ) -0.86 V (see Figure 4). The new wave is the follow-up of the fast chemical isomerization process from [5] + to [7] + , as shown by the independent cyclic voltammetric study of isolated [7] + . A decrease of the scan rate results in a decrease of the relative intensity for the cathodic wave corresponding to the conversion of [5] + to 5. This is as expected, because [5] + has more time to isomerize to [7] + . In addition, there is a decrease in the relative intensity of the anodic wave that corresponds to the conversion of 7 to [7] + . Since we know from the independent NMR study (vide supra) that the isomerization of 7 to 5 is very slow and negligible within the time scale of the voltammetric experiment, the concentration reduction of 7 may only be attributed to a reversibility for the process interconverting [5] + and [7] + (see Scheme 2). A thin-layer CV study (see Figure 5) and subsequent simulation confirm this hypothesis and allow the determination of both forward and reverse isomerization rate constants (k 1 ) 0.1 s -1 ; k -1 ) 6.7 × 10 -3 s -1 ). The equilibrium constant determined from these rates, K ) k 1 /k -1 ) 15, corresponds to an equilibrium [7] + : [5] + ratio of 93.8:6.2, in excellent agreement with the ratio suggested by the NMR study.

Protonation of Compound 5. In part 2 of this series, 3 we have shown that compound 1a is electrophilically attacked by the proton at the terminal position of the allyl ligand, generating propene. Since the allyl ligand of the homologous compound 5 is asymmetric, it was of interest to probe the position of electrophilic attack for this compound. 1 H NMR monitoring shows the selective formation of trans-2-pentene. The absence of 1-pentene shows that the attack occurs regioselectively at the unsubstituted terminal allyl carbon, whereas the absence of cis-2-pentene further confirms the syn configuration of the coordinated allyl ligand.

Molecular Orbital Calculations. As the [CpMo-(s-cis-supine-C 4 H 6 )(s-trans-C 4 H 6 )] + cation has not been crystallographically characterized, a tentative starting geometry was constructed by combining the CpMo(scis-supine-C 4 H 6 ) and CpMo(s-trans-C 4 H 6 ) fragments from the X-ray-determined structures of 1a and 1c, respectively. 2 The geometry was subsequently optimized at the DFT-B3LYP level. [START_REF] Becke | [END_REF] This computational method has proven quite reliable for both geometries and energies of transition metal complexes. 25,26 The optimized geometry, which differs only in minor details from the input geometry obtained from the X-raydetermined fragments, is shown in Figure 6. Selected bond distances are listed in Table 4.

The salient feature of the optimized structure (and the major difference relative to the tentative input geometry) is the lengthened distance between the metal and the endo terminal carbon of the s-trans ligand. The reason for this distortion is not obvious from the com- 2). putational results. It is interesting to see, however, that the endo carbon atom corresponds to the position of nucleophilic attack. A naive idea for a rationalization of this distortion could involve the contribution of a diene-allyl resonance structure as shown in II. This would rationalize the propensity of the terminal carbon toward attack by nucleophilic reagents, if this attack were charge-controlled. To probe for this effect, we have carried out an effective atomic charge analysis by three different methods: a Mulliken population analysis using the B3LYP density matrix, a natural population analysis of the B3LYP natural bond orbitals, 27 and a Mulliken population analysis of the molecular orbitals obtained from a Fenske-Hall calculation on the B3LYP-optimized geometry. The three results are compared in Table 5. The s-trans endo carbon (atom C13) indeed shows a more positive (or less negative) effective charge relative to the other diene terminal carbon atoms (C10, C9, and C6) at all levels of calculation. The charge differences observed, however, are not large and indicate that a resonance form such as II is not very important.

A closer inspection of the optimized bond distances in Table 4, notably the shorter C12-C13 bond relative to the C10-C11 bond, reiterates the relative unimportance of the limiting form II. These data suggest rather, that the s-trans diene ligand is best considered as a diolefin with a loosely metal-bound C12-C13 ene function. The s-cis diene ligand, on the other hand, binds symmetrically to the metal center, in a way that is consistent with the classical Dewar-Chatt-Duncanson view of metal-diene bonding (donation from the π 2 , back-bonding to the π 3 Huckel orbital). 28 Anucleophilic attack at a π ligand is not likely to be charge-controlled but, rather, orbital-controlled. For this reason, an analysis of the LUMO was also carried out. From the Fenske-Hall results, the largest contribution to this orbital is from Mo atomic orbitals (36.7%). The second largest contribution is by far from the orbitals of the endo carbon of the s-trans butadiene ligand (27.5%, mostly p z , the local z axis pointing toward the metal center). The relative contribution of the butadiene carbon orbitals to the LUMO is qualitatively illustrated in Figure 7. For an orbital-controlled nucleophilic addition, it is therefore expected that the nucleophile attacks the endo terminal carbon atom of the s-trans ligand, as experimentally observed. Attack at the metal center (the other large contributor with its atomic orbitals to the LUMO) rationalizes the path leading to the substitution products.

Discussion

Relative Reactivity of the Diene Ligands toward Nucleophiles. The reaction of [CpMo(s-cis-supine-C 4 H 6 )(s-trans-C 4 H 6 )] + (2) with nucleophilic reagents proceeds along two possible pathways, namely nucleophilic addition and substitution (see Scheme 3). The substitution pathway is preferred by neutral twoelectron donors (MeCN and t BuNC), whereas the addition pathway is preferred by anionic reagents that can form stable allyl ligands. There are, however, exceptions to the above rule. The allyl Grignard reagent also affords minor amounts of the substitution product, while PMe 3 selectively affords the addition product. Numerous precedents for the nucleophilic addition of phosphorus nucleophiles to π ligands, both cyclic and acyclic, are available. 29 It does not seem, however, that the Both reaction pathways observed for compound 2 involve the s-trans butadiene ligand, which is either replaced or subjected to nucleophilic addition. The s-cis ligand simply acts as a stabilizing spectator ligand like the cyclopentadienyl ring. Thus, the weaker binding of the s-trans diene ligand also corresponds to its stronger activation toward nucleophilic attack. As stated in the Introduction, nucleophilic additions to a coordinated s-trans diene have only been previously reported for [CpMo(CO) 2 (s-trans-CH 2 dCHCHdCHR)] + (R ) H, Me). 11 The study of the [CpMo(CO) 2 (s-trans-diene)] + class is rendered difficult by the fast isomerization to the more stable s-cis isomer. 8 Compound 2, on the other hand, is isomerically stable. Compounds of the isoelectronic CpMo(NO)(s-trans-diene) class are thermodynamically more stable than the s-cis isomers, but they are rather susceptible to electrophilic attack, e.g. by acetone 10 (cf. the reactivity toward protons of compounds 1), 3 while the addition of nucleophilic reagents such as tertiary phosphines only leads with difficulty to products of addition to the metal center. 6 It is interesting to note that the s-trans diene ligand is also more susceptible than the s-cis conformer toward the electrophilic attack by protons (see Scheme 1), as shown by the comparative protonation study of compounds 1a-c. 3 Position of Nucleophilic Attack. In the nucleophilic addition reactions, the nucleophile attacks selectively the terminal endo position of the s-trans butadiene ligand. This is clearly shown by a rapid monitoring of the reaction with MeLi. Compound 5 is the only product formed instantaneously by the nucleophilic addition of MeLi to 2. An attack at the exo position would yield compound 7 with a supine allyl ligand (Scheme 4). This alternative product was selectively obtained by another route (Scheme 2) and shown to convert into the isomer with the prone allyl ligand (compound 5) slowly at room temperature (t 1/2 ) 95 min). Thus, the formation of only 5 from this reaction proves the regioselective attack at the endo position of the s-trans diene ligand. This experimental result is fully consistent with the idea of an orbital-controlled nucleophilic addition and with the computational results, which indicate a greater contribution of the s-trans endo carbon orbitals to the LUMO (see Figure 7). The computational results also rationalize the similar reactivity pathway reported for [CpMo(CO) 2 (s-trans-CH 2 dCH-CHdCHMe)] + , 11 where the methyl group of the pentadiene ligand selectively occupies the endo position. This compound was shown to readily react with several nucleophiles, including H 2 O, alcohols, amines, ethanethiol, and methyllithium. Small nucleophiles (H 2 O, MeOH, EtOH, MeLi, and Pr i -NH 2 ) gave only the sterically less favored endo addition product, whereas the largest nucleophile (Pr i 2 NH) gave predominantly the exo addition product. In our case, only the endo addition product was observed in all cases. It is clear that the endo carbon is the electronically preferred position for both substrates. The nature of the ancillary ligands (two CO ligands in place of s-cisbutadiene) may electronically affect the relative reactivity of the two lateral carbon atoms, or the relatively small size of the PMe 3 ligand and the absence of substituents on the endo carbon atom in 2 may be insufficient steric factors to divert the reactivity toward the exo position.

supine/prone Allyl Isomerism: Thermodynamic Preference and Interconversion Rates. As stated above, it was possible to establish the regioselectivity of nucleophilic attack by virtue of the slow isomerization of the thermodynamically less favored supine allyl ligand in 7 to the more favored prone configuration in 5. The situation encountered here parallels that of the parent compound 1 in its isomeric forms 1a and 1b (see Scheme 1). 2 The two systems differ only by the synethyl substituent in the allyl ligand of 5/7. While the prone allyl configuration in 1a is thermodynamically preferred, the situation is reversed in the oxidized Mo-(III) system, [1b] + being favored over [1a] + . Another analogy between the two systems is the much faster rate of isomerization in the Mo(III) manifold (seconds at room temperature for [5] + f [7] + ) than in the Mo(II) manifold (t 1/2 ) 95 min at room temperature for 7 f 5).

There are only small quantitative differences in the thermodynamic and kinetic parameters between the two systems. Compound 1 is obtained as an equilibrium 98:2 mixture of 1a and 1b at room temperature, which sets the relative free energy as 2.3 kcal/mol in favor of 1a. The stability of [1b] + relative to [1a] + (∆G ) 5.8 kcal/mol) was calculated from the relative stability of 1a/1b and the difference in E 1/2 values for the two reversible redox processes (1b is oxidized at a potential 0.35 V more negative than 1a). 2 By comparison, the NMR and CV simulation studies independently point to an equilibrium [7] + /[5] + ratio of ca. 94:6 at room temperature, translating into a thermodynamic advantage of 1.6 kcal/mol for [7] + relative to [5] + . The E 1/2 value for 7/[7] + is 0.36 V more negative than the E 1/2 value for 5/[5] + (both potentials being shifted negatively with respect to those of system 1, as expected from the electron-releasing properties of the ethyl group). This sets a thermodynamic advantage of 6.7 kcal/mol for 5 relative to 7 (see Scheme 5). On the basis of this free energy difference, a Boltzmann ratio of 82 000:1 is calculated for 5:7, justifying our inability to observe any amount of 7 at equilibrium by the 1 H NMR technique. Concerning the rate of allyl isomerization, this is faster for the ethyl-bearing allyl complex relative to the parent allyl for both Mo(II) and Mo(III) systems. For the Mo(II) system, the isomerization half-life is 95 min for 7 compared with 6.5 h for 1b under the same conditions, translating to a reduction in activation barrier of 0.8 kcal/mol (from 23.6 for 1b to 22.8 kcal/ mol for 7). For the Mo(III) system, the rates determined by the electrochemical analysis set an activation barrier of 18.7 kcal/mol for the transformation of [5] + to [7] + . Correspondingly, the activation barrier for the isomerization of [1a] + to [1b] + was previously estimated ca. 0.7 kcal/mol higher, at 19.4 kcal/mol. 2 Thus, the acceleration factor due to the introduction of a syn-Et substituent on the allyl ligand is approximately independent of the metal oxidation state.

Conclusions

The present study, in conjunction with the previous report in this series, 3 illustrates that the s-trans butadiene ligand in Cp-substituted Mo(II) complexes can be subjected to either electrophilic attack by protons (in the electron-rich neutral allyl derivative 1c) or nucleophilic attack (in the electron-poorer, positively charged diene derivative 2) (see Scheme 6). While the allyl ligand in 1c competes with the s-trans diene ligand for the electrophilic reagent, the metal center competes for the nucleophilic reagent in 2. In both cases, the s-trans diene ligand reacts preferentially relative to the s-cis diene. Finally, whereas the proton attack is presumably charge-controlled and takes place regioselectively at the diene exo position, the nucleophilic addition is orbitalcontrolled and takes place regioselectively at the diene endo position.

  Hz), 4.39 (5H, Cp, s), 4.29 (1Ha, ddd, 3 JHH a′ ) 3 JHH b ) 7 Hz, 3 JHH c ) 9 Hz), 3.97 (1Hd, ddd, 3 JHH e ) 7 Hz, 3 JHH f ) 3 JHH f ′ ) 12 Hz), 2.51 (1Hb′, d, 3 JHH a′ ) 7 Hz), 2.45 (1He, 3 JHH d ) 7 Hz), 2.1 (1Hb, overlapping with the solvent signal), 1.95 (1Hh, m), 1.75 (1Hg, m), 1.02 (3Hi, dd, 3 JHH g ) 3 JHH h ) 7.5 Hz), 1.0 (1Hf and 1Hf ′, overlapping with Hi), 0.50 (1Hc′, d, 3 JHH a′ ) 9.5 Hz), 0.26 (1Hc, d, 3 JHH a ) 9 Hz) a Acetone-d6. b Acetonitrile-d3. c C6D6.

2

 2 For the butadiene ligand, the lateral Mo-C bonds are shorter than the internal ones (average ∆d ) -0.093 Å; cf. -0.065 Å for 1a) and the lateral C-C bonds are longer than the central one by 0.025 Å (cf. 0.032 Å for 1a). The allyl ligand has longer lateral Mo-C bonds (by 0.072 Å, cf. 0.086 Å for 1a). Chemical and Electrochemical Oxidation of Compound 5. The low-temperature oxidation of Cp-Mo(syn-prone-η-C 3 H 4 -1-Et)(s-cis-supine-η-C 4 H 6 ) (5) by ferrocenium hexafluorophosphate in acetone initially gives the unstable green intermediate [CpMo(syn-proneη-C 3 H 4 -1-Et)(s-cis-supine-η-C 4 H 6 )][PF 6 ] ([5] + PF 6 -). However, this transforms rapidly to the violet isomer [CpMo(syn-supine-η-C 3 H 4 -1-Et)(s-cis-supine-η-C 4 H 6 )]-[PF 6 ] ([7] + PF 6 -) upon warming to room temperature.

Figure 1 .

 1 Figure 1. View of the cation in compound 4 with the numbering scheme employed. Ellipsoids are drawn at the 30% probability level.

Figure 2 .

 2 Figure 2. EPR spectra of [CpMo(1-syn-EtC 3 H 4 )(C 4 H 6 )] + in acetone: (a) the prone-allyl-supine-diene species ([5] + ), after subtraction of the spectrum of [7] + , T ) -80 °C; (b) the supine-allyl-supine-diene species ([7] + ), T ) -80 °C.

Figure 3 .

 3 Figure 3. Kinetics of isomerization of 7 to 5 as determined by 1 H NMR integration (solvent C 6 D 6 , T ) 298 K).

Figure 4 . 2 Figure 5 .

 425 Figure 4. Cyclic voltammogram for compound 5 (10 -3 M) (solvent THF, scan rate 10 mV s -1 ). Scheme 2

Figure 6 .

 6 Figure 6. View of the B3LYP-optimized geometry of the [CpMo(s-cis-supine-C 4 H 6 )(s-trans-C 4 H 6 )] + cation, with the numbering scheme employed. The Cp carbon atoms are numbered C1-C5 (see Table2).

Figure 7 .

 7 Figure 7. Qualitative view of the LUMO composition, limited to the two diene ligands, for [CpMo(s-cis-supine-C 4 H 6 )(s-trans-C 4 H 6 )] + . Numbers represent the percent participation of atomic orbitals in the LUMO.

( 30 )

 30 Scheme 3Scheme 4

Table 1 . 1 H NMR Data for Compounds

 1 JHH a′ ) 8 Hz, 3 JHH b ) 7 Hz, 3 JHH c ) 9 Hz), 4.26 (1Ha′, ddd, 3 JHH a ) 8 Hz, 3 JHH b′ ) 7 Hz, 3 JHH c′ ) 9 Hz), 2.91 (1Hg, ddd, 2 JHP ) 15 Hz, 2 JHH h ) 12 Hz, 3 JHH f ′ ) 3 Hz), 2.89 (1Hb, d, 3 JHH a ) 7 Hz), 2.83 (1Hd, ddd, 3 JHH e ) 3 JHH f ) 10 Hz, 3 JHH f ′ ) 9 Hz), 2.80 (1Hb′, d, 3 JHH a′ ) 7 Hz), 2.45 (1Hh, ddd, 2 JHP ) 15 Hz, 2 JHH g ) 12 Hz, 3 JHH f ′ ) JHH h ) 12 Hz, 3 JHH g ) 3 Hz, 3 JHP ) 8 Hz), 0.87 (1Hc, dd, 3 JHH a ) 9 Hz, 2 JHH b ) 1.5 Hz), 0.73 (1Hc′, d, 3 JHH a′ ) 9 Hz), 0.55 (1Hf, dd, 3 JHH d ) 10 Hz, 3 JHH e ) 3.5 Hz) a 111.6 (1Ca, d, 1 J ) 168 Hz), 107.7 (1Ca, d, 1 J ) 170 Hz), 91.5 (5C, Cp, dm, 1 J ) 177 Hz), 71.4 (1Cd, d, 1 J ) 156 Hz), 39.6 (1Cbc, t, 1 J ) 156 Hz), 39.3 (1Cb′c′, t, 1 J ) 156 Hz), 38.1 (1Cf ′, dd, 1 J ) 152 Hz, 2 JHP JHH a ) 3 JHH b′ ) 7 Hz, 3 JHH c′ ) 9 Hz), 4.27 (5H, Cp, s), 3.99 (1Ha, ddd, 3 JHH a′ ) 3 JHH b ) 7 Hz, 3 JHH c ) 9 Hz), 2.86 (1Hb′, d, 3 JHH a′ ) 7 Hz), 2.76 (1Hb, d, 3 JHH a ) 7 Hz), 2.34 (1Hd, ddd, 3 JHH e

	). Anal. Calcd

Table 2 . Relevant Crystal Refinement Data for Compound 4

 2 P ) (max(Fo 2 ,0) + 2Fc 2 )/3.

	empirical formula	C16H26BF4MoP
	fw	432.09
	temp	153(2) K
	wavelength	0.710 73 Å
	cryst system	orthorhombic
	space group unit cell dimens	P2 12121 a ) 7.6932(4) Å b ) 12.5350(9) Å c ) 19.455(2) Å R ) 90°β ) 90°γ ) 90°V
	, Z	1876.1(3) Å 3 , 4
	density (calcd) abs coeff	1.530 Mg/m 3 0.815 mm -1
	F(000)	880
	cryst size θ range for data collectn o. of collected, indep rflns	0.500 × 0.2125 × 0.100 mm 1.93-25.03°n 3783, 3311 (R(int) ) 0.0206)
	max and min transmissn	0.9229 and 0.8442
	no. of data/restraints/params	3311/0/212
	goodness of fit on F 2 final R indices (I > 2σ(I)) a	1.055 R1 ) 0.0341, wR2 ) 0.0713
	R indices (all data) a largest diff peak and hole	(2749 data) R1 ) 0.0503, wR2 ) 0.0783 0.425 and -0.344 e Å -3

a wR2 ) ∑w(Fo 2 -Fc 2 ); w ) 1/[σ 2 (Fo 2 ) + (0.0487P) 2 + 0.2288P];

Table 3 . Selected Bond Distances (Å) and Angles (deg) for Compound 4

 3 Skillman22 used in conjunction with the XR-to-Slater basis program of Bursten and Fenske.23,24

Results Addition of Nucleophilic Reagents to Compound 2.

  The bis(butadiene) complex [CpMo(s-cis-supine-η-C 4 H 6 )(s-trans-η-C 4 H 6 )][BF 4 ] (

Table 5 . Effective Atomic Charges for the [CpMo(s-cis-supine-C 4 H 6 )(s-trans-C 4 H 6 )] + Cation a

 5 Atomic charges of the hydrogen atoms are summed into the attached carbon atom. b Mulliken population analysis of the B3LYP charge density matrix. c Natural population analysis of the B3LYP natural bond orbitals. d Mulliken population analysis of the Fenske-Hall molecular orbitals.

	atom	B3LYP-Mulliken b	B3LYP-NBO c	FH-Mulliken d
	Mo	-0.120	0.101	1.307
	C1 C2 C3 C4 C5	0.114 0.088 0.079 0.059 0.081	0.081 0.068 0.062 0.042 0.063	0.011 -0.006 -0.020 -0.037 -0.027
	C6	0.021	0.062	-0.135
	C7	0.125	0.077	0.073
	C8 C9	0.175 0.003	0.103 0.037	0.024 -0.114
	C10	0.015	0.063	-0.089
	C11	0.142	0.057	0.007
	C12 C13	0.169 0.050	0.058 0.126	0.040 -0.032

a

† Dedicated to Prof. Akira Nakamura on the occasion of his retirement.(1) (a) University of Maryland. (b) Universite ´de Bourgogne.(2) Wang, L.-S.; Fettinger, J. C.; Poli, R. J. Am. Chem. Soc. 1997, 119, 4453-4464.(3) Poli, R.; Wang, L.-S. J. Am. Chem. Soc. 1998, 120, 2831-2840.Scheme 1

Acknowledgment. We are grateful to the NSF (Grant No. CHE-9508521) and to the Re ´gion Bourgogne for support of this work and Mrs. Raveau-Fouquet for technical assistance. The EPR upgrade was made possible in part by an NSF shared equipment (Grant No. CHE-9225064).

Supporting Information Available: Text giving a detailed description of experimental procedures and tables of crystal data and refinement parameters, fractional atomic coordinates, bond distances and angles, anisotropic thermal parameters, and hydrogen atom coordinates for the X-ray structure of compound 4 (9 pages). Ordering information is given on any current masthead page.

Scheme 5

Scheme 6