An efficient electrostatic embedding QM/MM method using periodic boundary conditions based on particle-mesh Ewald sums and electrostatic potential fitted charge operators Simone Bonfrate, Nicolas Ferré, and Miquel Huix-Rotllant Aix-Marseille Univ, CNRS, ICR, Marseille, France.

(*Electronic mail: miquel.huix-rotllant@cnrs.fr) (Dated: 17 November 2023)

Hybrid quantum mechanics / molecular mechanics (QM/MM) models are successful at describing the properties and reactivity of biological macromolecules. Combining ab initio QM/MM methods and periodic boundary conditions (PBC) is currently the optimal approach for modeling chemical processes in an infinite environment, but frequently these models are too time-consuming for general applicability to biological systems in solution. Here, we define a simple and efficient electrostatic embedding QM/MM model in PBC combining the benefits of electrostatic potential fitted (ESPF) atomic charges and particle-mesh Ewald sums, that can efficiently treat systems of arbitrary size at a reasonable computational cost. To illustrate this, we apply our scheme to extract the lowest singlet excitation energies from a model for Arabidopsis thaliana cryptochrome 1 containing circa 93000 atoms, reproducing accurately the experimental absorption maximum.

Embedding methods in quantum chemistry allow a substantial reduction of the overall computational cost by treating a small subsystem of atoms with an accurate theoretical method while treating the rest of the system in a cheaper and often less accurate approach. 1 In such embedding schemes, the total energy is computed as the sum of energies of the constituent subsystems plus some interaction terms between each fragment. 2 One of the most popular embedding methods for treating biological macromolecules is quantum mechanics / molecular mechanics (QM/MM), 3 in which the energy is expressed as,

E = E QM + E MM + E int , (1)
where E QM is the energy of the (small) QM subsystem, E MM is the energy of the (large) MM subsystem, and E int is the interaction term between them. Usually, the interaction is electrostatic, complemented with other pairwise atom-atom interactions. The majority of ab initio QM/MM methods have been formulated employing an electrostatic Coulomb interaction between QM and MM subsystems, the complete macromolecular system being in the gas phase. 4 The accuracy of such QM embeddings depends on the locality of the property of interest, as well as parameters like the size of the QM subsystem or constraints imposed on the MM atom positions. [START_REF] Gómez | Multiple facets of modeling electronic absorption spectra of systems in solution[END_REF] There exist several attempts in the literature to formulate an ab initio QM/MM method for macromolecules surrounded by an extended environment (solvent, membrane, etc.), either using non-periodic continuum models 6 or periodic boundary conditions (PBC) employing the Ewald summation technique. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] Most QM/MM PBC formulations rely on atomic point charges for efficiently representing the long-range QM-QM interactions such as Mulliken, 7,8,11,12,15,19 , ChElPG, 14,16,21 , ESP, 17 or other types. 20,22 Such methods mainly use Ewald pair potentials, 7,14,16,17,21 , standard Ewald, 8,10,13,20 or exploit the efficiency of particle-mesh Ewald (PME) method. [23][24][25] The PME, which is state-of-the-art algorithm for efficiently calculating long-range interactions in large MM systems, has mainly been implemented for semi-empirical QM/MM methods. 11,12,15,19 We are aware of only two recent articles reporting its use in ab initio QM/MM methods 18,22 .

Here, we combine the advantages of electrostatic potential FIG. 1. Schematic representation of the electrostatic embedding QM/MM PBC method described here for a chromophore (QM) in water (MM). In the original cell (center), the QM subsystem is represented by a quantum charge density. In the replica cells, the QM atoms are represented as ESPF point charges (green circles). MM atoms are represented with blue and red point charges. All point charges are used to polarize the QM density in the original cell.

fitted (ESPF) charges, 4,26 and PME potentials to formulate an efficient ab initio electrostatic embedding QM/MM+PBC method, defining a unified consistent embedding energy from an interaction Hamiltonian. Our formulation takes full computational advantage of PME, it reduces the number of integrals to be computed and can be applied to any ab initio self-consistent field method. The definition of the ESPF QM/MM+PBC interaction (see Fig. 1) and interaction hamiltonian is based on the pairwise electrostatic interaction energy between QM and MM subsystems (see the detailed derivation in the supporting information). The interaction energy in terms of potentials is defined as,

E int = N QM ∑ A q A Φ MM A + 1 2 N QM ∑ A q A Φ QM A , (2)
where the first term accounts for the QM-MM interactions and the second term for the QM-QM interactions, with the 1/2 factor to avoid double counting. N QM is the number of QM atoms, q A = Z A -Q A are their partial charges, defined as the difference between the atomic charge Z A and the electronic charge population Q A = ∑ µν P µν Q A,µν , obtained as the contraction between the quantum density matrix P and an atomic charge operator matrix Q A to be defined later on. The notation Φ A is a short-hand notation for the external potential felt at atom position r A , that is, Φ A = Φ(r A ). We can obtain an interaction operator by deriving the interaction energy with respect to any density matrix element P µν , leading to

h int µν = - N QM ∑ A Q A,µν Φ MM A + Φ QM A . (3)
Up to this point, this is a general formulation for a QM/MM embedding when using charge operators including QM-QM interactions. The different QM/MM models are then distinguished by defining the MM energy, the interaction energy and the external electrostatic potential from a classical electrostatic interaction. For example, in QM/MM models of pairwise Coulomb interactions without PBC, the QM/MM procedure is defined given an external electrostatic potential

Φ A = Φ MM A = N MM ∑ j=1 q j r A j . (4)
Here, r A j = r A -r j is the distance vector between the QM particle A and the MM particle j. In this case, Φ QM A = 0, and therefore the interaction energy and operator matrix elements can be computed given the potential generated by MM atoms on QM centers.

The use of PBC allows one to account for the long-range interactions and to build a model of the macromolecule interactions with the solvent. However, the introduction of Coulomb interaction with replicas results in slow and conditionally convergent interaction energy. 27 The Ewald sums guarantee a faster convergence of the energy sums over replica cells. A general Ewald sum formulation in terms of potentials for N interacting charges can be written as

E Ew = 1 2 N ∑ α q α Φ short α + Φ long α + Φ sel f α . (5)
Here, Φ α has to be understood as the electrostatic potential calculated at the position of atom α in the original cell, that is, Φ α = Φ(r α0 ), where r α0 = r α + 0L, L being the length of the cubic unitary cell. The first term is computed in real space and recovers the short-range part of the electrostatic interaction. The short-range potential is given by

Φ short α = ∑ n=0 N ∑ ′ γ=1 q γ r αγn erfc(β r αγn ) , (6)
where r αγn = r α -r γ + nL. The first summation over n vectors runs over the original box and all the replicas, whereas the sum over γ runs over all the N particles in the system. The prime in the second sum means that we are excluding those terms for which α = γ when n = 0. Finally, the complementary error function, erfc(x) = 1erf(x), ensures the range separation and the convergence control through the parameter β . The second term in Eq. 5 corresponds to the long-range energy. The corresponding long-range potential, computed in the reciprocal space, is defined as

Φ long α = 1 πV ∑ m̸ =0 e -π 2 m 2 β 2 m 2 ℜ e -2πim•r α S(m) , (7)
where ℜ[z] is the real part of z. The summation runs over all the reciprocal space vectors m, using the so-called structure factors S(m), which are defined as

S(m) = N ∑ γ=1 q γ e 2πim•r γ . ( 8
)
Note that the long-range energy includes the spurious interaction of charges with themselves in the original cell. Such contribution is removed by the self-interaction energy, corresponding to the third term in Eq. 5. The associated selfinteraction potential is

Φ sel f α = - 2β √ π q α . (9)
Applying the general Ewald sums formula in the QM/MM framework defined in Eqs. 2 and 3 requires new expressions for the MM energy, the interaction energy, and potential. The purely MM electrostatic energy contribution can be easily obtained by restricting indexes α and γ in Eqs. 5 to 9 to MM atoms only. The Ewald interaction energy can be obtained by extracting the terms defined in Eq. 2 from Eq. 5, which results in

E int,Ew = N QM ∑ A q A Φ short,MM A + Φ long,MM A (10) + 1 2 N QM ∑ A q A Φ short,QM A + Φ long,QM A + Φ sel f ,QM A ,
recalling that the first term includes the interaction of QM charges with MM charges, while the second term includes the interaction of QM charges in the original cell with QM charges in the replicas. The Ewald potentials in Eq. 10 need to be defined for such definition of the interaction. Note that, at variance with the non-PBC case, electrostatic potentials now includes both a MM and a QM parts. The MM potential contains short and long-range contributions, defined as

Φ short,MM A = ∑ n=0 N MM ∑ i=1 q i |r Ain | erfc (β |r Ain |) Φ long,MM A = 1 πV ∑ m̸ =0 e -π 2 m 2 β 2 m 2 ℜ e -2πim•r A S MM (m) . ( 11
)
where S MM (m) refers to the structure factor (Eq. 8) in which the index α is restricted to MM charges. The self-correction correction is not necessary in the MM potential, since the long-range term involves particles of different nature: one QM, A, and all the MM ones. The QM potential includes three terms,

Φ short,QM A = ∑ n̸ =0 N QM ∑ B=1 q B |r ABn | erfc (β |r ABn |) Φ long,QM A = 1 πV ∑ m̸ =0 e -π 2 m 2 β 2 m 2 ℜ e -2πim•r A S QM (m) - N QM ∑ B̸ =A q B |r AB0 | erf (β |r AB0 |) Φ sel f ,QM A = - 2β √ π q A ( 12
)
where S QM (m) refers to the structure factor (Eq. 8) in which the index α is restricted to QM charges. In the short-range potential, the sum n only runs over the replicas since the QM-QM interactions in the original cell are already included in the QM calculation. Similarly, the long-range potential needs to be corrected by subtracting the long-range QM-QM interactions in the original cell. 7 While Ewald summation is undoubtedly useful for handling long-range interactions inside the PBC framework, its original formulation scales like O(N 2 ) and becomes soon computationally unfeasible when the MM system is large. As a consequence, different approaches, aimed at reducing the algorithmic complexity have been proposed. [28][29][30][31] Here, we make use of the Smooth Particle Mesh Ewald (SPME) method, firstly introduced by Pedersen and coworkers, [23][24][25] which features a reduced complexity of O(N log N). The main idea behind SPME consists in approximating the structure factor (Eq. 8) by interpolating the complex exponentials on a numerical grid of B-splines. 25 In practice, the QM atomic charges are projected along with the MM atomic charges in the PME grid, from which one can construct the total long-range potential, Φ long A which corresponds to the sum of the long-range QM and MM contributions to the potential, besides the correction due to the long-range QM-QM interactions in the original cell, which can be added a posteriori as a correction term with the same expression as in Eq. 12. Thus, no modification of the original SPME algorithm is required.

The electrostatic potentials (Eqs. 11-12) can be used to construct the interaction operator (Eq. 3) once the charge operator is defined. Here, we define the charge operator via ESPF method which allows an efficient mapping of the quantum electron density to a classical point charge description compatible with the most common forcefields. 32 In the ESPF procedure, the charge operator matrix elements are fitted to QM-only electrostatic integrals computed on a numerical grid constructed around the molecule. 26 For obtaining the charge operators used in Eq. 3, a system of linear equations, has to be solved. The r k are the point coordinates of a Lebedev atom-centered grid defined around the molecule, and χ are the atomic orbitals. A correction is added to the charge operator matrix elements to ensure the conservation of the total charge of the QM subsystem. 4 The presented methodology, combining SPME and ESPF charges, represents a consistent formulation between the energy and the Hamiltonian and an efficient method for computing the ground and excited state energies. To test this, we extract the lowest singlet excitation energies of 43 snapshots of Arabidopsis thaliana cryptochrome 1 (see Fig. 2 and the supporting information for the computational details). On the one hand, time-dependent density functional theory (TDDFT) has been performed on top of the QM/MM PBC ground state Kohn-Sham reference. In this model, we consider that the external potential is fixed in the excited state calculations, and therefore, the only excitation process occurs in the original cell, while the replicas remain in the ground state. No response terms have been added to the TDDFT equations. This approximate model, for which the average excitation energy is around 412 nm ± 26 nm, is in excellent accordance with the experimental absorption maximum of 420 nm. 33 The blue shift can be attributed to the lack of vibronic effects, which are known to be important in the absorption spectra of isoalloxazine. 34 On the other hand, we have implemented a restricted open-shell Kohn-Sham (ROKS) model to extract the lowest energy excited state directly from the SCF. 35 In this model, both the chromophore in the original cell and the replicas are excited. In this case, the average excitation energy is 518 nm ± 35 nm, thus underestimated by around 100 nm with respect to experiments. Of course, this model is limited by the fact that excited states are represented by a single configuration, but also the probably unrealistic situation that the photoexcited protein is surrounded by simultaneously excited proteins in the replicas.

∑ A Q A,µν |r k -r A | = d 3 r χ * µ (r) 1 |r -r k | χ ν (r) , (13)
In conclusion, we have presented an efficient QM/MM formulation in periodic boundary conditions based on electrostatic potential fitted charges and smooth particle-mesh Ewald sums. It is worth noting that in the QM/MM framework defined by Eqs. 2 and 3 is general, and extra energy terms are easily included as potential sources (see for example the derivation of surface-dipole and the non-neutral cell potentials in the supporting information). The method scales approximately like O(α •N 1.3 MM ) (α = 4•10 -6 , see supporting information for further details), opening up the route for a general application of QM/MD simulations in large-sized periodic systems. This will require the computation of analytic energy first derivatives, which we plan to develop in the future.

  FIG. 2. (top) ESPF QM/MM PBC model of Arabidopsis thaliana cryptochrome 1 in a water box. The isoalloxazine, D396, and W400 (62 atoms in total) are treated at the QM level, with the link atoms shown in purple; (bottom, left) Excitation energies for several snapshots computed with restricted open-shell Kohn-Sham and timedependent density functional theory. The mean values (dashed lines) are compared to experimental values from Ref. 33.

ACKNOWLEDGMENTS

We acknowledge the support from "Agence Nationle de la Recherche" through the project MAPPLE (ANR-22-CE29-0014-01). Centre de Calcul Intensif d'Aix-Marseille is acknowledged for granting access to its high-performance computing resources.

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.


Dr Long He

Dr Gregory Laurent

Dr Pascal Retailleau

Dr Benoît Folléas

Jean-Louis Brayer

Géraldine Masson
email: geraldine.masson@cnrs.fr

Dr J.-L Brayer

Highly Enantioselective Aza-Diels-Alder Reaction of 1-Azadienes with Enecarbamates Catalyzed by Chiral Phosphoric Acids

Keywords: Chiral phosphoric acid, cycloaddition reaction, aza-Diels-Alder reaction, organocatalysis, tetrahydropyridines

Chiral tetrahydropyridine framework represents a privileged sixmembered azacycle commonly found within a wide variety of biologically active natural products and synthetic compounds of medicinal interest. [1] Among the synthetic approaches to access these valuable heterocycles, the inverse electron-demand aza-Diels-Alder (IEDADA) reaction of 1-azadienes with electron-rich alkenes is one of the most convergent methods, resulting in the one pot formation of a C-C and C-N bond and up to three new stereocenters. [2] Nevertheless, this IEDADA reaction suffers from drawbacks such as a low reactivity and stability of 1-azadienes, which could be responsible for the slow development of its corresponding enantioselective version. [3] The introduction of strong electron-withdrawing groups (N-acyl, N-sulfonyl) [4,5] on the 1-aza-1,3-butadiene, enhancing its inherent electron-deficient character as well as its stability, have paved the way towards success in catalytic enantioselective IEDADA reaction. [3] The first example was disclosed by Bode et al., [6] who reacted N-sulfonyl-1-aza-butadienes with β-activated aldehydes in the presence of catalytic amounts of a chiral N-heterocarbene catalyst. One year later, Arrayás and Carretero et al. [7] reported that a DBFOX-Ph/Ni(II) complex was able to catalyze the asymmetric IEDADA reaction of Nheteroarylsulfonyl α,β-unsaturated imines with vinyl ethers. Afterward, other examples of organocatalysis relying on covalent attachment of the catalyst have been used, leading to significant advances in the enantioselective IEDADA reaction of N-sulfonyl-1azadienes. [8] To the best of our knowledge, no example of Brønsted acid-catalyzed [START_REF]For recent reviews on Brønsted acid catalysis[END_REF] IEDADA reaction of 1-azadienes has been reported, although Brønsted acids have been used successfully as catalysts in the cycloaddition of 2-azadienes. [START_REF] Akiyama | For Brønsted acid catalyzed IEDADA reactions[END_REF] Recently, we described that chiral phosphoric acids were efficient catalysts for the asymmetric IEDADA reaction of Narylimines 1 and enecarbamates 2 as dienophiles in a highly diastereo-and enantioselective manner. [10b,f-g] A study of the mechanism indicated that the simultaneous dual activation through hydrogen-bonding interactions of the bifunctional phosphoric acid with both N-arylimine 1 and the NH donor group 2 was critical for achieving high enantioselectivity. [START_REF] Akiyama | chiral phosphoric acid catalysis[END_REF][START_REF] Evano | Selected reviews dealing with enamides as nucleophiles[END_REF][START_REF] Terada | Selected example of using enamides as nucleophiles in phosphoric acid-catalyzed transformations: see: a)[END_REF] Based on these results, we reasoned that the enecarbamate 2 and the N-aryl-1-azadiene 5 could be well adapted as dienophile and diene, respectively, to develop an enantioselective IEDADA reaction catalysed by chiral phosphoric acid. Indeed, the simultaneous dual activation of the two reacting partners by the phosphoric acid catalyst might ensure high reactivity and stereoselectivity (Scheme 1). As shown in our previous work, the cycloaddition with non-α-substituted N-aryl-azadiene (R 3 = H), solely giving the Povarov products 4. [10b,f] We spectulated that the use of α,β-unsaturated ketoimines 5 might change the regioselectivity of the IEDADA reaction to lead to valuable 6amino-1,4,5,6-tetrahydropyridine derivatives 6. This latter structural motif is found in natural products such as Siastatin B, a potent neuraminidase inhibitor, [1c,e,f] or in synthetic compounds exhibiting significant in vitro antimicrobial activities. [1m] Scheme 1. Bifunctional catalyst for the enantioselective IEDADA reaction. [10b,f] In our initial study, we chose the N-aryl ,γ-unsaturated αiminoesters 5a [14] and benzylprop-1-enylcarbamate (E)-2a with chiral phosphoric acid catalyst as the model reaction. To our delight, syn-and anti-methyl (E)-4-(p-methoxyphenyl)-2-pphenyliminobut-3-enoate [1b,15] led to desired 6-amino-1,4,5,6tetrahydropyridine 6a with an excellent all trans diastereoselectivity (Scheme 2). After a brief survey of reaction conditions (catalysts, the solvents, the temperatures and the stoichiometries) we found that the reaction performed at room temperature in dichloromethane with 10 mol % of (R)-3,3'-bis(2,4,6triisopropylphenyl)-BINOL (TRIP) phosphoric acid (3) (cf. Supporting information) furnished the desired product in 71% yield with 93% ee. With the optimal conditions outlined above, a range of N-aryl-1azabutadiene 5 was subjected to the enantioselective IEDADA cycloaddition. As summarized in table 1, various ,γ-unsaturated αiminoesters bearing electron-donating and -withdrawing groups at γ position reacted smoothly to afford 4,5,6-trisubstituted 1,4,5,6tetrahydropyridines 6c-6j in good yields with excellent diastereoand enantioselectivities (entries 1 to 8). The presence of heteroaromatic rings such as furyl (entry 7) and thiophenyl (entry 8) is well tolerated in the cycloaddition as well. Additionally, enantioselectivities of products resulting from the reaction of Nsubstituted arylimines were generally high, independently of the electronic character of the aromatic ring (entry 13 to 17). Several 1azadienes bearing various ester moieties such as ethyl, isopropyl, propyl, and tert-butyl ester were investigated. In all the cases, chiral tetrahydropyridines were obtained with the same order of yields and ees (entries 9 to 12). The catalytic system also proved to be efficient for various carbamates affording the highly substituted tetrahydropyridines 6t-6y with excellent diastereomeric (all trans) and ees (entries 18 to 22). The enecarbamate 2g participated smoothly in the cycloaddition but with lower ee (entry 24). Finally, the current cycloaddition was extended to other 1-azadienes bearing phenyl group at the α-position of the ,γ-unsaturated imines and the cycloadditions with (E)-2a proceeded with complete regioselectivity, affording the desired products 6z and 6aa in high enantioselectivities, albeit with slightly moderate yields (entries 24-25). The absolute configuration of 6c was unambiguously determined to be 4S, 5R and 6R by single crystal X-ray analysis (cf. Supporting information).

On the basis of previous works, [2,16] we proposed two mechanism pathways that could be followed for the subsequent IEDADA cycloaddition: (a) a concerted mechanism between the 1azadiene and the enecarbamate or (b) a two-step mechanism consisting first of the enecarbamate attacking the ,γ-unsaturated αiminoester via a Michael reaction followed by an intramolecular aminalization of the formed anion to iminium ion. [2g,17] To distinguish between the two mechanisms, we evaluated the influence of the substitution at N-and Cγ-positions in ,γunsaturated α-iminoesters. Here, we observed that the presence of an electron-donating or -withdrawing group on the nitrogen has an influence on reaction times (cf. Supporting information). Likewise, reaction rates are influenced by the electronic nature of aryl substituents in γ-position. These findings seem consistent with a concerted mechanism. In addition, when EtOH (3 to 10 equivalents or as solvent) was added to the reaction to trap the iminium intermediate 7, neither the expected adduct nor the tetrahydropyridine were detected. [START_REF]The majority of the unreacted 1-azadienes was recovered[END_REF] Even though we cannot definitely rule out a possible stepwise mechanism, this supports a highly asynchronous concerted mechanism. Based on these Table 1. Substrate scope of the enantioselective synthesis of 4,5,6trisubstituted-1,4,5,6-tetrahydropyridines. [a] Entry R 1 / R 2 / R 3 R 4 / R 5 6 Yield/ee [%] [b,c] 1 PMP/4-ClC6H4/CO2Me Bn/Me 6c 75/95 [d] 2 PMP/4-MeC6H4/CO2Me Bn/Me 6d 72/90 [d] [d] 19 PMP/Ph/CO2t-Bu

/Me

6u 66/94 20 Ph/Ph/CO2Me 4-CF3C6H4CH2/Me 6v 84/91 [f] 21 Ph/Ph/CO2Me 4-BrC6H4CH2/Me 6w 73/92 [g] 22 Ph/Ph/CO2Me C6F5CH2/Me 6x 68/93 [f]

23

PMP/Ph/CO2i-Pr t-Bu/n-C3H7 6y 61/70 [e] 24 PMP/Ph/Ph Bn/Me 6z 59/93 25 PMP/Ph/4-BrC6H4 Bn/Me 6aa 57/88

[a] Reaction conditions: 1-azadiene 5 (0.1 mmol), enecarbamate (E)-2 (0.2 mmol), 3f (0.01 mmol) in CH2Cl2 (1.0 mL) at RT. [b] Yield of chromatographically pure product, all trans isomer (d.r.=95:5). [c] Determined by chiral HPLC analysis. [d] Reaction at 0 °C. [e] d.r.=7:1.

[f] d.r.=9:1. [g] d.r.=12:1.

3.

Activation model via a putative transition state.

observations, we propose a transition state to explain the observed (absolute) stereochemical outcome of the enantioselective IEDDA reaction (Scheme 3). In this system, the chiral phosphoric acid may serve as a bifunctional catalyst: the OH group activates the 1azadiene as a Brønsted acid and the phosphoryl oxygen activates the enecarbamates as a Lewis base. IEDADA Reaction might take place with endo selectivity, via a transition state in which the Si face of the azadiene would be attacked, affording (4S,5R,6R)-cycloadduct 6.

The importance of the hydrogen atom on enecarbamate 2 was supported by the moderate yield and enantioselectivity of the reaction with tertiary endocyclic enecarbamate (cf. Supporting information). This indicates that the presence of the NH group is crucial for both reactivity and enantioselectivity.

With the successful construction of tetrahydropyridines, we turned our attention to perform further transformations of cycloadduct 6 into valuable compounds. As illustrated in scheme 4, removal of the Cbz group in 6a by a Pd/C-catalyzed hydrogenolysis produced hemiaminal adduct 8 (a key precursor of a variety of chiral piperidines as described by other authors) [8a-b] in 60% yield with a very subtle erosion of enantioselectivity (Scheme 4). In summary, we have developed the first catalytic enantioselective IEDADA reaction of N-aryl α,β-unsaturated ketimines 5 and -substituted enecarbamates 2 using a chiral bifunctional phosphoric acid catalyst. This cycloaddition employs easily accessible starting materials to construct densely functionalized 4,5,6-trisubstituted 1,4,5,6-tetrahydropyridines 6 with three contiguous stereogenic centers (with up to 84% yield, 95:5 dr and 95% ee). Early mechanistic studies seem to indicate that the reaction proceeds via an asynchronous concerted mechanism. Further studies regarding the applications of this IEDADA reaction are ongoing and will be reported in due course. A highly enantio-and diastereoselective synthesis of 6-amino-trisubstituted tetrahydropyridine compounds has been developed through the inverse-electrondemand aza-Diels-Alder reaction of N-aryl α,β-unsaturated ketimines with enecarbamates. This cycloaddition is catalyzed by a chiral bifunctional phosphoric acid that achieves simultaneous activation of both the 1-azadiene and dienophile partners.

Entry for the Table of Contents

Scheme 2 .

 2 Scheme 2. Chiral phosphoric acid (3)-catalyzed enantioselective IEDADA reaction of 1-azadienes.

Scheme 4 .

 4 Scheme 4. Synthetic transformation of the tetrahydropyridine.

analysis. H.L also acknowledges ANR for post-doctoral fellowships. G.L. thanks Diverchim for a CIFRE grant Supporting information for this article is available on the WWW under http://www.angewandte.org or from the author.((Please delete if not appropriate))