Highly diastereoselective 1 , 3-dipolar cycloadditions of chiral non-racemic nitrones to 1 , 2-diaza-1 , 3-dienes : an experimental and computational investigation †

Asymmetric 1,3-dipolar cycloadditions between 1,2-diaza-1,3-dienes and chiral non-racemic nitrones to give 3-substituted-5-diazenyl isoxazolidines were studied both experimentally and theoretically. Whereas cyclic nitrones provide complete selectivity for the cycloaddition reaction (only one isomer is obtained), acyclic nitrones derived from D-glyceraldehyde and D-galactose lead to 1 : 1 mixtures of two isomers. A DFT analysis based on reactivity indices correctly predicts the regiochemistry of the reaction in agreement with the high electron-withdrawing character of the diazenyl group. The same theoretical studies considering solvent effects (PCM model) based on transition state theory are in qualitative agreement with the observed experimental results.


Introduction
1,2-Diaza-1,3-dienes (DDs, 1) are important synthetic intermediates and very attractive building blocks for the construction of a great variety of heterocycles. 1 The conjugated system of 1 can be utilized as a Michael acceptor 5 in 1,4-addition reactions of nucleophiles (Scheme 1). Among the nucleophiles are organometallic compounds such as Grignard derivatives 2 and a great number of carbanions derived from active methylene compounds including βketo, 3 β-cyano, 4 β-phosphono 5 and β-nitro 6 carbonyl 10 derivatives. The resulting hydrazones 2 can evolve towards the parent α-substituted carbonyl compounds 3 but in the case of β-functionalized carbonyls with the appropriate functionalities pyrazolines 4 7 and N-amino pyrroles 8 and dihydropyrroles 5 9 are obtained. Through the addition of 15 diverse heterocyclic derivatives, bicyclic systems can also be prepared. 10 The scope of the DD chemistry has been enhanced by less studied cycloaddition reactions. Compounds 1 are electron-deficient systems and thus they are suitable of 20 acting as dienes in inverse electron-demand [4+2] cycloadditions to give tetrahydropiridazines 6. 11 In the case of enol ethers and enamines the cycloaddition is stepwise and intermediate 7 is formed. This intermediate can evolve to 6 through a formal [4+2] cycloaddition but also to N-25 amino pyrroles 8 through a competitive formal [3+2] cycloaddition. 12 The reactivity of DDs as dienophiles has been much less studied and only the reaction with cyclopentadiene has been reported, 13  In 1,3-dipolar cycloadditions the C=C bond in compounds 1 can also act as dipolarophile as it has been 35 demonstrated in reactions with diazomethane 15 and mesoionic heterocycles. 16 However, to the best of our knowledge no report has been communicated on the reaction between 1 and a typical 1,3-dipole as the nitrone functionality, which has been widely demonstrated its 40 synthetic utility in the construction of several nitrogen heterocycles. 17 Herein, we report a study of the reaction of DDs, 1 with cyclic and acyclic chiral non-racemic nitrones 9 (Chart 1). Thermal and microwave activated cycloadditions have been 45 studied and the results have been rationalized by DFT calculations at several levels of theory considering solvent effects.
procedures. 1 The starting nitrones 9 used for this study were prepared from L-malic acid for nitrone 9a, 18 from Derythrose for nitrone9b 19 from D-arabinose for nitrone9c, 20 from D-glyceraldehyde for nitrone 9d 21 and from Dgalactose for nitrone 9e. 22 10 Initially, we screened various solvents and ratios nitrone/DD for the cycloaddition between DD1a and nitrone 9a to give 10a (Scheme 3, Table 1). Among the various solvents tested, chloroform (Table 1, entries 1-3), ethyl acetate (Table 1, entries 4-6) and THF (Table 1, entries 7 and   15 8) gave moderate yields of the only observed cycloadduct10a. By using methanol as a solvent (Table 1, entries 9-10) no reaction was observed after 24 h. In the absence of any solvent (Table 1, entries 11 and 12) moderate to good results were obtained. The best solvent was found to 20 be acetonitrile (Table 1, entries [13][14][15]. Increasing the temperature resulted in shorter reaction times with similar chemical yields. On the other hand, a 2:1 ratio DD/nitrone showed the best results (Table 1, entries 3, 6, 8,12 and 15). In acetonitrile as a solvent, at 60 ºC and with a ratio 9a:1a of 25 1:2, compound 10a was obtained as the only product of the reaction in 91% yield (Table 1, entry 15). Thus, the reaction showed to be completely regio-and stereoselective with complete asymmetric induction.
With optimized conditions in hand, we next examined 30 the reactivity and selectivity of nitrones 9 in cycloadditions with other DDs. As shown in Table 2 (entries 1- 18), cyclic nitrones 9a-c reacted with various DDs 1 under optimized conditions (ratio nitrone/diazadiene of 1:2, 60 ºC, neat or in MeCN as a solvent) from the less hindered side in an exo 35 mode, with respect to the ester moiety, to give cycloadducts 10-12 as the main products. Typically, treatment of nitrone 9a with DDs 1b-f at 60 ºC gave cycloadducts 10b-f (Table 2, entries 1-8) as the only products of the reaction in a similar way to 10a. Reactions of nitrones 9b and 9c with other DDs 40 also gave products 11 and 12, respectively, bearing the same stereochemical sense (Table 2, entries 9-19). In sharp contrast to the above reactions, cycloaddition of open chain (Z)-nitrones 9d and 9f, derived from D-glyceraldehyde and D-galactose, respectively, with DD 1b afforded adducts 13 45 and 14 as a 1:1 mixture of two isomers (Table 2, entries 20-25). Table 1 Scheme 2Cycloaddition between nitrone9a and DD1a (see Table 1) The configurational assignments of the products were based on straightforward analysis of NMR spectra. The relative configuration could therefore be readily assigned on 55 the basis of NOESY spectra. The most important information obtained from these experiments for compounds 10, 11 and 12 is the absence of the NOE interaction between the protons H-3 and H-4 of the isoxazolidine ring and the presence of a clear NOE interaction between the ester group 60 at C-4 and the methyl group at C-5 of the isoxazolidine ring ( Figure 1, blue arrows). The products derived from cyclic nitrones 9a-c are conformationally rigidified by the fused rings; consequently, the absolute configuration could be assigned through NOE relationship between H-3 and H-4, The cycloadducts 13b,d and 14b, obtained as 1:1 mixtures of isomers were separated by semipreparative HPLC. NOESY experiments confirmed the same relative configuration at the isoxazolidine ring for both isomers thus confirming the achievement of epimers at C-3 of the isoxazolidine ring ( Figure  1, blue arrows). Due to the rotation of the bond Cα-C3 in 13 and 14 the absolute configuration of each epimer could not be unambigously assigned by NMR studies (for a tentative assignment see Supporting Information). In addition to the thermal conditions described above, two further additional approaches in an attempt to improve the cycloaddition reactions were explored: microwave irradiation and Lewis acid catalysis. With regard to Lewis acid, various catalysts including MgBr 2 , Zn(OTf) 2 , ZnBr 2 , CuOTf, AgOTf, Sc(OTf) 3 and Yb(OTf) 3 were used in both catalytic and stoichiometric amounts. The 1 H NMR analysis of the corresponding reaction mixtures only revealed the disappearance of the DD and the complete recovery of the starting nitrone. Any attempt of isolating and/or identifying (by NMR of the crude mixture) any significative product derived from DDs failed and only complex mixtures were obtained. From these reaction mixtures only the starting nitrone could be recovered through column chromatography, likely due to the simple decomposition of starting DDs. The 1,3-dipolar cycloaddition between a nitrone and a DD is expected to be a normal-demand cycloaddition reaction, thus being controlled by a LUMO(dipolarophile)-HOMO(dipole) interaction. Accordingly, coordination of the Lewis acid to the dipolarophile (DD) should enhance the reactivity by lowering LUMO (dipolarophile) energy. DDs 1 bearing ester and/or amide groups have the possibility of forming chelates with Lewis acids thus favoring their coordination instead of undesired coordination of the nitrone species. Recovering of unreacted nitrone and disappearance of the DD is in agreement with the coordination of the latter but, unfortunately, also indicates the instability of DDs complexed with Lewis acids under reaction conditions. Indeed, parallel experiments subjecting DDs 1 in the presence of Lewis acids at 60ºC in MeCN and in the absence of nitrones showed, after 3 h, the complete disappearance of compounds 1. Any attempt of recovering 1 from the reaction mixture by eliminating the Lewis acid was unsuccessful supporting the hypothesis of the above mentioned instability of 1 in the presence of Lewis acids.
Microwave irradiation (300 W, Tmax = 70 ºC) decreased dramatically the reaction time of the cycloadditions (Table 3). For instance, in the case of the cycloaddition between nitrone 9a and diazadiene 1b (Table 3, entry 2), the reaction time decreased from 9 h to 1 min. In some cases, however, the NMR analysis of the crude mixture revealed the presence of a minor isomer (Table 3, entries 1-3 and 7-12) indicating a slightly lower selectivity with respect to thermal reactions. Also, in other cases, the chemical yield decreased considerably (Table 3, entries 4, 6 and 7). In all cases, the reactions were carried out without solvent and with a 1:1 ratio of nitrone/DD, what might contribute to the appearance of a minor isomer in some cases. Under microwave irradiation, the use of a 1:2 ratio of nitrone/DD did not enhance the chemical yield of the reaction and resulted in a more complex reaction mixture. In order to evaluate the electronic influence of the substituents on sterical and electronic properties we replaced substituents by their most simplified version, when possible (due to stability of DDs). Thus, we attempted the reaction between DD 16, generated in situ from precursor 15, and cyclic nitrone 9a (Scheme 3). However, under optimized conditions (MeCN or neat, 60 ºC, with or without MW irradiaton) no reaction was observed in any case, the starting nitrone being recovered almost completely, while degradation products deriving from DD were detected. This result evidences the necessity of using stabilized DDs with appropriate EWGs on the terminal carbon and nitrogen atoms of the azo-ene system that have been shown to enhance both stability and electrophilicity, such as compounds 1a-g. 24 Scheme 3 Cycloaddition between nitrone 9a and DD 16.

Computational Methods
Computations with density functional theory (DFT) were done using the exchange-correlation functional B3LYP 25 and Truhlar's functional M06-2X. 26 Standard basis sets 6-31G(d), 6-311G(d,p) 27 and ccpVTZ 28 were employed. For 3ζ optimizations with the B3LYP functional the recently developed 29 GD3BJ empirical correction for dispersion interactions was included. The nature of stationary points was defined on the basis of calculations of normal vibrational frequencies (force constant Hessian matrix). The optimizations were carried out using the Berny analytical gradient optimization method. 30 Minimum energy pathways for the reactions studied were found by gradient descent of transition states in the forward and backward direction of the transition vector (IRC analysis), 31 using the second order  The solvent (MeCN) effects modeled as a continuum model were considered in all cases based on the polarizable continuum model (PCM) of Tomasi's group. 33 In previous work, 34 calculations using B3LYP functional failed in predicting the correct selectivity and thermodynamics of the reaction, even though recent studies 35 have demonstrated that B3LYP performed very well for geometries, in particular for cycloaddition reactions. 36 On the other hand, a recent report 37 conclude that M06-2X calculations provide best geometries than B3LYP. Thus, for the purpose of comparison the following 2ζ levels of theory were calculated for full optimizations: i) B3LYP/6-31G(d)/PCM=MeCN (level 1) and ii) M06-2X/6-31G(d)/PCM=MeCN. Single point calculations were carried out at a 3ζ level basis set and considering inclusion of diffuse functions as well as the same solvent; thus, single point calculations were carried out at M06-2X/6-311+G(d,p)/PCM=MeCN level using geometries calculated at M06-2X/6-31G(d)/PCM=MeCN (level 3). Finally, full optimizations at 3ζ levels were also carried out: B3LYP-GD3BJ/6-311G(dp)/PCM=MeCN (level 4) and M06-2X/cc-pVTZ/PCM=MeCN (level 5). Reactivity indices were calculated at M06-2X/6-311+G(d,p)/PCM=MeCN level of theory. All calculations were carried out with the Gaussian 09 suite of programs. 38 Structural representations were generated using CYLview. 39 Consistently with the experimental work and regarding the computational costs, the only changes made in the model is the use of methyl groups instead benzyl groups. The rest of the molecules have been preserved. We have studied regio-and stereoselectivity for the reaction between nitrones N1 and N2 (as models of nitrones 9a and 9d, respectively), and DDs D1(1d) and D2(1c) (Figure 3). For DDs D1 and D2 a total of eight conformations have been calculated. 40 Once evaluated the stability of reactants the most stable conformations have been chosen for performing the study. Figure 3 displays the conformational features of the DDs. These conformations have been further employed for locating the corresponding transition states.

Analysis based on reactivity indices
The 1,3-dipolar cycloadditions between nitrones N1 and N2, and DDs D1 and D2 have been analyzed using the global indexes, as defined in the context of DFT, 41 which are useful tools to understand the reactivity of molecules in their ground states. For details and how to calculate the various reactivity indices, see Supporting Information. The values of µ,η, S and ω for compounds N1, N2, D1 and D2, calculated with the reported formulas, are listed in Table 4. The global electrophilicty indices (ω) for nitrones (1.04 and 1.05 for N1 and N2, respectively) are lower than those of DDs (2.36 and 2.30 for D1 and D2, respectively) indicating a normal demand character for the 1,3-dipolar cycloadditon reaction in which the nitrone acts as the nucleophile. In the same way, the electronic chemical potential, µ, of nitrones N1 and N2 is higher (-0.1501 and -0.1507) than that of the dipolarophiles D1 and D2 (2.0028 and 2.0581), thereby indicating that a net charge transfer will take place from the dipole (nitrone) to the dipolarophile (DD), i.e. HOMO(dipole)-LUMO(dipolarophile) interaction, in agreement with a normal-demand 1,3-dipolar cycloaddition. The regioselectivity of the reaction can be predicted by considering that in a polar cycloaddition reaction between nonsymmetrical compounds, the most favorable interaction is that between the most nucleophilic center of the nucleophile (characterized by the highest condensed Fukui function for electrophilic attack f k -) and the most electrophilic center of the electrophile (characterized by the highest local electrophilicity index ωk). The local electrophilic indices (ω k ) and the condensed Fukui functions (f k + and f k -) of nitrones N1 and N2, and DDs D1 and D2 are collected in Table 5.
For DDs D1 and D2, C2 has the higher local electrophilicity index, ω k thus being the preferred site for the nucleophilic attack of the nitrone. For nitrones N1 and N2 the carbon atom has higher f k than the oxygen atom. Consequently, C2 will be linked to the nitrone carbon atom predicting the formation of adducts P1 and P2, respectively (Scheme 4), in complete agreement with the experimental findings.

Analysis of transition structures
We have considered the formation of adducts predicted by the DFT analysis based on reactivity indices and observed experimentally. In consequence four model reactions have been studied (Scheme 5) corresponding to the cycloaddition between nitrones N1 and N2 and DDs D1 and D2; endo and exo approaches to the nitrone by Re and Si faces completed the study. Consequently four transition states leading to the four possible cycloadducts have been located for each nitrone and dipolarophile (a total of 16 transition structures have been located). The nomenclature for defining stationary points is given in Scheme 5.

Re exo
Re endo

Si endo
Si exo Scheme 5.Dipolar cycloadditions between nitrones N1 and N2, and DDsD1 and D2.Re and Si attacks refer to diastereofaces of the nitrones; endo and exo approaches refer to the methoxycarbonyl group; a and b series refer to R = OMe and R = NH2, respectively.  The absolute and relative free and electronic energies with respect to reactants for the 16 transition structures located are collected in Table 6 for the reaction between nitrone N1 and DDs D1 and D2, and in Table 7 for the reaction between nitrone N2 and DDs D1 and D2. Starting situations, consisting of calculation of the encounter complexes C1a,b-C8a,b using as initial geometries those provided by IRC calculations (see Supporting Information) have also been included. The energy differences between products and reactants are given, too. The geometry of the transition structures for the reaction between nitrone N1 and DDs D1 and D2 are given in Figures 4 and 5, respectively, and for the reaction between nitrone N2 and DDs D1 and D2 in Figures 6 and 7, respectively.
The energy values were calculated at five levels of theory, considering solvent effects (PCM=MeCN) in all cases: i) B3LYP/6-31G(d), ii) M06-2X/6-31G(d), iii) M06-2X/6-311+G(d,p)//M06-2X/6-31G(d), iv) B3LYP-GD3BJ/6-311G(dp) and v) M06-2X/cc-pVTZ. 43 All the discussions will be based on the highest level used (PCM=MeCN/M06-2X/cc-pVTZ). The analysis of relative free energies (∆G) shows that, in general,exo attacks (referred to the ester group) are preferred to the corresponding endo approaches. 42 For cycloadditions of cyclic nitrone N1 with DDs D1 and D2 all levels predict the Re exo approach as the preferred one. The barrier for the cycloaddition between N1 and D1 is 22.0 kcal/mol and the barrier for the cycloaddition between N1 and D2 is 23.4 kcal/mol. These results, predicting the formation of P3a,b(from a Re exoattack) are in good qualitative agreement with the experimental observations even though the small observed energy differences between transition states (less than 1.5 kcal/mol, within the experimental error) are more in agreement with the obtention of mixtures of isomers instead only one isomer as actually takes place. In this regard, all the calculations fail in predicting the observed complete diastereoselectivity. Initially, it should be possible to think that such a discrepancy might arise of using a methyl group instead the real benzyl group which could lead to higher energy differences between transition structures. However, we have calculated the stationary points corresponding to cycloaddition reactions of 9a at level 4 (PCM=MeCN/B3LYP-GD3BJ/6-311G(dp)), including reagents, transition structures and products,and quite similar values (differences of 0.8 and 2.5 kcal/mol between the two more stable TSs for the reaction with D1 and D2, respectively) to those obtained for N1 have been obtained (see Supporting information). These data support the validity of our model and demonstrate that the failure in quantitative prediction is inherent to the calculation. 44 As expected for a cyclic biased system like nitrone N1 the qualitatively predicted diastereoselectivity is in agreement with the addition of the dipolarophile by the less hindered Re face. Relative energy values between TSs referenced to isolated reagents and the corresponding encounter complexes (in brackets) are calculated at PCM=MeCN/M06-2X/cc-pVTZ level on theory and given in kcal/mol. Bond distances are given in Ǻ.
The preference by the exo approach with respect to the methoxycarbonyl group is a consequence of the presence of the diazo moiety which acts as directing-electron-withdrawing group and, as expected for normal-demand 1,3-dipolar cycloadditions, is oriented endo with respect to the dipole. For the acyclic nitrone N2, the barrier for the cycloaddition with D1 is 24.6 kcal/mol and the barrier for the cycloaddition with D2 is 26.9 kcal/mol. In this case, the differences observed between transition states (ca. 1.5-2.0 kcal/mol) are in agreement with the observed obtention of mixtures of isomers although there is a clear preference for the obtention of adducts P8a,b coming from a Si exo attack. Again, the preference by the exo approach with respect to the methoxycarbonyl group is a consequence of the presence of the diazo moiety which is oriented endo with respect to the dipole. The diastereofacial selectivity is in agreement with a classical Houk model in which the methylene and oxygen groups are placed as large and medium ones, respectively. All the transition states are concerted asynchronous as expected for a typical normal-demand 1,3-dipolar cycloaddition. In the case of cyclic nitrone N1 the C-O forming bonds are in the range of 1.88-2.10 Ǻ and the C-C forming bonds in the range of 2.02-2.16 Ǻ. For nitrone N2 the C-O forming bonds are in the range of 1.94-1.99 Ǻ and the C-C forming bonds in the range of 2.10-2.20 Ǻ. The geometry of the transition structures is very similar independently of the DD. In general, shorter C-O forming bonds were found for the endo approaches. The C-C forming bonds were, however, shorter for the exo approaches. The same trend was observed for both nitrones N1 and N2 although with higher differences in the case of the cyclic one N1. A More O'Ferrall-Jencks plot 45 using as reaction coordinates C-C and C-O forming bonds can be employed for better understand the transition state variation depending on the DD and the orientation between the reagents. In order to evaluate in a realistic way the asynchronicity of the reaction, relative values (in %) to standard C-C (1.55 Ǻ) and C-O (1.41 Ǻ) bonds in isoxazolidines are used. The More O'Ferrall-Jencks diagrams for the cycloaddition reactions of N1 and N2 are given in Figures 8 and 9, respectively.

Re-endo
Re In the case of nitrone N1 the difference between transition structures corresponding to a Si-exo attack (TS4a,b) and the rest of transition states is evident for both DDs D1 and D2.
Only in TS4a and TS4b the C-C bond is being formed more rapidly that the C-O bond. Notably, TS4a and TS4b are those which are close in energy to the experimentally preferred (and theoretically qualitatively predicted) Re-exo transition states TS3a and TS3b. This unexpected behaviour could be the origin for the inaccuracy observed in theoretical calculations for predicting quantitatively the diastereoselectivity of the reaction. For TS1a,b, TS2a,b and TS3a,b the C-O bond is formed more rapidly than the C-C bond. TS1a and TS1b corresponding to a Re-exo attack are the more asynchronous transition states for these reactions. On the other hand, similar situations regarding asynchronicity are found for the reactions of nitrone N2. For this nitrone, however, the C-O bond is formed more rapidly that the C-C bond in all cases, the less asynchronous transition states being TS6a and TS6b, corresponding to a Si-endo attack.

Conclusions
Diastereoselective 1,3-dipolar cycloadditions of chiral nonracemic nitrones with DDs have been studied both experimental and theoretically. Whereas cyclic nitrones only afforded one isomer showing a complete regio-diastereo-and enantioselectivity acyclic nitrones led to a 1:1 mixture of two isomers. Theoretical calculations based on reactivity indices correctly predict the regioselectivity of the cycloaddition reactions. The analysis of transition structures calculated at 3 3ζ levels of theory, i.e., M06-2X/6-311+G(d,p)//M06-2X/6-31G(d), B3LYP-GD3BJ/6-311G(dp) and M06-2X/cc-pVTZ, considering solvent effects (PCM=MeCN) in all cases, are in qualitative agreement with the observed experimental results. Noteworthy, while the complete diasereoselectivity observed for N1 is not exactly predicted by the calculations, the obtention of diastereomeric mixtures observed for N2 is correctly predicted in all cases. The geometry of the transition structures corresponds to typical asynchronous processes as confirmed by the corresponding More Jenks-O'Ferral diagram analyses. Further elaborations of the obtained cycloadducts will allow the preparation of a variety of heterocyclic systems and it will be reported on due course.

Experimental Section
The reaction flasks and other glass equipment were heated in an oven at 130 °C overnight and assembled in a stream of Ar. All reactions were monitored by TLC on silica gel 60 F254; the position of the spots were detected with 254 nm UV light or by spraying with either 5% ethanolicphosphomolybdic acid.
Column chromatography was carried out in a Buchi 800 MPLC system or a Combiflash apparatus, using silica gel 60 microns and with solvents distilled prior to use. Melting points were uncorrected. 1 H and 13 C NMR spectra were recorded on BrukerAvance 300, 400 or 500 instruments in the stated solvent. Chemical shifts are reported in ppm (δ) relative to CHCl 3 (δ = 7.26) in CDCl 3 . Optical rotations were taken on a JASCO DIP-370 polarimeter. Elemental analysis were performed on a Perkin Elmer 240B microanalyzer or with a Perkin-Elmer 2400 instrument. The microwave reactions were carried out with a Discover Focused Microwave System (CEM Corporation)