Chakib Fettal
email: chakib.fettal@etu.u-paris.fr

Lazhar Labiod
email: lazhar.labiod@u-paris.fr

Mohamed Nadif
email: mohamed.nadif@u-paris.fr

Efficient and Effective Optimal Transport-Based Biclustering

Bipartite graphs can be used to model a wide variety of dyadic information such as user-rating, document-term, and gene-disorder pairs. Biclustering is an extension of clustering to the underlying bipartite graph induced from this kind of data. In this paper, we leverage optimal transport (OT) which has gained momentum in the machine learning community to propose a novel and scalable biclustering model that generalizes several classical biclustering approaches. We perform extensive experimentation to show the validity of our approach compared to other OT biclustering algorithms along both dimensions of the dyadic datasets.

Introduction

Let G = (U, V, E) be a bipartite graph, which is a graph whose vertices can be divided into two disjoint sets U = {1, 2, . . . , |U |} with |U | = n, V = {1, 2, . . . , |V |} with |V | = d and the set of edges E where each edge connects a vertex of U to a vertex of V . The adjacency matrix for this type of graph has the following structure

A = 0 n×n B B ⊤ 0 d×d (1)
where B of size n × d is called the biadjacency matrix of G, its rows and columns corresponding to the two sets of vertices; each entry represents an edge between a row and a column. Biclustering (or Co-clustering) is the extention of clustering to this type of graph. Following [START_REF] John A Hartigan | Direct clustering of a data matrix[END_REF], several biclustering models have attempted to solve the problem by viewing B as a two-mode matrix and searching for a simultaneous partition of its rows and columns [START_REF] Inderjit S Dhillon | Co-clustering documents and words using bipartite spectral graph partitioning[END_REF]. In this way, biclustering seeks to reveal subsets of U which exhibit a similar behaviour across a subset of V in matrix B.

Biclustering has been used in a number of different contexts. [START_REF] Michael B Eisen | Cluster analysis and display of genome-wide expression patterns[END_REF] used microarray data to find relations between genes and conditions, finding that genes with similar functions often cluster together. [START_REF] Harpaz | Biclustering of adverse drug events in the fda's spontaneous reporting system[END_REF] applied this paradigm to data from the US Food and Drug Administration reporting system in order to identify groups of drugs with adverse effects. [START_REF] Dolnicar | Biclustering: Overcoming data dimensionality problems in market segmentation[END_REF] used it to find market segments among tourists so as to enable more effective targeted marketing. There have been various other applications [START_REF] Inderjit S Dhillon | Co-clustering documents and words using bipartite spectral graph partitioning[END_REF][START_REF] Templin | Diagnostic measurement: Theory, methods, and applications[END_REF][START_REF] Gu | Bayesian biclustering of gene expression data[END_REF].

Several solutions to the biclustering problem have been proposed in the literature (see [START_REF] Govaert | Co-clustering: models, algorithms and applications[END_REF]). [START_REF] Inderjit S Dhillon | Information-theoretic coclustering[END_REF] used an information-theoretic approach to solve the problem by minimizing the difference in mutual information between B and a summary matrix; they implicitly assume that the data points are generated from a Poisson latent block model [START_REF] Govaert | Mutual information, phi-squared and model-based coclustering for contingency tables[END_REF]. [START_REF] Michael | Modularity and community detection in bipartite networks[END_REF] adapted classical modularity to bipartite networks and then used it to identify modules within them. [START_REF] Wang | Fast nonnegative matrix trifactorization for large-scale data co-clustering[END_REF] proposed a biclustering paradigm based on nonnegative matrix tri-factorization of the biadjacency matrix.

Recently, Optimal Transport (OT) has taken the machine learning community by storm. OT has helped to solve a variety of data mining problems, and biclustering is no exception. [START_REF] Laclau | Coclustering through optimal transport[END_REF] proposed two models for biclustering: a first model, CCOT, which does co-clustering based on the scaling vectors obtained by applying the Sinkhorn-Knopp algorithm on a square subsampled version of matrix B, and a second model, CCOT-GW, which uses scaling vectors obtained by computing entropic Gromov-Wasserstein barycenters, and which does not require subsampling. Then came [START_REF] Vayer Titouan | Co-optimal transport[END_REF], where the authors did biclustering by minimizing a new metric, COOT, which generalizes the Gromov-Wasserstein distance between B and a summary matrix, similarly to what was done in [START_REF] Inderjit S Dhillon | Information-theoretic coclustering[END_REF]. More specifically, they proposed two new metrics: COOT, together with an entropically regularized metric COOT λ . However, both [START_REF] Laclau | Coclustering through optimal transport[END_REF] and [START_REF] Vayer Titouan | Co-optimal transport[END_REF] have certain drawbacks. First, both algorithms do not tackle the biclustering from the beginning; the co-clusters are deduced at the convergence. Thereby biclustering is a consequence and not a main goal. Secondly, they suffer from high computational complexity; CCOT and CCOT-GW also consume large amounts of memory. Finally, we will see that these algorithms are not suited to dyadic sparse data.

In this paper, while integrating the biclustering objective from the beginning, we propose a generic framework for biclustering through optimal transport, which generalizes some previous biclustering approaches. We propose two efficient methods for solving this problem: one that gives an almost hard biclustering, and another that gives a fuzzy or soft biclustering through entropic regularization. These methods outperform other optimal transport biclustering models, in terms of both document and term clustering, on several regular and large scale datasets, while being more computationally and memory efficient. We emphasize once again that the approach we propose is specifically tailored to datasets consisting of dyadic data.

Methodology

Notations. In what follows,

∆ n = {p ∈ R n + | n i=1 p i = 1} denotes the n-dimensional standard simplex. Π(w, v) = {Z ∈ R n×k + |Z1 = w, Z ⊤ 1 =
v} denotes the transportation polytope, where w ∈ ∆ n and v ∈ ∆ k are the marginals of the joint distribution Z and 1 n is a vector of ones. Matrices are denoted with uppercase boldface letters, and vectors with lowercase boldface letters. For a matrix M, its i-th row is m i and its j-th column is m ′ j We have that ∥.∥ 0 is the 0-norm which returns the number of nonzero elements of its argument.

Preliminaries

We first need to introduce exact discrete OT and its entropically regularized counterpart, and show how biclustering can be posed as an integer program.

Discrete OT as a linear program. The goal of discrete optimal transport is to find a minimal cost transport plan between a source probability distribution w and a target distribution v. Here we are interested in the discrete case of the Kantorovich formulation of OT, that is

OT(M, w, v) ≜ min Z∈Π(w,v) ⟨M, Z⟩ (2)
where M ∈ R n×k is the cost matrix, and m ij quantifies the effort needed to transport a probability mass from w i to v j .

Discrete entropy regularized OT. It has been suggested in the literature [START_REF] Cuturi | Sinkhorn distances: Lightspeed computation of optimal transport[END_REF][START_REF] Chizat | Faster wasserstein distance estimation with the sinkhorn divergence[END_REF] that the use of a regularization such as entropic regularization can lead to better computational and statistical efficiency.

OT λ (M, w, v) ≜ min

Z∈Π(w,v) ⟨M, Z⟩ -λH (Z) (3)
where H is the entropy defined as H(Z) ≜i,j z ij log z ij and λ controls the strength of regularization. The computational efficiency comes from the fact that the unique solution of this problem is of the structure Z := diag(a) exp(-M/λ)diag(b), a rescaled elementwise negative exponential of the cost M, where a and b are scaling vectors. These vectors can be found efficiently using the Sinkhorn-Knopp algorithm.

Biclustering as an integer program. The Block seriation problem [START_REF] François | Block seriation problems: A unified approach. reply to the problem of h. garcia and jm proth (applied stochastic models and data analysis[END_REF] consists in finding two permutation matrices, one for the rows and one for the columns s.t. dense blocks appear along the diagonal of the permuted matrix. A possible definition of the block seriation problem is as follows: given a matrix B ∈ R n×d s.t b ij gives the strength of the association between row i and column j (such as in the case of a biadjacency matrix, for example), we have

max C i,j b ij c ij (4) subject to ∀ i, j c ij ∈ {0, 1} ∀ j i c ij ≥ 1 ∀ i j c ij ≥ 1 ∀ i, j, i ′ , j ′ c ij + c ij ′ + c i ′ j ′ -c i ′ j ≤ 2 c i ′ j ′ + c i ′ j + c ij -c ij ′ ≤ 2 c i ′ j + c ij + c ij ′ -c i ′ j ′ ≤ 2 c ij ′ + c i ′ j ′ + c i ′ j -c ij ≤ 2
A solution C is a block diagonal matrix up to a permutation of its rows and columns. The block seriation problem is an integer programming problem that is NP-hard. One approach for solving this problem uses a simplified version where a rank constraint rank(C) ≤ k is added for k the number of desired biclusters. Integrating this constraint into (4), we can define a new problem by low-rank factorization of C, i.e. C = ZW ⊤ , which we formulate as

max Z∈Γ(n,k) W∈Γ(d,k) i,j,h b ij z ih w jh (5)
where

Γ(n, k) = {Z ∈ {0, 1} n×k | Z1 = 1} is the set of hard partitions of dimension n × k.
A simple heuristic for solving this problem involves alternatingly solving for Z given W, and vice-versa, using classical clustering algorithms, before identifying biclusters through the rearranged matrix C, which displays a block diagonal structure, as shown in figure 1a. The biclusters are identified by grouping together the rows and columns that form a block along the diagonal.

Biclustering using Optimal Transport

Here we propose a new biclustering problem based on block seriation and optimal transport. For this purpose we first define what we term an anti-adjacency matrix. Note that a similar concept has been discussed in [START_REF] Wang | The anti-adjacency matrix of a graph: Eccentricity matrix[END_REF].

Definition 1 (Anti-adjacency matrix) Given a graph characterized by an adjacency matrix A, we have a corresponding anti-adjacency matrix A s.t. a ij quantifies the discrepancy between nodes i and j.

We consider a bipartite graph characterized by its biadjacency matrix B = (b ij ) ∈ R n×d . The rows of B are endowed with weights w ∈ ∆ n and its columns with weights v ∈ ∆ d . We also consider a row exemplar distribution r ∈ ∆ r and a column exemplar distribution c ∈ ∆ c . Depending on the availability of a priori information about the data, these weight vectors can be set to uniform distributions.

Now let its anti-biadjacency matrix be B = L(B), where L : R n×d → R n×d means that b ij , the association between node i and node j, is transformed into a discrepancy measure L(B) ij . Thus, we define the optimal transport block seriation problem as the following bilinear program

BCOT(w, v, r, c) ≜ min Z∈Π(w,r) W∈Π(v,c) i,j,k L(B) ij z ik w jk ≡ min Z∈Π(w,r) W∈Π(v,c) L(B), ZW ⊤ (6)
where Z is a transport plan (or coupling) between between the row distribution w and the row exemplar distribution r, and similarly for W w.r.t. the column distribution v and the column exemplar distribution c. Inducing a biclustering via BCOT. We will now show how to obtain a partition of the rows and the columns given a solution pair (Z, W). In what follows our aim is to identify an almost-hard clustering couple for rows and columns from the couplings Z and W.

Definition 2 (h-almost hard clustering) We define an h-almost hard clustering as a clustering whose assignment matrix is C ∈ R n×k s.t. ∥C∥ 0 = n + h and for each row c of C we have that ∥c∥ 0 > 0. When h = 0, we obtain a standard hard clustering with one non-zero element per row.

Proposition 11 For w, v, r and c containing no zeros, there exists an optimal pair of coupling matrices Z and W that are h-almost hard clusterings with h ∈ {0, . . . , k -1}. Furthermore, when

n = k (resp. d = k) and w = r (resp. v = c), this Z (resp. W) becomes a hard clustering, i.e., Z ∈ Γ(n, n) (resp. W ∈ Γ(d, d)).
This means that the solutions are already almost a hard partition of the data, since k << n, d. To obtain a final hard clustering in the strict sense, we assign each row (resp. column) to the one corresponding to the row of Z (resp. W) with the largest value. This should not significantly change the structure of the solution. Figure 1b provides an illustration: here we see the block diagonal structure generated by the product of the two coupling matrices C = ZW ⊤ , with its similarity in appearance to the biclustering produced by the hard block seriation 1a, apart from a few nonzero entries off the block diagonal that are hard to see immediately.

Intuition for BCOT. To explain the intuition behind the proposed approach we need to look at how the problem is solved. The optimization procedure as described in algorithm 1 consists in alternating between the computation of an optimal transport plan Z given W and vice versa. As regards solving for Z given W, the problem can be rewritten as

BCOT(w, v, r, c) ≡ min Z∈Π(w,r) ⟨L(B)W, Z⟩ . (7)
This is an optimal transport problem with L(B)W as the cost matrix. The resulting transport plan Z can be seen as a kind of row cluster assignment matrix: if z ih > 0, then row i is assigned to cluster h. The same holds for W, which can be seen as a column cluster assignment matrix. This also means that since L(B) is the dissimilarity between the rows and the columns, then the cost matrix L(B)W represents the dissimilarity between rows and row exemplars (or representatives or centroids). In particular, L(B) i w h is the dissimilarity or cost of probability mass transportation between row i and row cluster exemplar h. The reasoning is the same for the columns and the optimal coupling W.

Low-rank optimal transport. Biclustering is the main purpose of the approach we proposed, but there is another interesting use case.

Proposition 2 For equal target row and column representative distributions, i.e., r = c, and containing no zero entries, then given a solution pair Z and W to BCOT, the matrix Q = Z diag(1/r)W ⊤ is an approximation of the optimal transport plan that is a solution to problem (2) and whose rank is at most min(rank(Z), rank(W)).

Some recent works [START_REF] Forrow | Statistical optimal transport via factored couplings[END_REF][START_REF] Scetbon | Low-rank sinkhorn factorization[END_REF] have suggested that this kind of low-rank regularization is preferable to entropic regularization as regards certain aspects. For example, the rank parameter is easier to select, since it has simple bounds (an integer between 1 and n). This may be contrasted with the regularization strength λ in the Sinkhorn algorithm, which is continuous.

Fuzzy Biclustering via Regularized Optimal Transport

As previously mentioned, using entropic regularization may be interesting because of its various useful features including statistical and computational efficiency. However, another feature of entropic regularization is that the optimal couplings Z and W are dense matrices as a consequence of the structure of the optimal solution of entropically regularized OT problems. We formulate the problem as follows

BCOT λ (w, v, r, c) ≜ min Z∈Π(w,r) W∈Π(v,c) L(B), ZW ⊤ -λ Z H (Z) -λ W H (W) (8)
where λ Z and λ W are the regularization parameters.

Fuzzy block seriation. We propose a fuzzy variant of the block seriation problem that allows us by extension to define a fuzzy variant for BCOT using entropic regularization. Let the fuzzy block seriation problem be defined as

max Z∈Γs(n,k) W∈Γs(d,k) i,j,h b ij z ih w jh + Ω(Z, W) (9)
where Ω(Z, W) is some regularization term introduced to make the partition matrices Z and W dense (for example, entropic regularization or low-rank constraints), and

Γ s (n, k) = {Z ∈ R n×k + |Z1 = 1}
is the set of fuzzy partitions. Intuitively, for a solution pair (Z, W), up to a constant factor, each entry in the block seriation matrix C = ZW ⊤ can be seen as the probability of its corresponding row and column belonging to the same bicluster i.e.

c ij = z i w j = r h=1 z ih w jh = p(b i , b ′ j ) = r h=1 p(b i , b ′ j ∈ h).
It is easy to see how problem ( 9) is related to problem [START_REF] Demšar | Statistical comparisons of classifiers over multiple data sets[END_REF] and that the couplings corresponding to solutions of the problem give the probability that the different rows and columns belong to the same biclusters. Figure 1c shows biclusters produced by the solutions of BCOT λ . Similarly to BCOT, a block diagonal structure is formed. However, there are also several off-block diagonal nonzero entries that represent the probabilities of the row-column pairs belonging to the same biclusters.

3 Links to Existing Work

Modularity Maximization in Bipartite Graphs

[3].
This model is able to co-cluster binary and contingency matrices by directly maximizing an adapted version of the modularity measure traditionally used for networks. The criterion that it optimizes is

max Z∈Γ(n,k) W∈Γ(d,k) i,j,h z ih w jh b ij - b .j b i. b .. . (10)
By setting L(B) = -(B -1 b.. B11 ⊤ B), this problem becomes equivalent to ours; the difference is in the constraints on Z and W. [START_REF] Hollocou | Modularity-based sparse soft graph clustering[END_REF].

Modularity-Based Sparse Soft Graph Clustering

Here the authors proposed a fuzzy variant of the above problem (although in the context of traditional clustering rather than biclustering). Solving the problem gives, for each element of the dataset, a probability of that element belonging to a given cluster. Our proposed entropic regularization variant represents a kind of extension of this problem to bipartite graphs. [START_REF] Salah | Model-based von mises-fisher co-clustering with a conscience[END_REF][START_REF] Affeldt | Regularized bi-directional co-clustering[END_REF]. This model makes use of the block von Mises-Fisher mixture model for co-clustering directional data on the unit-sphere. It optimizes the following criterion:

Directional Co-clustering with a Conscience

max Z∈Γ(n,k) W∈Γ(d,k) i,j,h 1 √ z .h w .h z ih w jh b ij . (11)
In our formulation, if we define L(B) = -B and apply cluster size normalization on the optimal transport plans Z = Zdiag(Z ⊤ 1) -1/2 and W = Wdiag(W ⊤ 1) -1/2 after computing Z and W respectively in algorithm 1, we obtain a more general version of the algorithm proposed by the authors for solving problem [START_REF] Dolnicar | Biclustering: Overcoming data dimensionality problems in market segmentation[END_REF].

Bipartite Correlation Clustering [2].

In the case where the cost function results in a complete bipartite graph with '+' and '-' edges with a function

L(B) ij = -1 if b ij > 0 +1 otherwise ( 12
)
we get what is known as Bipartite Correlation Clustering. The solution to this problem maximizes the number of agreements, i.e. the number of all '+' edges within clusters plus all '-' edges distributed across clusters. Optimization. Since the block seriation problem is NP-hard, computing an exact solution is prohibitive. An efficient and widely used heuristic for solving these kinds of problems involves the use of block coordinate descent, where row assignments are computed for fixed column assignments, and then vice versa, in alternation. We express the proposed algorithm in pseudo-code as algorithm 1. At each iteration we solve two intermediate optimal transport problems with cost matrices of dimensions n × k and d × k, since B is generally sparse, and L can be defined such that L(B) retains a similarly sparse structure. The computation of the intermediate cost matrices L(B)W and L(B) ⊤ Z is reasonably efficient. We also observed that the algorithm does not need many iterations to converge, as shown in figure 2, be it for BCOT or BCOT λ .

Optimization and Complexity

Algorithm 1: BCOT Input :B bi-adjacency matrix, w and v row and column weights, r and c row and column exemplar distributions Output :π r , π c row and column partitions

W ← W init ; while not converged do Z ← arg OT (L(B)W, w, r); W ← arg OT L(B) ⊤ Z, v, c ; end Generate π r , π c from Z and W;
Proposition 3 The computational complexity of the BCOT algorithm 1 when using an exact OT solver is O (tk∥B∥ 0 + tnk(n + k) log(n + k) + tdk(d + k) log(d + k))), and when using entropic regularization the complexity is O(tk∥B∥ 0 + tkn + tkd), where t is the number of iterations.

In table 1, we report the computational and spatial complexities of the different biclustering approaches. Our model has the same spatial complexity as the COOT variants and a better complexity Table 1: Computational and spatial complexity of the different OT biclustering approaches. For COOT variants, we report complexities for an euclidean cost matrix. For a generic cost, the time complexity is greater. For simplicity, we suppose that d ∈ O(n) and that we want a biclustering with the same number of row and column clusters for COOT and CCOT. t denotes the number of iterations and for CCOT, s denotes the number of necessary samplings.

Method Spatial complexity Time complexity

CCOT O(n 2 ) O(sn 3 ) CCOT-GW O(n 2 ) O(n 3 ) COOT * O(nk) O((n + k)nk + k 2 n + t(n + k)nk log(n + k)) COOT * λ O(nk) O((n + k)nk + k 2 n + tnk) BCOT O(nk) O(k∥B∥ 0 + t(n + k)nk log(n + k)) BCOT λ O(nk) O(k∥B∥ 0 + tnk)
than CCOT variants. As regards the computational complexity, our model should in most cases be faster with sparse data, and our experiments support this conjecture. For reproducibility, we publicly release our code2 .

Experiments

We ran experiments using term-document matrices. The benefit of using biclustering on this kind of data is that the resulting biclusters contain both documents and the words that characterize them, which is helpful in interpreting the clustering of the documents. Additional experiments over synthetic and gene expression data are available in the appendix.

Datasets

We evaluate BCOT in relation to six benchmark document-term datasets: ACM, DBLP, PubMed, Wiki, Ohscal, and 20 Newsgroups. Their characteristics are shown in Table 2. ACM, DBLP, Pubmed and Wiki are attributed networks from which we use only the node-level features that correspond to term-document matrices. We also selected the Ohscal collection and 20 Newsgroups as large-scale document-term matrices to serve as computational efficiency benchmarks.

Experimental Setup

In our experiments we define the loss function as L(B) = -cB, where c is selected from {1, k, d, n}.

For BCOTλ, the regularization parameter lambda is selected from {10 -4 , 10 -3 , 10 -2 , 10 -1 , 1, 10}.

The best hyper-parameters are those that minimize the number of empty clusters. In the case of ties, we select according to the value of the Davies-Bouldin index of the partition [START_REF] David | A cluster separation measure[END_REF]. Random restarts are not used for any of the algorithms, including k-means. We use the implementation provided by the authors for CCOT, CCOT λ and CCOT-GW. The code for CCOT was not available, and so we had to implement it based on the code for CCOT-GW. All the reported figures are the averages of 10 runs.

All the experiments were performed on the same machine with an Intel(R) Xeon(R) CPU and 12GB RAM. For OT solvers we made use of the POT package [START_REF] Flamary | Pot: Python optimal transport[END_REF].

Document Clustering

Metrics. Here, the evaluation is straightforward, we adopt three popular clustering metrics: clustering accuracy (CA), normalized mutual information (NMI) [START_REF] Cai | Non-negative matrix factorization on manifold[END_REF], adjusted rand index (ARI) [START_REF] Hubert | Comparing partitions[END_REF]. Performance. Document clustering results on ACM, DBLP, PubMed and Wiki are given in table 3 for the three metrics. In all cases the best result is obtained either by BCOT or by BCOT λ . Moreover, on Wiki, BCOT λ gives competitive results when compared with state-of-the-art attributed graph clustering methods presented in [START_REF] Fettal | Efficient graph convolution for joint node representation learning and clustering[END_REF], despite not having access to the graph structure information in the Wiki citation network.

Efficiency. BCOT offers the best accuracy while BCOT λ is fastest method on both datasets. We see that for both BCOT and COOT, the entropic-regularized versions outspeed their exact counterparts and that CCOT suffers from very high computation times, due mainly to the fact that this method requires pairwise distance matrices to be computed on the rows and columns. Figure 3: Accuracy against training time on NG20 and Ohscal. BCOT λ is the fastest and has a competitive level of accuracy. BCOT gives the best accuracy while remaining relatively efficient. The multiplication factors shown for the training times take BCOT λ as the reference (and so, for example, ×4.5 shown for BCOT means that it is approximately 4.5 times slower than BCOT λ ). We were not able to benchmark CCOT-GW since it failed to scale to these datasets.

Term Clustering

Metrics. Unlike document clustering, there is no ground truth partition for terms, so we need to find another way of evaluating term clustering results. One generally acceptable technique is to analyse the semantic coherence of the clusters obtained. To this end we introduce a metric based on point mutual information (PMI). PMI is a frequently used information-theoretic metric for quantifying the relationship between pairs of discrete random variable outcomes. The PMI measure was chosen because prior research [START_REF] Newman | External evaluation of topic models[END_REF] has shown that it is closely associated with human judgements in determining word relatedness. The PMI between the terms w i and w j is calculated as PMI(w i , w j ) = log p(w i , w j ) p(w i )p(w j )

In the context of term clustering, given the word co-occurrence matrix K = B ⊤ B, the PMI is estimated as in

PMI(w i , w j ) = log k .. k ij k i. k .j (14)
To evaluate a partition of terms P, we propose a metric based on intra and inter PMI metrics as follows:

PMI intra (P ) = i∈P j∈P k ij (15) PMI inter (P ) = i∈P j̸ ∈P k ij (16)
In this way, a good clustering should reveal a high intra-cluster semantic relatedness, corresponding to higher PMI values. Using the intra and inter PMIs, we propose the following coherence index coherence(P) = 1

P ∈P |P | P ∈P |P | (PMI intra (P ) -PMI inter (P )) . ( 17
)
Our reasoning is this: the greater the semantic proximity between terms in the same clusters, and the greater the sematic distance between terms in different clusters, the higher the value of coherence.

Results. Since there is no ground truth number of term clusters, we use the cluster number estimations produced by CCOT-GW for all the other models so that it is easy to compare coherence values between them. Comparisons based on different numbers of clusters would favor the model using the larger number of clusters. Table 4 shows the coherences obtained across the different datasets using our approach, along with those of the baselines. is clear that BCOT succeeds in capturing more semantics than the other approaches since, whatever the dataset, one or other of the two BCOT variants gives the highest coherence.

Statistical Significance

We performed a Nemenyi post-hoc test [START_REF] Peter | Distribution-free multiple comparisons[END_REF][START_REF] Demšar | Statistical comparisons of classifiers over multiple data sets[END_REF] with a confidence level of 90% on the document and term clustering results that we obtained, to determine whether our model outperforms other OT biclustering approaches in a statistically significant way. To conduct this test we generated 20 performance rankings of the OT biclustering models based on their performance for each dataset and quality metric pair for both document and term clustering. Figure 4 shows the results of the test. We see that two differently performing groups were identified, one comprising BCOT and BCOT λ and giving better results than the other group comprising the remaining COOT and CCOT variants. This indicates that with this specific number of datasets and metrics the test was unable to tell COOT and CCOT apart in a statistically significant way.

Conclusion

Clustering and biclustering through optimal transport is still at a nascent stage, with many challenges remaining unsolved. This paper introduces a novel problem for biclustering using optimal transport that takes into account the sparse nature of certain types of dyadic data such document-term matrices, to enable more computationally efficient resolution. The problem is posed as a bilinear program that we solve using an efficient block coordinate descent algorithm to find a vertex solution. Experiments on a number of document-term datasets suggest that the proposed approach does a good job in finding clusters that correspond to ground truth document classes, while generating semantically coherent partitions for the terms. In this setting, our model outperforms recent OT biclustering methods by a significant margin, while being more computationally efficient.

Figure 1 :

 1 Figure 1: Biclusters formed using three different methods on the Pubmed dataset. Classical block seriation results in a biclustering that is hard. BCOT results in a biclustering that is almost hard with few nonzero entries outside the main block diagonal. BCOT λ results in a soft biclustering with many nonzero elements outside the block diagonal.

Figure 2 :

 2 Figure 2: Loss for BCOT and BCOT λ on Pubmed.

Figure 3

 3 plots the document clustering performance (accuracy against training time) of the different methods on the two large-scale document-term matrices 20 Newsgroup and Ohscal.

Figure 4 :

 4 Figure 4: Result of the Nemenyi post hoc test.

Table 2 :

 2 Characteristics of the datasets.

	Dataset	#Documents #Terms #Document clusters Sparsity (%)
	ACM [13]	3025	1870	3	95.52
	DBLP [13]	4057	334	4	96.4
	PubMed [32]	19717	500	3	89.98
	Wiki [37]	2405	4973	17	86.99
	Ohscal [22]	11162	11465	10	99.47
	20 Newsgroups [26]	18846	14390	20	99.41

Table 3 :

 3 Document clustering performance on the four datasets. OOM denotes out of memory.

	Method		ACM			DBLP			PubMed			Wiki
		CA	NMI	ARI	CA	NMI	ARI	CA	NMI	ARI	CA	NMI	ARI
	k-Means	51.1±11.3 13.7±11.2 14.0±10.6 36.9±2.4 10.4±2.0 4.3±2.0 52.3±4.7 18.2±10.5 15.3±10.1 26.0±6.1 18.6±9.3 3.3±2.9
	CCOT	12.4±2.0 1.0±0.2	0.4±0.2 28.6±0.5 0.6±0.0 0.4±0.0 32.7±0.2 3.0±0.0	3.1±0.1 10.6±0.5 4.9±0.1 0.6±0.15
	CCOT-GW 8.1±0.0	1.5±0.0	0.3±0.0 9.4±0.0 1.7±0.0 0.3±0.0		OOM		10.9±0.0 4.3±0.0 0.48±0.0
	COOT*	39.0±0.0 1.9±0.0	2.0±0.0 30.5±1.4 1.4±0.3 1.2±0.3 43.2±1.5 1.7±0.6	1.3±1.5 25.9±1.8 28.7±2.2 12.3±1.7
	COOT λ	41.5±0.2 1.9±0.1	2.2±0.0 30.6±0.0 0.7±0.0 0.6±0.0 42.4±1.5 1.7±0.5	1.0±1.3 17.2±0.0 1.7±0.0 0.31±0.0
	BCOT	76.6±1.5 38.3±2.2 43.3±2.6 61.5±6.2 27.4±4.3 28.3±5.5 53.6±4.5 15.9±1.9 12.9±2.4 49.8±1.5 47.9±1.0 30.6±1.0
	BCOT λ	76.2±0.6 37.6±0.8 42.4±1.0 59.4±9.9 26.6±7.6 27.2±9.5 56.5±3.1 18.4±1.3 15.4±1.8 50.8±1.5 49.4±0.9 31.9±0.8

Table 4 :

 4 Term clustering performance on the four datasets. OOM denotes out of memory.

	Method	ACM	DBLP	PubMed	Wiki	Ng20	Ohscal
	k-Means	0.19±0.01 0.05±0.03	0.31±0.18	0.28±0.02	0.28±0.04	0.01±0.02
	CCOT	0.03±0.00 -0.07±0.06 0.02±0.01	0.02±0.00	0.05±0.00	0.06±0.00
	CCOT-GW 0.08±0.00 0.03±0.00	OOM	0.01±0.00	OOM	OOM
	COOT	0.12±0.01 0.07±0.00	0.14±0.01	0.40±0.00	0.43±0.02	0.23±0.01
	COOT λ	0.21±0.00 0.04±0.00 -0.00±0.00 -0.08±0.00 -0.02±0.00 -0.13±0.00
	BCOT	0.27±0.01 0.22±0.04	0.54±0.03	0.64±0.01	0.79±0.01	0.44±0.00
	BCOT λ	0.24±0.00 0.16±0.02	0.57±0.01	0.62±0.01	0.27±0.01	0.35±0.00

Proofs for the propositions are given in the appendix.

https://github.com/chakib401/BCOT

Acknowledgments and Disclosure of Funding

This work has been funded by Informatique Caisse des Dépôts et Consignations (ICDC), Association Nationale de la Recherche et de la Technologie (ANRT), and Idex-Spectrans of Université Paris Cité.


Loïc Jeanmart

Kalina Mambourg

Gilles Hanquet
email: ghanquet@unistra.fr

Steve Lanners
email: steve.lanners@unamur.be

The Diels-Alder reaction of 1,4-quinones in hexafluoroisopropanol

Keywords: Diels-Alder reaction, quinones, hexafluoroisopropanol, sulfinylquinones, asymmetric synthesis

The Diels-Alder reaction of quinones is both of historical and current importance, and numerous asymmetric and catalytic versions have been described. Herein we describe the dramatic rate enhancement observed in the Diels-Alder reactions of a large variety of quinones with moderately activated dienes when hexafluoroisopropanol is used as a solvent, even allowing reactions that are not observed in dichloromethane. When chiral sulfinylquinones are used, hexafluoroisopropanol has a marked effect on stereoselectivity. Since the Diels-Alder reactions of sulfinylquinones are known to be an entry into several classes of natural products, and many other quinone cycloadditions have found wide-spread use in synthesis, the findings described herein will further facilitate their application.

Introduction

The ability of the Diels-Alder [4+2]-cycloaddition to generate molecular complexity rapidly via the simultaneous formation of two carbon-carbon bonds in a chemo-, regio-and stereoselective manner is almost unrivalled, and is illustrated by the numerous reported applications of this reaction for the preparation of six-membered rings, including natural products. Historically, the use of quinones as dienophiles is highly significant, being the very first example investigated by Diels and Alder. 1 1,4-benzoquinone and various quinone derivatives have been used in numerous well-known syntheses of natural products. 1,2 In addition to their electron-deficient nature, which leads them to react with electron-rich or electron-neutral dienes, 1,4-quinones incorporate functional groups which can be transformed after the Diels-Alder reaction, 2 and therefore facilitate the synthesis of complex molecules. 3-8 Controlling the regioselectivity of cycloadditions with quinones is an essential task en route to the synthesis of these targets. 1 Lewis 3 and Brønsted 8 acid catalysts are known to improve the regioselectivity of cycloadditions with unsymmetrical quinones by coordination (or protonation) with the least sterically hindered or the most basic carbonyl group of the quinones. 7 Some asymmetric catalysts have been reported to promote highly enantio-and regioselective reactions with quinones. 9-11 The regioselectivity of the Diels-Alder reaction can also be controlled by remote substituents in benzo-, naphtho-and 1,4phenanthrenequinones. 5,8,12,13 In those cases, Lewis acid catalysts are also used to improve the regioselectivity. The introduction of Cl or Br atoms (X) at the quinone's dienophilic double bond has been used with the double aim of controlling regioselectivity and recovering the quinone skeleton after the cycloaddition by elimination of HX. 14 Sulfoxides 15,16 and boronic acids 8 have also been used to this end. With enantiomerically pure sulfinylquinones, we have reached excellent regio-and stereochemical control in the cycloadditions, en route to salvinorin A. 17,18 The group of C. Carreño successfully applied this strategy to the synthesis of a number of complex molecules. 19-21 Solvents play a crucial role in Diels-Alder reactions. They greatly influence the reaction rates, the regioselectivity as well as the endo/exo selectivity of cycloadditions. 22-24 Solvents with a high hydrogen-bonddonating (HBD) ability, namely fluorinated alcohols, lead to selectivities that are comparable to those obtained when Lewis acids are used as catalysts. 25 In fact, 1,1,1,3,3, is widely used as a reaction medium since it is a strong hydrogen bonding donor, but a weak acceptor and nucleophile. It has been shown to accelerate a variety of transformations, 26,27 and has emerged as a remarkable solvent for [4 + 2] cycloaddition reactions. 23,28,29 To our knowledge, only few examples have been reported in which HFIP facilitates a cycloaddition using 1,4-quinones, among which one describes exclusive endoand very high regioselectivity. 27,30

Results and Discussion

In the context of a total synthesis, we set out to explore the reactivity of sulfinylquinone 1a, which had already been shown to be a convenient chiral starting material for the enantioselective synthesis of terpene natural products, towards moderately reactive dienes (Figure 1). We screened a variety of solvents in order to determine the optimal conditions in terms of reaction rate and stereoselectivity (Table 1). This screening is similar to the one performed by Carreño's group on a less substituted sulfinylquinone. 31 Table 1. Time, conversions, yields and products ratios for the Diels-Alder reaction between sulfinylquinone 1a and cyclopentadiene 2a in different solvents at room temperature.

The first trials were run in aprotic solvents and the major cycloadduct was β-3a, corresponding to an approach of the diene 2a on the C3-Si face of the sulfinylquinone. The best stereoselectivity was observed in benzene (entry 1). More polar aprotic solvents gave less good stereoselectivities (entries 2, 3, 5 and 7).

On the other hand, when protic solvents were used (entries [9][10][11][12], the major isomer was the α-adduct (at the exception of ethanol, entry 11). This inversion of selectivity was also accompanied by a decrease of the reaction time. This phenomenon had been described in Carreño's work. 31 Although they insisted on the importance of the solvent polarity, we hypothesized that the hydrogen bond between the solvent and the dienophile best explains this change of selectivity. The stronger a hydrogen bond donor the solvent is, the better the selectivity towards α-3a and the lower the reaction times. Among those results, we noticed that HFIP and water gave the highest diastereoselectivities (entries 10 and 12). Even though water gave the best selectivity, HFIP offered both a good selectivity and a very high reaction rate compared to the other solvents.

Among the screened solvents, THF, DMF, and DMSO (entries 4,6,and 8) did not afford the expected cycloadducts but gave rise to the formation of addition products whose structure is so far elusive.

Given the remarkable results obtained in HFIP, we decided to further study its use as a solvent in Diels-Alder reaction of other quinones.

Entry

Solvent Time Conversion [a] (%) α:β [b] Isolated Yield (%) NMR ratio of the starting material and the products. b Based on the 1 H NMR ratio of the products.

Study of the influence of HFIP as solvent on the reaction rate and selectivity of Diels-Alder reactions

In order to assess the effect of HFIP in those cycloadditions, differently substituted quinones (Figure 2) were engaged in Diels-Alder reactions.

O R 4 R 3 R 1 R 2 O O R 4 R 3 O O R 4 R 3 R 1 R 2 O O R 4 R 3 2a, solvent Time, rt pyrolysis Only if R 1 = S(O)pTol and R 2 = H -4k,m -4k,m -3a-m -3a-m O O R 4 R 3 R 1 R 2 O O R 4 R 3 R 1 R 2 R 5 R 5 R 6 R 7 R 6 R 7 O O R 4 R 3 O O R 4 R 3 R 5 R 5 R 6 R 7 R 6 R 7 O O R 4 R 3 R 2 O O R 4 R 3 R 2 R 6 R 7 R 6
O O R 1 R 2 R 4 R 3 1a-m O O R 1 R 2 R 4 R 3 1a-m
Scheme 1. Diels-Alder reactions between quinones 1a-l and dienes 2a-c and cycloadducts thereof. Presentation of the possible products with sulfinylquinones 1a,k-m.

In the case of the quinones 1b-j, standard endo-selective Diels-Alder reactions are expected. However, when a sulfoxide is present in R 1 (1a,k-m), a pyrolysis reaction can occur after the cycloaddition. Indeed, some of the sulfinyl-containing cycloadducts are not stable at room temperature and may undergo a β-syn elimination if a hydrogen atom is properly placed on the same face as the sulfoxide moiety. The results obtained with quinones 1b-g are presented in Table 2.

On first glance, it can be noted that the use of HFIP greatly decreased the reaction time for every reaction compared to the ones run in dichloromethane (from days to hours or minutes in some of the cases). The use of HFIP allowed for rather hindered quinones to reach a total conversion, as opposed to partial conversions (entries 11, 13, 15, 21, and 29) or total absence of reaction (entries 17, 23, and 27) observed in dichloromethane. However, the reaction of quinone 1g with diene 2c (entry 32), two very hindered partners, never reached completion, even in HFIP. 1 H NMR ratio of the starting material and the products in the crude mixture.

Without any surprise, the substituents on the quinone substrates greatly influence their reactivity. Compared to 1,4-benzoquinone 1b, the addition of methyl or methoxy groups (1d-g) decreases the reaction rate due to both their electron-donating character and steric hindrance. Both are known to be major factors in Diels-Alder reactions.

On the other hand, when electron withdrawing groups are added (1h-j), the reactivity of the quinone is generally strongly increased (Table 3). For example, when quinone 1h reacts with cyclopentadiene, the reaction is complete within a minute, even in dichloromethane. Quant. 82 a Based on the 1 H NMR ratio of the starting material and the products in the crude mixture.

However, in that series, one example that caught our attention was the reactivity of quinone 1j (entries [13][14][15][16]. It is the only case showing different double bond selectivities between the reaction run in dichloromethane and in HFIP with dienes 2b and 2c, but gave the same expected cycloadduct with cyclopentadiene (2a). Both unexpected products are presented in Table 5 and will be discussed in the next section.

In the case of sulfinylquinones 1a,k-m (Table 4), the relationship between their structure and their reactivity is less obvious as they possess a rather bulky electron-withdrawing group. The main factor in those cases seems to be steric hindrance, as less substituted sulfinylquinones (1k,l) react rapidly (less than 24h with every diene) while 1a needs days to achieve complete conversion in CH2Cl2. The reactivity of 1k, 1l and 1a in dichloromethane was already known 31-34 and we compared those results to the ones in HFIP. For the cycloadditions involving quinones 1a and 1k, in dichloromethane, the β-adduct (either followed by pyrolysis or not) was the major one for all three dienes, when the latter reacted on the expected double bond (entries 1, 3, 5, and 7). A model explaining that selectivity with sulfinylquinones (invoking a specific orientation of the sulfinyl moiety, blocking one face or the other) had already been proposed by Carreño's group 35 and supported by Hanquet's group. 17 When the solvent is replaced by HFIP, with cyclopentadiene, the selectivity is inverted towards the α-adduct (entry 2). 1 H NMR ratio of the starting material and the products in the crude mixture. b Based on the 1 H NMR ratio of the non-pyrolyzed adducts in the crude mixture. c Based on the 1 H NMR ratio of the nonpyrolyzed α-adduct and the pyrolyzed β-adduct in the crude mixture. d No product could be isolated, although the presence of thiosulfinate in the crude mixture suggests the formation of a cycloadduct followed by pyrolysis. e Assignment of the structure based on the selectivity for 1a. f The exact selectivity could not be determined.

We reasoned that a strong hydrogen bond between the solvent molecules and the solute might change the orientation of that sulfinyl group and, therefore, influence the approach of the diene. Surprisingly, acyclic dienes (2b and 2c) did not show the same inversion of selectivity. Instead, the same selectivity as in dichloromethane was observed (entries 4 and 6). Such observations had already been made by Carreño's group by studying the reaction of diverse quinones with cyclopentadiene and piperylene in the presence of Lewis acids. 33 When they used a chelating Lewis acid (ZnBr2), favoring the s-trans conformation and the approach of the diene on the opposite face of the quinone, an inversion of facial selectivity was observed compared to the reaction without catalyst or with a non-chelating Lewis acid (BF3•OEt2). However, with acyclic dienes, such as piperylene, the stereoselectivity was the same whether chelating or non-chelating Lewis acids were used. In order to rationalize those different behaviors, they postulated a significant difference in the transition state energies between cyclic and acyclic dienes, leading to the selection of one face or the other with sulfinylquinones in the presence of chelating Lewis acids.

Despite the presence of (p-tolyl) 4-methylbenzenesulfinothiolate in the crude mixture, suggesting the formation of the cycloadduct, followed by pyrolysis, we were not able to isolate and identify any Diels-Alder adduct from the reaction between quinone 1k and diene 2b, neither in HFIP nor by reproducing Carreño's procedure, 33 and therefore could not assess the effect of the solvent in this particular case.

Finally, we tested quinone 1m that was never described in Diels-Alder reactions so far. When it was reacted with diene 2a (entries 9 and 10), we obtained, after chromatography, the pyrolyzed product 4m, both in dichloromethane or HFIP. However, the cycloaddition being quite fast in both solvents, we were able to analyze the cycloadducts by 1 H NMR before they pyrolyzed. Each one of them possessed a different spectrum with the presence of only one diastereoisomer, leading us to the conclusion that we may have obtained both αand β-adducts individually depending on the solvent we used. The opposite optical rotations for each sample after pyrolysis confirmed that hypothesis. We suspected that, as for quinone 1a, the product formed in dichloromethane is β-4m and the one obtained in HFIP is α-4m, corresponding to an inversion of selectivity, as observed for quinone 1a with cyclopentadiene. When the same quinone was reacted with diene 2b (entries 11 and 12), the cycloadduct 5m could not be observed, probably due to a rather fast pyrolysis and we isolated 7m as product of that reaction. Although we did not assess the stereoselectivity obtained from both reactions, we measured the specific optical rotations of both samples; +100.9° for dichloromethane and +85.1° for HFIP. We assumed, for the same reasons as described earlier, that the major adduct obtained in dichloromethane was the β-isomer (possessing a positive optical rotation). The relatively high positive optical rotation measured for the HFIP sample, would indicate that, although the selectivity was slightly decreased, the β-adduct remained the major one, just as observed with quinone 1a.

Although the involvement of strong hydrogen bonds is consistent with the spectacular acceleration of the reactions, its influence on the diastereoselectivity of the Diels-Alder reactions with sulfinylquinones remains unclear.

Unexpected outcomes of the Diels-Alder reactions Some of the cycloadducts and their pyrolysis products (in the case of quinones 1k-m) are not stable or do not react as expected. The reactions that led to unexpected products are presented in Table 5.

When benzoquinone 1b was reacted with two equivalents of cyclopentadiene (2a) in HFIP at room temperature, the trans double cycloaddition was reached in forty minutes (entry 1). In dichloromethane, thirty minutes were needed to reach the mono-cycloaddition. In order to obtain a single addition with 1b in HFIP, only one equivalent of cyclopentadiene must be used (Table 2, entry 2). Next, when bromoquinone 1f was used with acyclic dienes 2b and 2c (entries 2-5), even though the reactions were much faster in HFIP than in dichloromethane, the cycloaddition products could not be isolated. Any attempt to dry the crude mixture led to the degradation of the products. We identified them as being naphthoquinone derivatives coming from the elimination of bromide followed by oxidative aromatization.

In order to obtain those products more cleanly, we treated the cycloadducts with Et3N to control the elimination process (HFIP was removed and replaced by dichloromethane for that step). We were then able to isolate naphthoquinones 12 and 13 in acceptable yields. As explained for quinone 1j, the reactions in dichloromethane and HFIP did not give the same products for dienes 2b and 2c. In dichloromethane, not only the reaction did not occur on the expected double bond, but it also gave products which were not Diels-Alder cycloadducts. Through 1 H-13 C correlation NMR experiments, we determined the structure to be the result of a [2+2]-cycloaddition of the diene on the more electron-rich double bond of the quinone. The relative configurations were determined by a series of n.O.e experiments (Figure 3). Even though this quinone presents a strong electron-withdrawing group, and should behave as 1h and 1i, it also presents a methoxy group and a methyl group, which both disfavor the standard Diels-Alder reaction by electron donation and steric hindrance, respectively. As seen in its X-ray structure (Figure 4), the ester moiety of 1j is 53.98° out of the quinone plane, probably due to an electrostatic repulsion between both oxygen atoms of the quinone carbonyl and the ester group, as well as steric hindrance caused by the methyl group. Assuming the conformation in apolar and aprotic solvent (such as dichloromethane) is similar to the one in the solid state, the out-of-plane conformation of the ester reduces its electron-withdrawing effect, decreasing the reactivity of that double bond in a Diels-Alder reaction. We also supposed that, being almost perpendicular to the quinone plane, the ester group, combined with the methyl group, causes a significant steric hindrance, disfavoring the approach of a diene on that double bond (Figure 4). However, as can be seen in Table 3, the expected Diels-Alder reaction with cyclopentadiene (2a) (entry 13) took place, albeit very slowly. We supposed that the forced s-cis conformation of 2a increases its reactivity enough to outweigh the steric hindrance.

Due to the strong hydrogen bond donation of HFIP, the ester group could be brought back into the quinone plane (as shown in Figure 4), increasing its electron-withdrawing effect and decreasing its steric hindrance, thereby increasing the reactivity of the quinone double bond. Indeed, reactions with dienes 2b and 2c in HFIP gave the expected cycloadducts and the reactions for all three dienes 2a-c were complete within hours (Table 3, entries [14][15][16].

A similar phenomenon as for quinone 1f was observed with sulfinylquinone 1k and diene 2c (entries 10 and 11). As described by Carreño's group, 33 after the formation of the cycloadduct, the latter undergoes a pyrolysis followed by aromatization. Unfortunately, the cycloadduct could not be observed and the stereoselectivity could not be determined as an achiral product (17) was formed. Given the poor yields, this product may not be the major one, but no others were isolated.

The same observation was made for quinone 1m reacting with diene 2c (entries 18 and 19). After the cycloaddition, the pyrolysis process most probably occurred on the ring junction (leading to intermediate 8m), followed by an oxidative aromatization leading to compound 13 in moderate yields.

Another unusual observation was made with quinone 1k reacting with diene 2a (entries 8 and 9) and quinone 1l reacting with dienes 2a and 2c (entries 12, 13, 16 and 17). Counterintuitively, the Diels-Alder reaction occurred on the more electron-rich double bond. This phenomenon was already described in Carreño's work who studied the effect of different parameters on the selectivity of those reactions. 32,34 In the case of quinone 1k, they observed a preference for the α-adduct that was reinforced when the reaction occurred in protic solvents. As expected, when the reaction is run in HFIP, not only the reaction rate, but also the selectivity towards the α-product, increase.

In the case of the reaction of quinone 1l with cyclopentadiene (2a), a similar selectivity was observed towards the α-adduct and reinforced in HFIP (based on the structural assignment proposed by Carreño's group 34 ). When the same quinone was reacted with diene 2c, one diastereoisomer stood out and was assigned as the α-adduct in Carreño's work, in agreement with the stereoselectivities observed so far for those particular examples. 34 But when the reaction is run in HFIP, an inversion of selectivity, supposedly towards the β-adduct, occurred. These last results confirm that the stereoselectivities observed for sulfinylquinones are far from trivial. Even though the models proposed up to now seem to give rational explanation for the observed selectivity in aprotic solvents, the ones proposed for reactions in protic solvents do not apply to every example presented in this work.

Finally, the reaction between quinone 1l and diene 2b (entries 14 and 15) was rapidly finished in both dichloromethane (twenty hours) and HFIP (ten minutes), but complex mixtures of isomers were obtained and we were not able to isolate the different constituents nor to identify them. We suppose that the reaction occurred on the least hindered double bond (as for dienes 2a and 2c reacting with 1l) and that two regioisomers (20 and 21, Figure 5) were formed as the regioselectivity on that bond is poorly controlled. This is supported by the observation of the mass of the expected cycloadducts by HRMS in the crude reaction mixtures (HRMS (ESI+) for [M+H] + calc.: 349.0660, found: 349.0656).

Limitation of the use of HFIP

Although HFIP showed attractive properties in Diels-Alder reactions with quinones, its use cannot be extended to all dienes. One major limitation comes from its relatively high acidity. We tried to react sulfinylquinone 1a with oxygenated dienes, such as Danishefsky's diene or 2-trimethylsilyloxybutadiene, but the only reaction occurring was the cleavage of the silyl enol ether group, leading to the ketone. However, this does not represent a major drawback, since both dienes are quite reactive, even in apolar solvents.

We also observed that at temperatures of and above 30°C, a clear precipitate was forming but the Diels-Alder reaction was not occurring. We suspected a polymerization of the diene.

The sensitivity of the reactants to acidic media should be then taken into account before attempting to use HFIP as solvent.

Conclusions

In summary, we have shown that the use of HFIP as solvent could greatly accelerate Diels-Alder reactions of quinones, thanks to its strong hydrogen bond donating ability. We could reach complete conversion in many cases at room temperature for reactions that otherwise needed higher temperatures and longer reaction times to be complete. Therefore, reactions that are inconveniently slow (or even not observed at all) in traditional solvents can be run in minutes or hours in HFIP. HFIP also showed the capacity to favor Diels-Alder reactions where other apolar and aprotic solvents gave other unexpected outcomes, such as [2+2]-cycloadducts.

We could also highlight the impact of HFIP on the stereoselectivity observed for sulfinylquinones. It was observed that the selectivities obtained with cyclopentadiene reacting on the sulfoxide-bearing double bond were inverted between dichloromethane and HFIP, whereas acyclic dienes conserved the same facial selectivity. It was then concluded that the models proposed so far to explain the selectvities obtained in apolar solvents were not sufficient in the case of protic solvents.

Finally, we have also shown that HFIP may change the selectivity between the double bonds of the quinone, restoring the expected reactivity. The above findings establish that HFIP is a solvent of choice to accelerate moderately or very slow Diels-Alder reactions whilst assuring high levels of regio-and diasteroselectivity.

Experimental Section

General: Reagents and solvents were purchased as reagent grade and used without further purification, at the exception of cyclopentadiene 2a, which is commercially available under its dimer form. The monomer was freshly distilled after the cracking of the dimer. THF and dichloromethane were purified and dried using an MBraun SPS Compact solvent purification system. Column chromatography: silica gel 60 (230-400 mesh, 0.040-0.063 mm). Demetallated silica gel was prepared according to a published procedure. 36 Thin Layer Chromatography (TLC) was performed on aluminum sheets coated with silica gel 60 F254 Merck (unless otherwise stated), visualization by UV light, KMnO4 stain, or p-anisaldehyde stain followed by heating. NMR spectra ( 1 H and 13 C) were recorded on a Jeol JNM 400 MHz or 500 MHz ( 1 H NMR at 400 MHz or 500 MHz and 13 C NMR at 100 MHz or 125 MHz spectrometer). Chemical shifts are reported in ppm with the solvent resonance at δ 7.26 ppm for CDCl3 and 7.16 ppm for C6D6 in 1 H spectra, and relative to the central CDCl3 resonance δ 77.16 ppm for CDCl3 and the central resonance at δ 128.06 ppm for C6D6 in 13 C spectra, unless stated otherwise. NMR data are reported as (s = singlet, d = doublet, t = triplet, q = quartet, m = multiplet, br = broad; coupling constant(s) in Hz; integration). Optical rotations were measured using a MCP200 Polarimeter (Anton Paar). The solutions were prepared using analytical grade solvents and concentrations (c) are given in g/100 mL. Synthesis of quinones (+)-(S)-5-methoxy-2-methyl-3-(p-tolylsulfinyl)cyclo-hexa-2,5-diene-1,4-dione (1a): Compound 1a was synthesized according to the procedure of Hanquet et al. 17,18 ; Rf (5/5 cyclohex./AcOEt): 0.43; mp: 130-132°C; [α]D 20 (c = 1.0, CH2Cl2): +469.4°; 1 H NMR (500 MHz, CDCl3) δ 7.64 (2H, d, J = 8.1 Hz, 2 × CH p-tolyl ), 7.29 (2H, d, J = 8.1 Hz, 2 × CH p-tolyl ), 5.96 (1H, s, MeOCCH), 3.79 (3H, s, MeO), 2.50 (3H, s, Me quinone ), 2.39 (3H, s, ArMe p-tolyl ); 13 C NMR (125 MHz, CDCl3) δ 185. 37, 179.30, 157.96, 148.23, 144.67, 141.89, 139.48, 130.24, 125.02, 108.06, 56.68, 21.54, 9.55. 2,3,5-trimethylcyclohexa-2,5-diene-1,4-dione (1d): A solution of CAN (27.9 g, 50.9 mmol) in water (150 mL) was added to solution of 2,3,5-trimethylhydroquinone (3.07 g, 20.2 mmol) in acetonitrile (300 mL). After ten minutes at room temperature, the acetonitrile was evaporated and the aqueous residue was extracted with dichloromethane. The organic phase was washed with water and brine and dried over MgSO4. It was filtered and the solvents evaporated in vacuo to give 1d (2.00 g, 66%) as a yellow solid which was used without any further purifications; Rf (6/4 cyclohex./AcOEt): 0.64; mp: 34-36°C; 1 H NMR (500 MHz, CDCl3) δ 6.54 (1H, q, J = 1.6 Hz, MeCCH), 2.02 (3H, d, J = 1.6 Hz, MeCCH), 2.01 (3H, dd, J = 2.3, 1.2 Hz, MeCCMe), 1.99 (3H, dd, J = 2.3, 1.2 Hz, MeCCMe); 13 C NMR (125 MHz, CDCl3) δ 188. 01, 187.63, 145.45, 141.02, 140.85, 133.19, 16.00, 12.47, 12.17.

2,3-dimethoxy-5-methyl-cyclohexa-2,5-diene-1,4-dione (1e): A solution of CAN (6.63 g, 12.1 mmol) in water (75 mL) was added to a solution of 1,2,3,4-tetramethoxy-5-methylbenzene (1.01 g, 4.77 mmol) in acetonitrile (75 mL). After twenty minutes at room temperature the acetonitrile was evaporated and the aqueuous residue was extracted with dichloromethane. The organic phase was washed with water and brine and dried over MgSO4. The solution was filtered and the solvents evaporated in vacuo to give 1e (815 mg, 94%) as a red solid which was used without any further purifications; Rf (7/3 cyclohex./AcOEt): 0.56; mp: 58-60°C; 1 H NMR (500 MHz, CDCl3) δ 6.43 (1H, q, J = 1.6 Hz, MeCCH), 4.02 (3H, s, MeO), 3.99 (3H, s, MeO), 2.03 (3H, d, J = 1.6 Hz, MeCCH); 13 C NMR (500 MHz, CDCl3) δ 184.56, 184.34, 145.16, 144.98, 144.19, 131.43, 61.40, 61.33, 15.62. 2-bromo-6-methoxycyclohexa-2,5-diene-1,4-dione (1f): A solution of CAN (12.7 g, 23.2 mmol) in water (150 mL) was added to a solution of 2-bromo-6-methoxybenzene-1,4-diol 37 (2.01 g, 9.19 mmol) in acetonitrile (150 mL). After one hour at room temperature, the acetonitrile was evaporated and the aqueous residue was extracted with dichloromethane. The organic phase was washed with water and brine and dried over MgSO4. The solution was filtered and the solvent evaporated. The crude was recrystallized in boiling ethanol to give 1f (1.64 g, 72%) as orange needles; Rf (6/4 cyclohex./AcOEt): 0.37; mp: 167-169°C; 1 H NMR (500 MHz, CDCl3) δ 7.20 (1H, d, J = 2.3 Hz, BrCCH), 5.96 (1H, d, J = 2.3 Hz, MeOCCH), 3.85 (3H, s, MeO); 13 C NMR (125 MHz, CDCl3) δ 184.76, 174.67, 158.38, 138.61, 134.39, 107.76, 56.95. 3-bromo-5-methoxy-2-methylcyclohexa-2,5-diene-1,4-dione (1g): A solution of CAN (26.3 g, 48.2 mmol) in water (250 mL) was added to a solution of 3-bromo-1,2,5-trimethoxy-4-methylbenzene 17 (5.00 g, 19.2 mmol) in acetonitrile (250 mL). After thirty minutes at room temperature, the acetonitrile was evaporated and the aqueous residue was extracted with dichloromethane. The organic phase was washed with water and brine and dried over MgSO4. The solution was filtered and the solvent evaporated. The crude was recrystallized in boiling ethanol to give 1g (4.06 g, 92%) as yellow needles; Rf (5/5 cyclohex./AcOEt): 0.54; mp: 101-104°C; 1 H NMR (500 MHz, CDCl3) δ 5.96 (1H, s, MeOCCH), 3.84 (3H, s, MeO), 2.23 (3H, s, MeCCBr); 13 C NMR (125 MHz, CDCl3) δ 184.11, 174.74, 158.42, 146.78, 133.13, 107.39, 56.82, 17.23; HRMS (ESI+): for [M+H] + calc.: 230.9657, found: 230.9651. Methyl 3,: Methyl 2,5-dihydroxybenzoate: A solution of 2,5-dihydroxybenzoic acid (10.0, 65.1 mmol) and H2SO4 (5 mL) in methanol (70 mL) was refluxed overnight. The methanol was removed and replaced by dichloromethane. The organic phase was washed with water and a saturated solution of NaHCO3 and dried over Na2SO4. The solution was filtered and the solvents evaporated to give methyl 2,5-dihydroxybenzoate (9.70 g, 89%) as a white solid; Rf (7/3 PhMe/AcOEt): 0.60; mp: 89-92°C; 1 H NMR (500 MHz, CDCl3) δ 7.24 (1H, d, J = 3.3 Hz, MeO2CCCH), 6.99 (1H, dd, J = 9.0, 3.3 Hz, middle aromatic H), 6.84 (1H, d, J = 9.0 Hz, third aromatic H), 3.89 (3H, s, CO2Me); 13 C NMR (125 MHz, CDCl3) δ 170.37, 155.34, 148.29, 124.26, 118.41, 114.85, 112.24, 52.47. Methyl 3,6-dioxocyclohexa-1,4-diene-1-carboxylate (1h): A solution of methyl 2,5-dihydroxybenzoate (2.00 g, 11.9 mmol), MgSO4 (4.10 g, 34.1 mmol) and Ag2O (4.06 g, 17.5 mmol) in diethyl ether (20 mL) was stirred four hours at room temperature. The solution was filtered over Celite ® and the solvent evaporated to give 1h (1.88 g, 95%) as an orange solid which was used without any further purifications; Rf (7/3 PhMe/AcOEt): 0.65; mp: 51-52°C; 1 H NMR (500 MHz, CDCl3) δ 7.11 (1H, dd, J = 2.0, 0.5 Hz, HCCH), 6.83 (1H, d, J = 2.0 Hz, HCCH), 6.82 (1H, d, J = 0.5 Hz, MeO2CCCH), 3.91 (3H, s, CO2Me); 13 C NMR (125 MHz, CDCl3) δ 186.95, 183.11, 163.27, 137.14, 137.07, 136.70, 136.28, 53.28.

Methyl 1,4-dioxonaphthalene-2-carboxylate (1i): Compound 1i was synthesized according to the procedure of Lee et al. 38 ; Rf (7/3 cyclohex./AcOEt): 0.47; mp: 88-90°C; 1 H NMR (500 MHz, CDCl3) δ 8. m,aromatic CH),m,aromatic CH),m,2 × aromatic CH),7.26 (1H,s,MeO2CCCH); 13 C NMR (125 MHz, CDCl3) δ 184.68, 181.24, 163.91, 139.54, 138.45, 134.70, 134.38, 131.88, 131.69, 127.14, 126.42, 53.27. Methyl 5-methoxy-2-methyl-3,6-dioxocyclohexa-1,4-diene-1-carboxylate (1j): Methyl 2,3,5-trimethoxy-6-methylbenzoate: A solution of hexyllithium (2.3 M in hexanes, 6.5 mL, 15.0 mmol) was added to a solution of 3-bromo-1,2,5-trimethoxy-4-methylbenzene 17 (3.06 g, 11.7 mmol) in dry THF (100 mL) cooled down to -78°C. After ten minutes, methyl chloroformate (1.2 mL, 15.5 mmol) was added dropwise and the reaction mixture was allowed to warm up to room temperature. After one hour, the mixture was cooled down to 0°C, quenched with distilled water and diluted with diethyl ether. The phases were separated, the organic phase was dried over Na2SO4 and the solvents were evaporated. The crude mixture was purified by flash chromatography on silica gel (95/5 cyclohex./AcOEt) to give the title compound (2.33 g, 83%) as a white powder. Rf (8/2 cyclohex./AcOEt): 0.36; mp: 51-53°C; 1 H NMR (500 MHz, CDCl3) δ 6.52 (1H, s, MeOCCH), 3.92 (3H, s, CO2Me), 3.87 (3H, s, ArOMe), 3.81 (3H, s, ArOMe), 3.80 (3H, s, ArOMe), 2.06 (3H, s, ArMe); 13 C NMR (125 MHz, CDCl3) δ 168. 46,154.20,151.00,139.57,130.39,115.71,98.92,61.84,56.53,56.36,52.39,: A solution of CAN (12.91 g, 23.5 mmol) in water (100 mL) was added to a solution of Methyl 2,3,9.33 mmol) in acetonitrile (100 mL). After fifteen minutes, acetonitrile was evaporated and the aqueous phase was extracted with dichloromethane. The organic phase was then dried over Na2SO4 and the solvents were evaporated. The crude mixture was dissolved in a minimum of dichloromethane and the product was precipitated by the addition of pentane. The yellow precipitate was filtrated, washed with pentane and dried under vacuum to give the title compound (1.62g, 83%) as a bright yellow powder. Rf (7/3 cyclohex./AcOEt): 0.38; mp: 98-100°C; 1 H NMR (500 MHz, CDCl3) δ 5.98 (1H, s, MeOCCH), 3.92 (3H, s, CO2Me), 3.83 (3H, s, ArOMe), 2.06 (3H, s, MeO2CCCMe); 13 C NMR (125 MHz, CDCl3) δ 186.42, 178.65, 164.48, 158.14, 143.44, 135.81, 107.71, 56.58, 53.00, 13.59; HRMS (ESI+): for [M+Na] + calc.: 233.0420, found: 233.0412. Crystals for quinone 1j were obtained by slow evaporation from dichloromethane at room temperature. HCCH quinone ), 6.71 (1H, d, J = 10.1 Hz, HCCH quinone ), 2.39 (3H, s, ArMe p-tolyl ); 13 C NMR (100 MHz, CDCl3) δ 185. 23, 183.71, 155.46, 143.09, 138.31, 137.53, 136.56, 131.69, 130.39, 125.94, 21.62. (+)-(S)-2-chloro-3-(p-tolylsulfinyl)cyclohexa-2,5-diene-1,4-dione (1l): Compound 1k was synthesized according to the procedure of Carreño et al. 34 ; Rf (5/5 cyclohex./AcOEt): 0.41; mp: 138-140°C; [α]D 20 (c = 1.0, CHCl3): +638°; 1 H NMR (500 MHz, CDCl3) δ 7.72 (2H, d, J = 8.2 Hz, 2 × CH p-tolyl ), 7.33 (2H, d, J = 8.2 Hz, 2 × CH p-tolyl ), 6.91 (1H, d, J = 10.1 Hz, CH quinone ), 6.78 (1H, d, J = 10.1 Hz, CH quinone ), 2.40 (3H, s, ArMe p-tolyl ); 13 C NMR (125 MHz, CDCl3) δ 181. 27, 177.91, 146.28, 143.71, 142.61, 138.03, 130.34, 125.17, 21.63.

(+)-(S)-2-methoxy-5-(p-tolylsulfinyl)cyclohexa-2,5-diene-1,4-dione (1m):
1-bromo-2,5-bis(ethoxymethoxy)-4-methoxybenzene: To an ice bath (0°C) cooled down solution of 2-bromo-5methoxybenzene-1,4-diol 39 (2.50 g, 11.4 mmol) and BnEt3NCl (267 mg, 1.17 mmol) in dry THF (25 mL) was added NaOH (2.761 g, 69.0 mmol) and ethoxymethyl chloride (4.2 mL, 45.3 mmol). The solution was stirred one hour at 0°C and one hour at room temperature. It was then poured in water (25 mL). After ten minutes, the phases were separated, the organic layer was washed with brine and dried over MgSO4. It was filtered and the solvent was evaporated. The crude was chromatographied on silica gel (9/1 cyclohex./AcOEt) to give the title compound (2.81 g, 73%) as a yellowish oil; Rf (7/3 cyclohex./AcOEt): 0.57; 1 H NMR (500 MHz, CDCl3) δ 7.32 (1H, s, BrCCH), 6.82 (1H, s, MeOCCH), 5.22 (2H, s, MeCH2OCH2OC), 5.18 (2H, s, MeCH2OCH2OAr), 3.84 (3H, s, MeO), 3.84 (2H, q, J = 7.1 Hz, MeCH2OCH2O), 3.80 (2H, q, J = 7.1 Hz, MeCH2OCH2O), 1.24 (3H, t, J = 7.1 Hz, MeCH2OCH2O), 1.23 (3H, t, J = 7.1 Hz, MeCH2OCH2O); 13 C NMR (125 MHz, CDCl3) δ 150. 08, 149.57, 142.26, 121.41, 102.72, 102.60, 95.00, 94.92, 64.68, 64.57, 56.27, 15.22, 15.18. (-)-(S)-1,4-bis(ethoxymethoxy)-2-methoxy-5-(p-tolylsulfinyl)benzene: A solution of Hexyllithium (2.3 M in hexane, 2.7 mL, 6.21 mmol) was added to a solution of 1-bromo-2,5-bis(ethoxymethoxy)-4-methoxybenzene (2.06 g, 6.15 mmol) in dry THF (60 mL) cooled down to -78°C. After thirty minutes at -78°C, the lithium solution was quickly cannulated over a solution of menthyl (-)-S(S)-p-tolylsulfinate 40 (1.88 g, 6.38 mmol) in dry THF (60 mL) cooled down to -78°C. The final mixture was stirred one hour at -78°C, one hour at room temperature and quenched with saturated NH4Cl. The phases were separated and the organic layer was washed with brine and dried over MgSO4. It was filtered and the solvent was evaporated. The crude was chromatographied over silica gel (8/2 to 6/4 cyclohex./AcOEt) to give the title compound (1.67 g, 69%) as a yellowish oil; Rf (7/3 cyclohex./AcOEt): 0.11; [α]D 20 (c = 1.0, CHCl3): -75.2°; 1 H NMR (500 MHz, CDCl3) δ 7.57 (1H, s, ArS(O)CCH), 7.55 (2H, d, J = 8.1 Hz, CH p-tolyl ), 7.21 (2H, d, J = 8.1 Hz, CH p-tolyl ), 6.73 (1H, s, MeOCCH), 5.21 (2H, dd, AB, JAB = 6.6 Hz, ΔνAB = 10.7 Hz, MeCH2OCH2O), 5.14 (2H, dd, A'B', JA'B' = 7.1 Hz, ΔνA'B' = 19.2 Hz, MECH2OCH2O), 3.84 (3H, s, MeO), 3.75 (2H, q, J = 7.1 Hz, MeCH2OCH2O), 3.58 (2H, ddq, CDX, JCD = 9.6 Hz, JCX = JDX = 7.1 Hz, ΔνCD = 45.2 Hz, MeCH2OCH2O), 2.34 (3H, s, ArMe p-tolyl ), 1.19 (3H, t, J = 7.1 Hz, MeCH2OCH2O), 1.15 (3H, dd, CDX, JCX = JDX = 7.1 Hz, MeCH2OCH2O); 13 C NMR (125 MHz, CDCl3) δ 153.43, 149.68, 142.09 (two signals at the same shielding), 141. 24, 129.74, 125.34 (two signals at the same shielding), 113.73, 100.24, 94.97, 93.95, 64.65, 64.53, 56.31, 21.50, 15.16, 15.13. (+)-(S)-2-methoxy-5-(p-tolylsulfinyl)cyclohexa-2,5-diene-1,4-dione (1m): A solution of CAN (5.27 g, 9.61 mmol) in water (25 mL) was added to a solution of (-)-(S)-1,4-bis(ethoxymethoxy)-2-methoxy-5-(p-tolylsulfinyl)benzene (1.50 g, 3.80 mmol) in acetonitrile (50 mL). after thirty minutes, the acetonitrile was evaporated and the aqueous residue was extracted with dichloromethane. The organic layer was washed with brine and dried over MgSO4. The solution was filtered and the sovents evaporated to give 1l (935 mg, 89%) as an orange powder which was used without any further purifications; Rf (5/5 cyclohax./TBME) 0.20; mp: 121-123°C; [α]D 20 (c = 1.0, CHCl3): +428.8°; 1 H NMR (500 MHz, CDCl3) 5.85 (1H,s,MeOCCH),3.91 (3H,s,MeO), 2.38 (3H, s, ArMe p-tolyl ); 13 C NMR (125 MHz, CDCl3) δ 183.65, 179.70, 159.73, 156.54, 149.94, 138.54, 130.35, 129.73, 125.98, 107.64, 56.87, 21.60; HRMS (ESI+): for [M+H] + calc.: 277.0535, found: 277.0529.

Diels-Alder reactions and derived products

General procedure for the Diels-Alder reaction: The quinone was dissolved in dichloromethane or HFIP (10 mL/mmol of quinone). The diene (1 or 2 equivalents) was then added at room temperature. Once the reaction reached complete or maximum conversion, the solvent was evaporated and the crude purified if necessary (otherwise it was pure enough to be analyzed without any further purification). See Tables 2 to 5 for times of reactions, equivalents of dienes, conversions and yields.

(-)-(1R,4S,4aS,8aR)-6-methoxy-8a-methyl-4a-((S)-p-tolylsulfinyl) -1,4,4a,8a-tetrahydro-1,4methanonaphthalene-5,8-dione (α-3a): Quinone 1a (257 mg, 0.885 mmol in CH2Cl2; 260 mg, 0.896 mmol in HFIP) and diene 2a (0.15 mL, 1.78 mmol in CH2Cl2; 0.15 mL, 1.78 mmol in HFIP) were reacted following general procedure. The crude product was purified by flash chromatography on silica gel (40/1/0.2 CH2Cl2/AcOEt/acetone) to isolate α-3a (103 mg, 33% in CH2Cl2; 186 mg, 58% in HFIP) in the first fraction as a brown powder; Rf (40/5/1 CH2Cl2/AcOEt/acetone): 0.61; mp: 124-126°C (decomp.); [α]D 20 (c = 1.0, CHCl3): -249.6°; 1 H NMR (500 MHz, CDCl3) δ 7.49 (2H, d, J = 8.0 Hz, 2 × CH p-tolyl ), 7.27 (2H, d, J = 8.0 Hz, 2 × CH p-tolyl ), 6.23 (1H, dd, J = 5.0, 2.6 Hz, HCCH diene ), 6.08 (1H, dd, J = 5.0, 2.6 Hz, HCCH diene ), 5.48 (1H,s,MeOCCH),4.07 (1H,s(br), CH bridge ), 3.32 (3H,s,MeO),3.23 (1H,s(br), CH bridge ), 2.39 (3H, s, ArMe p-tolyl ), 2.25 (1H, d, J = 10.0 Hz, ½ × CH2 bridge ), 1.85 (3H, s, Me angular ), 1.68 (1H, d, J = 10.0 Hz, ½ × CH2 bridge ); 13 C NMR (125 MHz, CDCl3) δ 200.13, 187.01, 164.32, 157.21, 142.69, 140.39, 136.81, 129.79, 126.46, 111.57, 81.25, 58.29, 56.03, 54.46, 49.99, 43.47, 25.78, 21.55. Crystals for compound α-3a were obtained by slow evaporation from dichloromethane at room temperature.

(+)-(1S,4R,4aR,8aS)-6-methoxy-8a-methyl-4a-((S)-p-tolylsulfinyl) -1,4,4a,8a-tetrahydro-1,4methanonaphthalene-5,8-dione (β-3a): The same procedure as α-3a was followed to give β-3a (189 mg in CH2Cl2, 60%; 25 mg, 7.9% in HFIP) in the second fraction as a brown powder; Rf (40/5/1 CH2Cl2/AcOEt/acetone): 0.37; mp: 130-132°C (decomp.); [α]D 20 (c = 1.0, CHCl3): +189.6°; 1 H NMR (500 MHz, CDCl3) δ 7.42 (2H, d, J = 8.0 Hz, 2 × CH p-tolyl ), 7.38 (2H, d, J = 8.0 Hz, 2 × CH p-tolyl ), 6.25 (1H, dd, J = 5.0, 3.0 Hz, HCCH diene ), 5.83 (1H, s, MeOCCH), 5.80 (1H, dd, J = 5.0, 3.0 Hz, HCCH diene ), 3.77 (3H,s,MeO),3.27 (1H,s(br), CH bridge ), 2.87 (1H, s(br), CH bridge ), 2.48 (3H, s, ArMe p-tolyl ), 2.17 (3H, s, Me angular ), 2.07 (1H, d, J = 9.0 Hz, ½ × CH2 bridge ), 1.58 (1H, d, J = 9.0 Hz, ½ × CH2 bridge ); 13 C NMR (125 MHz, CDCl3) δ 200.84, 190.57, 164.91, 143.53, 141.18, 136.66, 135.69, 129.57, 126.93, 112.04, 79.35, 59.58, 56.65, 53.24, 51.04, 43.41, 25.04, 21.92. (-)-(R)-2-methoxy-4a,8-dimethyl-4a,5-dihydronaphthalene-1,4-dione (β-9a): Quinone 1a (187 mg, 0.645 mmol in HFIP) and diene 2b (0.13 mL, 1.30 mmol in HFIP) were reacted following the general procedure. Once the cycloaddition was over, HFIP was removed in vacuo and replace by CH2Cl2 (7 mL) to let the adduct pyrolyze overnight. The solvent was evaporated and the crude product purified by flash chromatography on demetallated silica gel (9/1 to 8/2 cyclohex./AcOEt) to give β-9a (111 mg, 79% in HFIP) as a yellow oil that crystallizes in the fridge; Rf (2/1 cyclohex./AcOEt): 0.31; mp : 129-131°C; [α]D 20 (c = 0.40, CHCl3): -109.2°; 1 H NMR (400 MHz, CDCl3) δ 6.25 (1H, ddd, J = 9.2, 6.4, 2.4 Hz, H2CCHCHCMe), 6.08 (1H, dd, J = 9.6, 3.2 Hz, H2CCHCHCMe), 5.87 (1H, s, MeOCCH), 3.81 (3H, s, MeO), 2.62 (1H, dd, J = 19.2, 6.0 Hz, ½ × CH2), 2.43 (1H, ddd, J = 19.2, 5.0, 2.8 Hz, ½ × CH2), 2.32 (3H, s, H2CCHCHCMe), 1.23 (3H, s, Me angular ); 13 C NMR (100 MHz, CDCl3) δ 201. 25, 181.42, 164.09, 147.56, 134.07, 131.16, 128.32, 107.71, 56.51, 45.51, 32.48, 26.44, 22.28. (+)-(S)-2-methoxy-4a,6,7-trimethyl-4a,5-dihydronaphthalene-1,4-dione (α-10a): Quinone 1a (198 mg, 0.682 mmol in HFIP) and diene 2c (0.16 mL, 1.41 mmol in HFIP) were reacted following the general procedure. The crude product was purified by flash chromatography on demetallated silica gel (9/1 to 8/2 cyclohex./AcOEt) to isolate α-10a (HFIP: 15 mg, 9.7%) in the first fraction as a yellow oil; Rf (5/5 cyclohex./AcOEt): 0.56; [α]D 20 (c = 0.40, CHCl3): +12.8°; 1 H NMR (500 MHz, CDCl3) δ 7.16 (1H, s, MeCCH), 5.94 (1H, s, MeOCCH), 3.84 (3H, s, MeO), 2.56-2.43 (2H, m, CH2), 1.92 (3H, s(br), MeCCMe), 1.89 (3H, s(br), MeCCMe), 1.21 (3H, s, Me angular ); 13 C NMR (125 MHz, CDCl3) δ 201. 14, 179.79, 163.67, 140.45, 138.82, 131.49, 125.18, 109.48, 56.52, 44.78, 39.42, 26.06, 20.86, 17.16. (-)-(4aS,8aR)-2-methoxy-4a,6,7-trimethyl-8a-((S)-p-tolylsulfinyl)-4a,5,8,8a-tetrahydronaphthalene-1,4-dione (β-6a): The same procedure as for α-10a was followed to isolate β-6a (181 mg, 71% in HFIP) as a light orange solid foam; Rf (5/5 cyclohex./AcOEt): 0.49; mp: 125-126°C; [α]D 20 (c = 1.0, CH2Cl2): -207.0°; 1 13 C NMR (125 MHz, C6D6) δ 197.42, 186.31, 161.67, 142.50, 136.42, 129.94, 122.81, 122.81, 121.93, 113.32, 79.11, 55.27, 49.77, 45.21, 30.10, 21.19, 18.58, 18.50, 16.94. (1R,4S,4aR,8aS)-1,4,4a,8a-tetrahydro-1,4-methanonaphthalene-5,8-dione (3b): Quinone 1b (208 mg, 1.92 mmol in CH2Cl2; 51 mg, 0.476 mmol in HFIP) and diene 2a (0.33 mL, 3.92 mmol in CH2Cl2; 0.04 mL, 0.476 mmol in HFIP) were reacted following the general procedure to give 1b (326 mg, 94% in CH2Cl2; 83 mg, >98% in HFIP) as a grey powder; Rf (8/2 cyclohex./AcOEt): 0.26; mp: 66-69°C ; 1 H NMR (500 MHz, CDCl3) δ 6.57 (2H, s, HCCH quinone ), 6.06 (2H, dd, ABXYZ, JAX = JAY = 1.8 Hz, HCCH diene ), 3.54 (2H, m, ABXYZ, 2 × CH bridge ), 3.22 (2H, dd, ABXYZ, JYZ = 2.3 Hz, JBZ = 1.5 Hz, 2 × CH angular ), 1.48 (2H, dddd, ABXYZ, JAB = 8.8 Hz, JAX = 1.8 Hz, JBZ = 1.5 Hz, ΔνAB = 55. 7 Hz, CH2 bridge ); 13 C NMR (125 MHz, CDCl3) δ 199.62, 142.20, 135.43, 48.91, 48.85, 48.47. (±)-rel-(4aR,5R,8aS)-5-methyl-4a,5,8,8a-tetrahydronaphthalene-1,4-dione (5b): Quinone 1b (217 mg, 2.01 mmol in CH2Cl2; 56 mg, 0.516 mmol in HFIP) and diene 2b (0.40 mL, 4.01 mmol in CH2Cl2; 0.10 mL, 1.00 mmol in HFIP) were reacted following general procedure to give 5b (324 mg, 92% in CH2Cl2; 88 mg, 97% in HFIP) as a grey oil; Rf (7/3 cyclohex./AcOEt): 0.50; 1 H NMR (500 MHz, CDCl3) δ 6.75 (1H, d, J = 10.3 Hz, HCCH quinone ), 6.69 (1H, d, J = 10.3 Hz, HCCH quinone ), 5.70-5.59 (2H, m, HCCH diene ), 3.34 (1H, dd, J = 6.0, 5.9 Hz, MeCHCH angular ), 3.24 (1H, ddd, J = 7.5, 5.9, 3.9 Hz, CH2CH angular ), 2.57 (1H, m, MeCH), 2.49 (2H, m, CH2), 0.94 (3H, d, MeCH); 13 C NMR (125 MHz, CDCl3) δ 201. 31, 199.71, 141.21, 140.60, 130.99, 123.48, 50.52, 45.49, 31.86, 22.50, 18.69. (4aR,8aS)-6,7-dimethyl-4a,5,8,8a-tetrahydronaphthalene-1,4-dione (6b): Quinone 1b (206 mg, 1.90 mmol in CH2Cl2; 56 mg, 0.521 mmol in HFIP) and diene 2c (0.43 mL, 3.80 mmol in CH2Cl2; 0.12 mL, 1.06 mmol in HFIP) were reacted following general procedure to give 6b (288 mg, 80% in CH2Cl2; 95 mg, 96% in HFIP) as a grey powder; Rf (7/3 cyclohex./AcOEt): 0.59; mp: 120-123°C; 1 H NMR (500 MHz, CDCl3) δ 6.65 (2H, s, HCCH quinone ), 3.24-3.12 (2H, m, 2 × CH angular ), 2.46-1.98 (4H, m, 2 × CH2), 1.62 (6H, s, 2 × Me); 13 C NMR (125 MHz, CDCl3) δ 200.42, 139.45, 123.41, 47.18, 30.55, 18.97. (1R,4S,4aR,9aS)-1,4,4a,9a-tetrahydro-1,4-methanoanthracene-9,10-dione (3c): Quinone 1c (195 mg, 1.23 mmol in CH2Cl2; 51 mg, 0.323 mmol in HFIP) and diene 2a (0.21 mL, 2.50 mmol in CH2Cl2; 0.06 mL, 0.714 mmol in HFIP) were reacted following general procedure to give 3c (257 mg, 93% in CH2Cl2; 72 mg, >98% in HFIP) as a grey powder; Rf (8/2 cyclohex./AcOEt): 0.33; mp: 108-110°C; 1 H NMR (500 MHz, CDCl3) δ 8.02 (2H, dd, J = 5.9, 3.3 Hz, 2 × CH Ar ), 7.69 (2H, dd, J = 5.9, 3.3 Hz, 2 × CH Ar ), 5.98 (2H, dd, ABXYZ, JAX = JXY = 1.8 Hz, HCCH diene ), 3.66 (2H, m, ABXYZ, 2 × CH bridge ), 3.45 (2H, dd, ABXYZ, JYZ = 2.5 Hz, JBY = 1.4 Hz, 2 × CH angular ), 1.55 (2H, dddd, ABXYZ, JAB = 8.6 Hz, JAX = 1.8 Hz, JBZ = 1.4 Hz, ΔνAB = 17.2 Hz, CH2 bridge ); 13 C NMR (125 MHz, CDCl3) δ 197.97, 135.93, 135.86, 134.24, 126.98, 49.66, 49.63, 49.35. (±)-rel-(1R,4aS,9aR)-1-methyl -1,4,4a,9a-tetrahydroanthracene-9,10-dione (5c): Quinone 1c (208 mg, 1.32 mmol in CH2Cl2; 66 mg, 0.419 mmol in HFIP) and diene 2b (0.26 mL, 2.61 mmol in CH2Cl2; 0.08 mL, 0.802 mmol in HFIP) were reacted following general procedure to give 5c (300 mg, >98% in CH2Cl2; 96 mg, >98% in HFIP) as a grey oil; Rf (7/3 cyclohex./AcOEt): 0.81; 1 H NMR (500 MHz, CDCl3) δ 8.09-8.00 (2H, m, 2 × CH Ar ), 7.77-7.71 (2H, m, 2 × CH Ar ), 5.76-5.65 (2H, m, HCCH diene ), 3.51 (1H, dd, J = 5.9, 5.8 Hz, MeCHCH angular ), 3.43-3.38 (1H, m, CH2CH angular ), 2.85-2.75 (1H, m, ½ × CH2), 2.73-2.55 (1H, m, MeCH), 2.26-2.18 (1H, m, ½ × CH2), 0.84 (3H, d, J = 7.4 Hz, MeCH); 13 C NMR (125 MHz, CDCl3) 199.14, 198.35, 135.90, 135.43, 134.33, 134.24, 131.29, 126.76, 126.63, 123.65, 50.90, 46.03, 23.09, 18.49. (4aR,9aS)-2,3-dimethyl-1,4,4a,9a-tetrahydroanthracene-9,10-dione (6c): Quinone 1c (196 mg, 1.24 mmol in CH2Cl2; 56 mg, 0.354 mmol in HFIP) and diene 2c (0.28 mL, 2.47 mmol in CH2Cl2; 0.08 mL, 0.707 mmol in HFIP) were reacted following general procedure. The crude product was purified by flash chromatography on silica gel (9/1 cyclohex./AcOEt) to give 6c (176 mg, 59% in CH2Cl2; 81 mg, 95% in HFIP) as a grey powder; Rf (7/3 cyclohex./AcOEt): 0.70; mp: 146-149°C; 1 H NMR (500 MHz, CDCl3) (125 MHz,CDCl3) 198.55,134.37,134.22,126.97,123.60,47.48,30.79,19.04. (±)-rel-(1R,4S,4aR,8aS)-4a, 6,7-trimethyl-1,4,4a,8a-tetrahydro-1,4-methanonaphthalene-5,8-dione (3d): Quinone 1d (118 mg, 0.783 mmol in CH2Cl2; 52 mg, 0.345 mmol in HFIP) and diene 2a (0.13 mL, 1.55 mmol in CH2Cl2; 0.06 mL, 0.713 mmol in HFIP) were reacted following general procedure. The crude product was purified by flash chromatography on silica gel (95/5 PhMe/AcOEt) to give 3d (101 mg, 60% in CH2Cl2; 75 mg, >98% in HFIP) as a pale yellow oil; Rf (8/2 PhMe/AcOEt): 0.73; 1 H NMR (500 MHz, CDCl3) δ 6.06 (1H, dd, J = 5.6, 2.9 Hz, HCCH diene ), 5.92 (1H, dd, J = 5.6, 2.8 Hz, HCCH diene ), 3.43-3.36 (1H, m, CH bridge ), 3.09-3.02 (1H, m, CH bridge ), 2.81 (1H, d, J = 3.9 Hz, CH angular ), 1.91 (6H, s, MeCCMe quinone ), 1.54 (2H, dd, AB, JAB = 9.0 Hz, ΔνAB = 78.9 Hz, CH2 bridge ), 1.43 (3H, s, Me angular ); 13 C NMR (125 MHz, CDCl3) δ 202.48, 199.14, 147.06, 146.82, 138.28, 134.82, 56.96, 53.68, 52.47, 49.09, 46.40, 26.92, 13.50, 13.12; HRMS (ESI+): for [M+H] + calc.: 235.1329, found: 235.1322.

(±)-rel-(4aR,8S,8aS) -2,3,4a,8-tetramethyl-4a,5,8,8a-tetrahydronaphthalene-1,4-dione (5d): Quinone 1d (215 mg, 1.43 mmol in CH2Cl2; 86 mg, 0.569 mmol in HFIP) and diene 2b (0.29 mL, 2.91 mmol in CH2Cl2; 0.11 mL, 1.10 mmol in HFIP) were reacted following general procedure. The crude product was purified by flash chromatography on silica gel (8/2/0.1 cyclohex./CH2Cl2/acetone) to give 5d (97 mg, 31% in CH2Cl2; 124 mg, >98% in HFIP) as a pale yellow oil; Rf (6/4/0.2 CH2Cl2/cyclohex./acetone): 0.70; 1 H NMR (500 MHz, CDCl3) δ 5.67-5.52 (2H, m, HCCH diene ), 2.93-2.82 (2H, m, ½ × CH2 + CH angular ), 2. m,MeCH), 2.09-2.03 (1H, m, ½ × CH2), 2.00 (3H, q, J = 1.0 Hz, MeCCMe), 1.98 (3H, q, J = 1.0 Hz, MeCCMe), 1.40 (3H, s, Me angular ), 0.72 (3H, d, J = 7.3 Hz, MeCH); 13 C NMR (125 MHz, CDCl3) δ 203.25, 199.43, 146.07, 144.75, 130.17, 122.79, 50.34, 50.02, 39.56, 24.29, 20.93, 19.35, 13.36, 12.80; HRMS (ESI+): for [M+H] + calc.: 219.1385, found: 219.1380.

18

 18

Figure 1 .

 1 Figure 1. General strategy towards the synthesis of natural products.

Figure 2 .

 2 Figure 2. Structures of the quinones studied in this work.

O

R 7 -

 7 5a-m: R 5 =Me; R 6 =R 7 =H -6a-m: R 5 =H; R 6 =R 7 =Me -5a-m: R 5 =Me; R 6 =R 7 =H -6a-m: R 5 =H; R 6 =R 7 =Me -7k,m: R 5 =Me; R 6 =R 7 =H 8k,m: R 5 =H; R 6 =R 7 =Me -7k,m: R 5 =Me; R 6 =R 7 =H 8k,m: R 5 =H; R 6 =R 7 =Me -9a,k-m: R 5 =Me; R 6 =R 7 =H -10a,k-m: R 5 =H; R 6 =R 7 =Me -9a,k-m: R 5 =Me; R 6 =R 7 =H -10a,k-m: R 5 =H; R 6

Figure 3 .

 3 Figure 3. Tridimensional representation of products 14 and 15 and n.O.e correlations.

Figure 4 .

 4 Figure 4. X-ray structure of quinone 1j, torsion angle between the ester group and the quinone plane, and representation of the supposed approaches of an acyclic diene in dichloromethane and in HFIP.

Figure 5 .

 5 Figure 5. Proposed structures of the products obtained from the reaction between quinone 1l and diene 2b.

(

  +)-(S)-2-(p-tolylsulfinyl)cyclohexa-2,5-diene-1,4-dione (1k): Compound 1k was synthesized according to the procedure of Carreño et al. 32 ; Rf (5/5 cyclohex./AcOEt): 0.63; mp: 124-126°C; [α]D 20 (c = 1.0, CHCl3): +1011°; 1 H NMR (400 MHz, CDCl3) δ 7.66 (2H, d, J = 8.1 Hz, 2 × CH p-tolyl ), 7.43 (1H, d, J = 2.5 Hz, ArS(O)CCH quinone ), 7.29 (2H, d, J = 8.1 Hz, 2 × CH p-tolyl ), 6.79 (1H, dd, J = 10.1, 2.5 Hz,

  δ 7.65 (2H, d, J = 8.2 Hz, 2 × CH p-tolyl ), 7.34 (1H, s, ArS(O)CCH), 7.29 (2H, d, J = 8.2 Hz, 2 × CH p-tolyl ),

  δ 8.04 (2H, dd, J = 5.8, 3.3 Hz, 2 × CH Ar ), 7.73 (2H, dd, J = 5.8, 3.3 Hz, 2 × CH Ar ), 3.40-3.29 (2H, m, 2 × CH angular ), 2.53-2.05 (4H, m, 2 × CH2), 1.64 (6H, s, 2 × Me); 13 C NMR

  1

Table 2 .

 2 Reaction times, products, conversions and yields for the Diels-Alder reactions between quinones 1b-g and dienes 2a-c (equivalents of diene in parentheses) in dichloromethane and HFIP at room temperature.

	Entry Quinone Diene (eq.) Solvent	Time	Products	Conversion a (%)	Isolated yield (%)
	1	1b	2a (2)	CH2Cl2	30 min	3b	Quant.	94
	2	1b	2a (1)	HFIP	< 1 min	3b	Quant.	>98
	3	1b	2b (2)	CH2Cl2	6 d	5b	Quant.	92
	4	1b	2b (2)	HFIP	< 1 min	5b	Quant.	97
	5	1b	2c (2)	CH2Cl2	8 d	6b	Quant.	80
	6	1b	2c (2)	HFIP	5 min	6b	Quant.	96
	7	1c	2a (2)	CH2Cl2	3h	3c	Quant.	93
	8	1c	2a (2)	HFIP	< 1 min	3c	Quant.	>98
	9	1c	2b (2)	CH2Cl2	14 d	5c	Quant.	>98
	10	1c	2b (2)	HFIP	30 min	5c	Quant.	>98
	11	1c	2b (2)	CH2Cl2	>15 d	6c	68	59
	12	1c	2b (2)	HFIP	40 min	6c	Quant.	95
	13	1d	2a (2)	CH2Cl2	>15 d	3d	68	60
	14	1d	2a (2)	HFIP	2 h	3d	Quant.	>98
	15	1d	2b (2)	CH2Cl2	>15 d	5d	40	31
	16	1d	2b (2)	HFIP	31 h	5d	Quant.	>98
	17	1d	2c (2)	CH2Cl2	>15 d	-	0	-
	18	1d	2c (2)	HFIP	35h	6d	Quant.	>98
	19	1e	2a (2)	CH2Cl2	10 d	3e	Quant.	98
	20	1e	2a (2)	HFIP	1 h	3e	Quant.	>98
	21	1e	2b (2)	CH2Cl2	>15 d	5e	35	23
	22	1e	2b (2)	HFIP	19h	5e	Quant.	95
	23	1e	2c (2)	CH2Cl2	>15d	-	0	-
	24	1e	2c (2)	HFIP	24h	6e	Quant.	70
	25	1f	2a (2)	CH2Cl2	2h	3f	Quant.	>98
	26	1f	2a (2)	HFIP	< 1min	3f	Quant.	>98
	27	1g	2a (2)	CH2Cl2	>15 d	-	0	-
	28	1g	2a (2)	HFIP	22h	3g	Quant.	>98
	29	1g	2b (2)	CH2Cl2	>15 d	5g	13	-
	30	1g	2b (2)	HFIP	20h	5g	Quant.	>98
	31	1g	2c (2)	CH2Cl2	>15d	-	0	-
	32	1g	2c (2)	HFIP	>15d	6g	55	36
	a Based on the

Table 3 .

 3 Reaction times, products, conversions and yields for the Diels-Alder reactions between quinones 1h-j and dienes 2a-c (equivalents of diene in parentheses) in dichloromethane and HFIP at room temperature.

	Entry Quinone Diene (eq.) Solvent	Time	Products	Conversion a (%)	Isolated yield (%)
	1	1h	2a (2)	CH2Cl2	<1 min	3h	Quant.	88
	2	1h	2a (2)	HFIP	<1 min	3h	Quant.	92
	3	1h	2b (2)	CH2Cl2	1h	5h	Quant.	>98
	4	1h	2b (2)	HFIP	<1 min	5h	Quant.	>98
	5	1h	2c (2)	CH2Cl2	100 min	6h	Quant.	>98
	6	1h	2c (2)	HFIP	<1 min	6h	Quant.	98
	7	1i	2a (2)	CH2Cl2	10 min	3i	Quant.	95
	8	1i	2a (2)	HFIP	<1 min	3i	Quant.	97
	9	1i	2b (2)	CH2Cl2	6h	5i	Quant.	>98
	10	1i	2b (2)	HFIP	<1 min	5i	Quant.	>98
	11	1i	2c (2)	CH2Cl2	18h	6i	Quant.	>98
	12	1i	2c (2)	HFIP	<1 min	6i	Quant.	>98
	13	1j	2a (2)	CH2Cl2	15 d	3j	Quant.	85
	14	1j	2a (2)	HFIP	7h	3j	Quant.	82
	15	1j	2b (2)	HFIP	8h	5j	Quant.	79
	16	1j	2c (2)	HFIP	14h	6j

Table 4 .

 4 Reaction times, products, conversions, selectivities and yields for the Diels-Alder reactions between sulfinylquinones 1a,k,m and dienes 2a-c (equivalents of diene in parentheses) in dichloromethane and HFIP at room temperature.

	Entry Quinone	Diene (eq.)	Solvent Time	Products	Conv. a (%) α:β ratio	Isolated yield (%)
	1	1a	2a (2)	CH2Cl2	5d	3a	Quant.	35:65	93
	2	1a	2a (2)	HFIP	35 min	3a	Quant.	88:12	66
	3 17	1a	2b (2)	CH2Cl2	10d	9a	Quant.	<2:98<	90
	4	1a	2b (2)	HFIP	2h	9a	Quant.	<5:95< b	79
	5 17	1a	2c (2)	CH2Cl2	12d	α-10a + β-6a	Quant.	10:90	81
	6	1a	2c (2)	HFIP	24h	α-10a + β-6a	Quant.	12:88 c	81
	7 33	1k	2b (1)	CH2Cl2	20h	7k	Quant.	<3:97<	71
	8	1k	2b (1)	HFIP	5 min	-	Quant.	-	-d
	9	1m	2a (2)	CH2Cl2	20 min	4m	Quant.	<5:95< b,e	36
	10	1m	2a (2)	HFIP <1 min	4m	Quant.	>95:5> b,e	46
	11	1m	2b (2)	CH2Cl2	16 h	7m	Quant.	α << β e,f	59
	12	1m	2b (2)	HFIP	3 min	7m	Quant.	α < β e,f	63

a Based on the

Table 5 .

 5 Results for the Diels-Alder reactions that did not lead to the standard cycloadducts and pyrolysis products presented in Scheme 1.

	Entry Quin.	Diene (eq.)	Solv.	Time	Products	Conv. a (%)	Ratio b Yield (%)
	1	1b	2a (2)	HFIP	40 min		Quant.	-
	2	1f	2b (2) CH2Cl2 24h		Quant.	-
	3	1f	2b (2)	HFIP 3 min		Quant.	-
	4	1f	2c (2) CH2Cl2 42h		Quant.	-
	5	1f	2c (2)	HFIP	10 min		Quant.	-
	6	1j	2b (2)	HFIP >15 d		54	-
	7	1j	2c (2)	HFIP >15 d		30	-
	8	1k	2a (1) CH2Cl2	1h		Quant. 68:32 c
	9	1k	2a (1)	HFIP	<1 min		Quant. 77:23 c
	10	1k	2c (1) CH2Cl2 20h		Quant.	-
	11	1k	2c (1)	HFIP 5 min		Quant.	-
	12	1l	2a (2) CH2Cl2	1h		Quant. 56:44 c
	13	1l	2a (2)	HFIP	<1 min		Quant. 77:23 c
	14	1l	2b (2) CH2Cl2 20h		Quant.	-	-
	15	1l	2b (2)	HFIP	10 min	Complex mixture	Quant.	-	-
	16	1l	2c (2) CH2Cl2 20h		Quant. 79:21 c
	17	1l	2c (2)	HFIP	10 min		Quant. 39:61 c
	18	1m	2c (2) CH2Cl2 22h		Quant.	-
	19	1m	2c (2)	HFIP 3 min		Quant.	-

a Based on the

1

H NMR ratio of the starting material and the products in the crude mixture. b Based on the

1

H NMR ratio of the products in the crude mixture. c Assignment of the structure as proposed in Carreño's work.

  H NMR (500 MHz, C6D6) δ 7.21 (2H, d, J = 7.7 Hz, 2 × CH p-tolyl ), 6.87 (2H, d, J = 7.7 Hz, 2 × CH p-tolyl ), 6.10 (1H, s, MeOCCH), 2.97 (3H, s, MeO), 2.64 (1H, d, J = 17.4 Hz, ½ × ArS(O)CCH2), 2.20 (1H, d, J = 17.4 Hz, ½ × angular MeCCH2), 2.07 (1H, d, J = 17.4 Hz, ArS(O)CCH2), 1.89 (3H, s, ArMe p-tolyl ), 1.82 (1H, d, J = 17.4 Hz, angular MeCCH2), 1.78 (3H, s, Me angular ), 1.44 (3H, s, MeCCMe), 1.22 (3H, s, MeCCMe);

Acknowledgements

We thankfully acknowledge the work of Pr. Johan Wouters and Dr. Nikolai Tumanov (Unité de Chimie Physique Théorique et Structurale, Laboratoire de Chimie Biologique et Structurale, University of Namur) for the X-ray analyses of our crystalline compounds.

Supplementary Material

Copies of 1 H and 13 C NMR spectra of synthesized compounds, as well as crystallographic data of compounds 1j, α-3a, 3f, 3g, 5i and 5j are available in the supplementary material file associated with this paper. References used to compare the data of compounds that were already described in the literature are also cited in the supplementary material file.