Understanding the mechanism of the chiral phosphoric acid-catalyzed aza-Cope rearrangement†

The first catalytic enantioselective aza-Cope rearrangement was reported in 2008 by Rueping et al. The reaction is catalyzed by a 1,1’-bi-2-naphthol-derived (BINOL-derived) phosphoric acid and achieved high yields and enantioselectivities (up to 97 : 3 er with 75% yield). This work utilizes Density Functional Theory to understand the mechanism of the reaction and explain the origins of the enantioselectivity. An extensive conformational search was carried out to explore the different activation modes by the catalyst and, the Transition State (TS) leading to the major product was found to be 1.3 kcal mol lower in energy than the TS leading to the minor product. The origin of this stabilization was rationalized with NBO and NCI analysis: it was found that the major TS has a greater number of non-bonding interactions between the substrate and the catalyst, and shows stronger H-bond interactions between H atoms in the substrate and the O atoms in the phosphate group of the catalyst.


Introduction
In 2008, Rueping et al. 1 reported the first catalytic enantioselective aza-Cope rearrangement 2 (Fig. 1), which consists in a sigmatropic rearrangement [3][4][5][6] involving a nitrogen-containing species of which a diastereoselective version had previously been reported. 7 This important reaction provides a valuable route for the synthesis of chiral homoallylic amines, useful intermediates in the synthesis of natural products, 8 and other organic compounds such as β-amino acids, aminoalcohols, aminoepoxides, pyrrolidines, and piperidines. [9][10][11] The reaction is catalyzed by a 1,1′-bi-2-naphthol-derived (BINOL-derived) phosphoric acid. This kind of catalyst has been utilized in enantioselective versions of a wide range of reactions, 12,13 and has been the focus of studies of several computational works, [14][15][16][17][18][19][20] including many in our group. [21][22][23][24] In this work, we studied the mechanism of the reaction using Density Functional Theory (DFT). An extensive conformational search was carried out to explore the different activation modes by the catalyst and the transition states (TSs) of the C-C forming step were located, different activation modes were analyzed, and the origin of the enantioselectivity was explained. NCI plots showed a greater number of non-bonding interactions and Natural Bond Analysis showed stronger H-bond interactions, between the substrate and catalyst for the TS leading to the major product.

Computational methods
We have performed DFT calculations with Gaussian 09 25 using the M06-2X 26 functional. An ultrafine integration grid was used for all calculations. Optimizations were carried out with the 6-31G* basis set in the gas phase. Single point energies 27 were obtained for the optimized structures using the M06-2X functional with the polarized, triple-zeta valence quality def2-TZVPP basis set 28 and the SMD 29 solvent model. Dibutylether was used as a model solvent for MTBE, since it was previously found to give valid results. 30 Reported energies refer to single point energies for the model system, and to free energies for the full system (i.e. single point energies with thermal corrections arising from translational, rotational, vibrational and electronic motions as implemented in Gaussian 09, calculated at the M06-2X 6-31G* level).
Conformational searches were carried out with MacroModel version 12.3 31 using the OPLS3 force field 31 in the gas phase and a mixed torsional Monte Carlo Multiple Minimum (MCMM) and low frequency mode (LMOD) sampling. A sufficient number of steps were chosen so as to obtain each conformation at least five times. In order to minimize the number of conformations of the full catalyst, the cyclohexyl rings were fixed in the lowest energy conformation, as was pre-viously reported. 22 The H-bond between the NH in the substrate and the phosphate in the catalyst was fixed at 1.8 Å, and the breaking and forming bonds were fixed at 1.7 Å and 2.0 Å respectively, which correspond to the TS distances consistent with previous work 32 and model calculations. The Paton group have investigated sampling ion-pairs with explicitly solvated MD simulations to great effect. 33 We opted for constrained conformational sampling to enable us to proceed straight to TS optimization in Gaussian.

Results and discussion
A chiral phosphoric-acid catalyzed 2-aza-Cope rearrangement reaction has recently been reported. 1 The reaction has been tested with a variety of aldehydes (11 substrates) and amine 3a. The largest er was observed with aldehyde 2j leading to product 4j, in the presence of 10% catalyst 1h. The reaction was also evaluated in different solvents with substrate 2a, leading to product 4a, and the highest er was obtained in toluene (87.5 : 12.5 er) and methyl tert-butyl ether (MTBE, 91 : 9 er) ( Table 1).
The proposed mechanism of the 2-aza-Cope rearrangement ( Fig. 2) starts with the formation of an imine by reaction between the starting amine and the aldehyde. The Brønsted-acid catalyzed rearrangement proceeds via a six-membered transition state, activated by the formation of an H-bond between the intermediate imine and the catalyst, in which a new C-C bond is formed with the terminal alkene acting as the nucleophile and the imine as the electrophile, generating a new tetrahedral carbon center. The newly formed product then loses the association with the phosphoric acid, regenerating the catalyst.
In this work, the origin of the enantioselectivity in the A to B rearrangement step was studied using DFT. First, different activation modes of the transition state were located through a comprehensive conformational search followed by optimization, by using butadiene phosphoric acid as a model catalyst and a phenyl substituent as R′ (Fig. 3). Only TS structures with a chair conformation of the six membered ring, and with the bulky R′ group in equatorial position were considered, as both literature and our calculations showed that conformations in boat conformation or with the R′ group in axial position were too high in energy. 34 73 such conformations were located, in which different H-bond patterns are observed between the H atoms of the reacting substrate and the O atoms of the catalyst. The numbering of atoms is shown in Fig. 3. H-bonds were considered to be formed if the O-H distance was below 2.6 Å. The simplest activation pattern TS-I is observed by the formation of a single H-bond between the N-H atom and the negatively charged O atom, with a 1.52 Å distance (Fig. 4). However, this conformation was found to be 7.8 kcal mol −1 higher in energy than the lowest energy conformation, therefore a substantial extra stabilization is observed by the formation of additional H-bonds. The lowest energy conformation TS-A shows four H-bonds, one between N-H and O1, two H-bonds between both H2 and H3 and O2, and a further H-bond between H2  Organic & Biomolecular Chemistry Paper and the bridging O3. All other activation modes show either three or four total H-bonds, with the highest energy conformation TS-H being 3.1 kcal mol −1 above TS-A.
Once the different activation modes were investigated, a conformational search and optimization was carried out for the full catalyst 1h and the transition state leading to product 4j. 31 structures were located for the TS leading to the major product, and 32 for the TS leading to the minor product. The lowest energy TS structures leading to the major product (TS-1major) and the minor product (TS-1-minor) are shown in Fig. 5 and 6. TS-1-major was found to be 1.21 kcal mol −1 and 1.26 kcal mol −1 lower in energy in toluene and dibutylether (as a model for MTBE) respectively than TS-1-minor.
An analysis of the activation modes observed for the major and minor TSs, in comparison with those observed for the model catalyst, can bring important conclusions. Firstly, all activation modes for the full catalyst show three or four H-bonds between the phosphate and the C-H or N-H atoms. Activation mode TS-I, which showed only one H-bond, was not observed in the full catalyst system. However, as this conformation was found to be 7.8 kcal mol −1 higher in energy, it is not expected to be significant in the full system. Given the higher steric hindrance of the full catalyst, and extra bromine atoms in the substrate, the relative order of the different activation modes changes. For instance, activation mode TS-B in the model catalyst (ΔΔE ‡ of 0.6 kcal mol −1 ), which shows three simultaneous H-bonds between the O atom from the phosphate and the three H atoms from the substrate, was found to be much higher in energy in the full catalyst system: TS-5major (ΔΔG ‡ of 3.79 kcal mol −1 ) and TS-6-minor (ΔΔG ‡ of 2.77 kcal mol −1 ).
To further investigate the mechanism of the enantiodetermining step, the structures of intermediates A and B were optimized. The energy profile of this step is shown in Fig. S1, † alongside the structures of the optimized intermediates. The obtained activation barrier of 21.9 kcal mol −1 is compatible with the experimental results and reaction conditions of this reaction and it is consistent with other related phosphoric-acid catalyzed transformations. [35][36][37][38][39][40] In order to account for the difference in stabilization energy of TS-1-major vs. TS-1-minor, analyses of the intermolecular interactions between the substrate and the catalyst were carried out using the Non-Covalent Interactions (NCI) index method. Default parameters were used for the calculations and plots. TS-1-major (Fig. 7) shows a strong attractive interaction between the N-H group in the substrate and an O atom from the phosphate in the catalyst (shown in blue). Then, it      between TS-1-major and TS-1-minor shows that the latter has a fewer number of interactions, since it does now show phenyl aromatic interactions. This is consistent with the greater stabilization energy present in TS-1-major.

Organic & Biomolecular Chemistry Paper
The intermolecular interactions were further investigated using a Natural Bond Order (NBO) analysis of the second order perturbation energies. The greatest interaction was found between the H atoms in the reacting six membered ring in the substrate and the O atoms in the phosphate group in the catalyst. In total, the H bonds account for a stabilization of 36.8 kcal mol −1 in TS-1-major and 34.4 kcal mol −1 in TS-1-minor. The largest interactions are shown in Fig. 8. TS-1-major shows an interaction of 10.32 kcal mol −1 between an empty N-H σ* orbital and a partially-filled P-O1 σ* orbital, an interaction of 3.88 kcal mol −1 between an empty C-H3 σ* orbital and a filled O3 lone pair n, and an interaction of 2.34 kcal mol −1 between an empty C-H2 σ* orbital and an partially-filled PO1 σ* orbital. TS-1-minor shows an interaction of 9.98 kcal mol −1 between an empty N-H1 σ* orbital and a partially-filled PO1 σ* orbital, and interaction of 1.76 kcal mol −1 between an empty C-H3 σ* orbital and a filled O3 lone pair n, and an interaction of 1.53 kcal mol −1 between an empty C-H2 σ* orbital and a filled O2 lone pair. These interaction energies are consistent with the activation modes observed for these TS structures and provide a rationale for the greater stabilization of TS-1-major vs. TS-1-minor. These greater H bond energies, together with the greater intermolecular interactions observed using the NCI plot between the phenyl groups in the substrate and the aromatic rings in the catalyst, account for the origins of enantioselectivity of the reaction.
Finally, we have studied the distortion 41-43 of the catalyst and substrate upon the formation of the transition states, a    process that has been reported as being fundamental to some related reactions, such as chiral phosphoric-acid catalyzed oxetane desymmetrizations 44 and ring-openings of meso-aziridinium and episulfonium cations. 33 We have calculated the single point energy of the catalyst and substrate in the TS-1-major and TS-1-minor conformations using M06-2X def2-TZVPP in dibutylether (SMD). The substrate conformation in TS-1-major is in fact 0.26 kcal mol −1 higher than in TS-1-minor, and the catalyst conformation is 0.88 kcal mol −1 higher, accounting for a total distortion energy of 1.15 kcal mol −1 , so in fact the conformation of the constituents leading to TS-1-major are disfavored over TS-1-minor. These results highlight the significance of the intermolecular interactions described above, which account for the origin in the stabilization of TS-1-major over TS-1-minor, consistent with the experimental results.

Conclusions
In conclusion, DFT calculations were carried out on the chiral phosphoric-acid catalyzed 2-aza-Cope rearrangement reaction. Different activation modes of the C-C bond forming step model TS were located, and TS-A was found to be lowest in energy. It shows four H-bonds, one between N-H and a phosphate O atom, and three C-H⋯O bonds between the substrate and the phosphate group in the catalyst. Then, the origin of the enantioselectivity was evaluated by locating the TSs for the full catalyst 1h and substrate leading to product 4j. The lowest energy conformations were found to be TS-1-major and TS-1minor. The full energy reaction profile was investigated and the obtained reaction barrier of 21.9 kcal mol −1 is consistent with the experimental results. NCI and NBO analyses were performed in order to rationalize the difference in stabilization energy between TS-1-major and TS-1-minor. The NCI plot showed that TS-1-minor has a lower number of interactions and it does not show interactions between the phenyl groups in the substrate and the aromatic rings in the catalyst. The NBO analysis showed stronger H-bond interactions between the H atoms in the substrate and the O atoms in the phosphate group from the catalyst. Finally, the distortion of the catalyst and substrate upon TS formation was explored but was not found to account for the stabilization of the preferred reaction pathway. These results provide valuable insights into the mechanism of the reaction and the different stabilization modes in the TS and can be used for the design of more effective catalysts for this and related reactions.

Conflicts of interest
There are no conflicts to declare. Computing (ICHEC) for granting use of computational resources which allowed us to perform the experiments included in this work. Part of this research was funded by the Synthesis and Solid State Pharmaceutical Centre (SSPC), supported by Science Foundation Ireland (SFI) and cofunded under the European Regional Department Fund (SFI 12/RC/ 2275_p2/R18867). M.N.G. thanks the University of Bath for financial support. Dr. Zhongyue Yang is thanked for his helpful discussions regarding this work.