Computational ligand design in enantio- and diastereoselective ynamide [5+2] cycloisomerization

Transition metals can catalyse the stereoselective synthesis of cyclic organic molecules in a highly atom-efficient process called cycloisomerization. Many diastereoselective (substrate stereocontrol), and enantioselective (catalyst stereocontrol) cycloisomerizations have been developed. However, asymmetric cycloisomerizations where a chiral catalyst specifies the stereochemical outcome of the cyclization of a single enantiomer substrate—regardless of its inherent preference—are unknown. Here we show how a combined theoretical and experimental approach enables the design of a highly reactive rhodium catalyst for the stereoselective cycloisomerization of ynamide-vinylcyclopropanes to [5.3.0]-azabicycles. We first establish highly diastereoselective cycloisomerizations using an achiral catalyst, and then explore phosphoramidite-complexed rhodium catalysts in the enantioselective variant, where theoretical investigations uncover an unexpected reaction pathway in which the electronic structure of the phosphoramidite dramatically influences reaction rate and enantioselectivity. A marked enhancement of both is observed using the optimal theory-designed ligand, which enables double stereodifferentiating cycloisomerizations in both matched and mismatched catalyst–substrate settings.

7o: Assignment of stereochemistry for 7o is made on the basis of nOe enhancements, measured using 1 H-1 H NOESY experiments. For 7o, a strong nOe enhancement was observed between the C2 methyl group and H3, and between the Me group and H3a. A similar strong enhancement was seen between H3a and H3, thus indicating all these groups to be on the same face of the bicycle. A complementary enhancement was observed between H2 (on the -face), and H3. A weak enhancement was observed between H2 and H3.
14o: The assignment of stereochemistry in 14o is clearly achieved through the observation of strong nOe enhancements between the C2 methyl group and H3 ( face), and between H2 and H3, and H3 and H3a. Weak enhancements are observed between H2 and H3a, and between H3 and H2.
7q: H3a and one of the C2 sidechain protons (H2') are overlapping, rendering an unequivocal stereochemical assignment difficult. However, strong nOe enhancements are again seen between H2 and H3α, the latter of which does not show an enhancement with either of the H2' protons, or H3a, implying H2' and H3a to be on the opposite (-) face. A strong enhancement is also observed between H3 and one of H2', as well as the overlapping H2'/H3a signals. This assignment is supported by equivalent nOe data for the C3a epimer, 14q (see below).
14q: The assignment of stereochemistry in 14q is clearly achieved through the observation of strong nOe enhancements between the C2 sidechain protons H2', and H3 ( face), and between H2 and H3, and H3 and H3a. A weak enhancement is observed between H3 and H2.

7p:
The assignment of stereochemistry of 7p is made by analogy with the data from 7o and 7q (this material being isolated as an inseparable mixture with its C3a epimer, 14p).
7r: By analogy with compounds 7l-n, a coupling constant of 12 Hz between H3a and H3 indicates an anti relationship, and therefore stereochemistry as depicted below: For the diastereomeric compound 14l, the H3a-H3 coupling constants is 7.5 Hz, indicating a different conformation and configuration.
7s: The regiochemistry of this product was assigned by HMBC correlations, which identified the position of the C6 sidechain (rather than this being at C7) by a clear mutual correlations between H9/C9 and C7/H7. Stereochemical assignment was achieved using a 1 H-1 H NOESY experiment. A strong enhancement between H3a and H7, the latter of which also showed a weak enhancement with H6'. On the -face, H7 showed an enhancement with one of H9, while the other H9 proton showed an enhancement with H6. These enhancements suggest a conformation as depicted below, where a strong puckering of the ring places the C6' sidechain in a pseudo-equatorial position, and distorts the positioning of the C9 sidechain to be closer to protons on the -face of the ring system.

II Assignment of absolute stereochemistry
As the C2 stereogenic centres in 7q and 14q are unambiguously defined from their synthesis (from (R)-glycidol), the above assignments therefore enable a definitive assignment of the stereochemistry at H3a in each compound, and therefore the sense of catalyst stereoinduction in both the catalyst / substrate matched and mismatched settings. We extend this assignment of (R)-configuration at the C3a stereogenic centre to the enantioselective reaction using (S,R,R)-ligands, assuming the same sense of catalyst stereocontrol operates in this enantioselective reaction as in the diastereoselective cases.

Infrared Spectroscopy
Absorption spectra were obtained in CHCl 3 as solvent on a Bruker Tensor 27 FT-IR spectrometer.
The sample was prepared as a thin film on a diamond/ZnSe PIKE Miracle ATR module.
Wavelengths of maximum absorbance (ν max ) are quoted in wavenubers (cm -1 ). Only selected, characteristic IR absorption data are provided for each compound.

Polarimetry
Optical rotations were recorded on a Perkin Elmer 241 or 341 polarimeter with a path length of 1 dm (using the sodium D line, 589 nm). are reported in units of 10 -1 deg cm 2 g -1 .
Concentrations are reported in g/100 mL. Temperatures are reported in °C.

Elemental Analysis
Samples were analyzed by Mr. Stephen Boyer, Science Centre, London Metropolitan University.

Chromatography
Column chromatography refers to normal phase column chromatography and was performed on silica gel (35-70 mm) using head pressure by means of a nitrogen line. The combined organic extracts were dried (MgSO 4 ), filtered and concentrated in vacuo.

General Procedure F: Racemic [5+2] cycloisomerization
To an oven-dried vial containing the ynamide vinylcyclopropane (1.0 equiv.) under Ar was added a solution of [(C 10 H 8 )Rh(cod)]SbF 6 (5 mol%) in degassed CH 2 Cl 2 (10 mL / mmol of ynamide). The reaction mixture was stirred at room temperature under Ar until consumption of the ynamide was observed by TLC (see Figure 3 for reaction times). The reaction mixture was then concentrated, and the resulting crude product was purified by flash chromatography (SiO 2 , petroleum ether / ethyl acetate eluent).
The reaction mixture was then concentrated, and the resulting material was purified by flash chromatography (SiO 2 , petroleum ether / ethyl acetate eluent).

Computational Methods
All quantum chemical calculations were carried out with the Gaussian 09, D01program package. 5 Molecular geometries were fully optimized at the level of density functional theory, using the dispersion-corrected ω-B97XD 6 functional without any symmetry constraints. The effective core potentials (ECPs) of Hay and Wadt with a double-ζ basis set (LanL2DZ) 7 were used for Rh, S and P, and the 6-31G(d) basis set was used for H, C, N and O(BS1). The energies were further estimated using a larger basis set (6-311+G (d, p) basis set for H, C, N, O, S and P) and triple-ζ basis set (LanL2TZ) 8 for Rh (BS2) by single-point calculations, in implicit solvent treated with the SMD universal solvation model 9 . CH 2 Cl 2 was used as solvent with a dielectric constant value of 8.93 and using UAHF (United Atom Hartree-Fock) radii for the respective atoms (Rh, H, C, N, O, S and P) in the SMD calculations. Structures of the ynamide substrate and a series of phospohoramidite ligands were computed in full, while the -NTs p-tolyl group was modeled as methyl group in the interests of computational tractability. Additional density functionals such as B3LYP 10 , B3LYP-D3 11 and M06 12 were used with selected transition states to evaluate the functional influence. All optimized species were verified as either minima or transition structures by the presence of zero or a single imaginary vibrational frequency. Free energies were evaluated at 298K using harmonic vibrational frequencies. Saddle points were connected to minima in the usual way with intrinsic reaction coordinate (IRC) calculations 13 . The energies given throughout the paper are relative energy values computed with Gaussian 09 at 298 K and P=1 atm. NBO version 6.0 14 were employed to calculate the energy of second order perturbation for the proposed Rh-arene interaction.
Computed structures are displayed with CYLVIEW 15 or PyMol 16 . Nonbonding interactions in stereo-determining transition structures were visualized using the NCI (Non-Covalent Interactions) visualization index, based on the density and its derivatives. 17 Promolecular densities were used to analyse the interaction surface between substrate and chiral ligand. NCI analysis has emerged as a means to probe the role of weak interactions in asymmetric catalysis. 18

V Model for stereoinduction of transition states by chiral ligand
Having identified TS3 as the stereo-determining transition structure based on a full exploration of the potential energy surface with L1, the effect of varying the phosphoramidite ligand was studied on this step computationally. We separately optimized transition structure TS3 with different ligands (L4-L6) at the ω-B97XD/6-31G(d)/Lanl2DZ (BS1) level of theory. The single point energy was further evaluated with a large basis set ω-B97XD/6-311+G (d, p)/Lanl2TZ(BS2) and an implicit solvent treated SMD model. Details of atomic distances and dihedral angles are shown in Figure S1(a), which relate to the Rh-arene and π-π interactions as discussed in the main text.
Across all of the ligands studied, the distance from Rh to the closest carbon (C 3 ) of the proximal arene group is in the region of 2.67-2.82 Å, and for L5 this distance takes its longest value among all ligands studied. This suggests a weaker interaction between F-Ph with Rh, which corroborates recent collision-induced dissociation measurements of the effect of fluorination upon the relative binding affinities of cationic Rh-η 6 -arene complexes. 19 The TS leading to the major enantiomer (alkene Re face) benefits from this interaction (ie. 2.69 Å in Re and 2.79 Å in Si for L1). While these interactions are largely electrostatic in origin, the energies (i.e. π donor to vacant d-orbital of Rh and Rh back donation to π* of C=C) obtained from second-order perturbation theory of the basis set of natural bonding orbitals (NBOs) indicate the presence of non-classical Rh-arene interactions shown in Figure S1(b), which suggested electron 2π donor from arene to vacant d-orbital of Rh majorly contributes to this interaction rather than back donations.
Another important attractive nonbonding interaction is apparent in TS3 between the ligand biaryl backbone and the terminal alkyne substituent. For the phenyl-substituted alkyne this is a π-π interaction, [20][21][22] for which the physical origin lies in medium/long range electron correlation (i.e. dispersion effects), and we also expect attractive interactions to also occur when this substituent is aliphatic rather than aromatic. In TS3 the corresponding two fragments (phenyl and naphthyl) are oriented nearly parallel to each other separated by a perpendicular distances of 3.49-3.93 Å, which should be assigned as a parallel-displaced shape. A closer distance between two centre of phenyl and naphthyl in L5 suggests a tighter interaction within the substrate and ligand. The importance of this noncovalent interaction is underlined by the effect of partial saturation of the ligand backbone: we compute a significant drop in enantioselectivity to 7% ee as the gap between the two stereoisomers falls to 0.1 kcal mol -1 . This was confirmed experimentally, with an observed selectivity of 11% ee.
We present a simplified model in Figure S1(c), where TS3 can be divided into three parts, which describe the critical interactions that enable chiral relay from the ligand to metal and substrate. The Rh-arene interaction as "left arm" represents an interaction between metal and ligand, the noncovalent π-π interaction as the "right arm" representing an interaction between substrate and ligand, both of which act on the main "body" in TS3, the metal-complexed substrate. We have found that the extent of organization in the transition state can be quantified in terms of the dihedral angle made between substrate alkyne atoms and the two points of contact between metal and ligand (P atoms and arene C atom). As shown in Figure S1(a), the largest difference in this dihedral angle for the Re and Si TS is computed for the most selective reactions (L1 and L5). It is noticeable that the higher degree of coplanarity corresponds to the lower energy TSs, more closely corresponding to the optimial square-planar coordination of the metal centre. The excellent agreement between the computed selectivities and experimental results gives us confidence in this model to rationalize the selectivity.

VI NCI analysis
Optimized structures for TS show a parallel-displaced arrangment of ligand-backbone and substrate aromatic groups, which upon saturation of the ligand led to a marked erosion in enantioselecitivity.
We further probed the existence and nature of noncovalent interactions involving the chiral ligand in TS3 using the Non-Covalent Interaction (NCI) index based on the reduced density gradient of the promolecular electron density, as shown in Figure S2. A large surface is seen between the two aromatic groups of the ligand-backbone and substrate, indicative of a weakly attractive interaction between the two, supporting our earlier interpretation of this attractive interaction between catalyst and substrate. It is difficult to make quantitative arguments based on this analysis, however, the fact that the energy difference between Re-and Si-face is lessened by 2.6 kcal mol -1 when the aromatic portion of the ligand is reduced (i.e. with L6) supports the idea that this interaction is more favourable in the Re-face TS. Also apparent in the NCI surface is the previously identified Rh-arene interaction, which can be seen as an attractive (blue) region between the metal and the closest carbon atom of the proximal arene group of the ligand. Both of these aspects provide further support for our simplified model in Figure 1(c), and rely only the density rather than distance-based criteria.

VII Functionals Analysis for TS3
Relative energy was further evaluated by other common functionals for selected transition state TS3 with different coordination mode shown in Table S1. The selected transition states represent the closest energy gap based on our original calculation in main content, and therefore could be a good sample for functional evaluation. From table S1, the relative energy follows the order of B3LYP-D3 < ω-B97XD < M06 << B3LYP suggesting the significant importance of the dispersion within functional, which could be rationalized by a lot of non-covalent interaction. And the energy of our chosen ω-B97XD functional right located in the middle of B3LYP-D3 and M06 functionals, thus should be fair good to investigate in this reaction.