Asymmetric Induction in C ‑ Alkylation of Tropane-Derived Enamines: Congruence Between Computation and Experiment

: Quantum chemical studies of C -ethylation of 1-methyl- and 1,4,4-trimethyl-tropane-derived enamines predict good (89:11 er, B3LYP) and high (98:2 er, B3LYP) levels, respectively, of asymmetric induction in the resulting α alkylated aldehydes. The nonracemic tropanes were synthesized using Mannich cyclization strategies (Robinson-Scho ̈ pf and by way of a Davis-type N -sul ﬁ nyl amino bisketal, respectively), and ethylation of the derived enamines was found to support the predicted sense and magnitude of asymmetric induction (81:19 er and 95:5 er, respectively). A comparison of several computational methods highlights the robustness of predicted trends in enantioselectivity, enabling theory to guide synthesis.


■ INTRODUCTION
Chiral α-alkyl-substituted aldehydes are important building blocks for organic synthesis. Several methods to make them involve a chiral auxiliary alkylation strategy and have proven effective for asymmetric induction, but each approach is not without specific drawbacks. 1 The primary method for generation of enantioenriched α-alkyl-substituted aldehydes through alkylation by nucleophilic substitution with S N 2 reactive electrophiles involves the use of Enders' lithiated SAMP/RAMP hydrazones, although the requirement for low temperature (usually −80 to −120°C) and the need for subsequent ozonolysis in cleavage of the auxiliary can cause problems. 2,3 Alkylations are well-known with Evans' oxazolidinone 4 or Myers' pseudoephedrine 5 auxiliaries, but once again further manipulation to the aldehyde is required by the removal of these auxiliaries through reduction. 6 Catalytic α-alkylation of aldehydes by way of transient enamines has attracted much attention in recent years, 1 with the process being described as the "Holy Grail" of organocatalysis. 7 This task with S N 2 reactive electrophiles has proven to be challenging, particularly due to undesired side-reactions such as self-aldolization of the aldehydes, and N-or O-alkylation of the catalysts. Work by MacMillan on asymmetric one-electron-mediated organic transformations using photoredox-organocatalysis constitutes an elegant strategy for performing such catalysis, however this method with organohalides requires a radical capto-stabilizing group on the alkylating partner, reducing the scope of this technique. 8,9 While organocatalytic α-alkyl-substituted aldehyde generation through intermolecular nucleophilic substitution remains problematic, 1,7,10 we have been investigating alkylation of preformed chiral aldenamines as an expedient route to αalkylated aldehydes. Steric shielding around N is required in such systems to provide bias for C-alkylation. Our early studies with α,α,α′-trialkylsubstituted piperidine-based auxiliaries pro-vided a promising start (88:12 to 94:6 er for ethylation). 11 Issues with conformational flexibility and inactive ground state conformers (lacking N lone pair−π* overlap) led us to then examine rigidified systems: tropane-derived enamine 1 and homotropane-derived enamine 2 (Scheme 1). 12 On ethylation, these latter systems gave 2-ethylhexanal (3) in 45:55 and 72:28 ers, respectively, with the low er from tropane 1 being accompanied by an initially unexpected reversal in the sense of asymmetric induction. These observations were rationalized through computational investigations of the competing alkylation transition structures (TSs). 12 The (slight) bias for ethylation of tropane-derived enamine 1 from the 5-rather than the 6-membered side of the bicycle, even though the 5membered side possesses ostensibly the greatest steric hindrance, was particularly intriguing. In contrast to this earlier study, where DFT calculations were used to rationalize empirical results, the present work describes the use of computation as a predictive tool. The computational prediction and design of catalysts and reactions is still far from routine, 13 and few examples of stereoselective catalysts or reactions synthesized according to computational designs have been reported. 14, 15 In the current study, we show computed trends in enantioselectivity that are relatively robust across different theoretical methods, allowing confident, qualitative, predictions to be made. Initial investigation of the intrinsic bias of tropanederived enamine alkylation proved the model's accuracy experimentally. These results were then used to inform the design of a new tropane auxiliary with sufficient hindrance on the 6-membered side to induce a significantly improved level of asymmetric alkylation.

■ RESULTS AND DISCUSSION
The stereoselective ethylation of enamines 1 and 2 was modeled by us previously with the B3LYP density functional. 12 A large body of work (most notably from Houk) using this level of theory has successfully rationalized the stereochemical outcome of enamine reactions. 16 Despite the shortcomings of the B3LYP functional, it remains a cost-effective method for geometry optimization in the face of multiple conformations and organic reaction pathways. 17 In our case, TS conformers were systematically optimized and the levels of stereoselectivity computed from the B3LYP Boltzmann populations. Qualitatively, the reversal in facial selectivity between 1 and 2 was reproduced, and the quantitative magnitudes of stereoselectivity were also described reasonably well. The use of quasi-rigid rotor harmonic oscillator (qRRHO) corrected Gibbs energies lessens the influence of erroneously large vibrational entropies associated with low frequency normal modes on the computed selectivities. 18 As in our earlier studies, 11,12 the n-butyl group of the experimentally examined enamines was truncated to a methyl group for computational work. The 27-fold reduction in conformational space makes the computational study feasible, while retaining the important steric effects.
Computations for the bicyclic amine-derived enamines showed that the presence of the bridgehead methyl group leads, due to minimization of allylic strain, to only one relevant rotamer about the exocyclic C−N bond (the anti form, referring to the relationship between the double bond and the N−C bond bearing the bridgehead methyl). 11d Furthermore, the calculations indicated that tropane-derived enamine 1* preferentially adopts a conformation in which the fivemembered ring is oriented further away from the enamine than the six-membered ring. As a result, the exo-methyl of the gem-dimethyl group is unable to exert a steric influence in the alkylation transition states, and the modest preference for alkylation on the side of the five-membered ring is directed by an axial exo-hydrogen of the six-membered ring ( Figure 1). There is no such conformational bias in homotropane-derived enamine 2*, where the exo-methyl lies closer to the site of reactivity and modestly influences alkylation to occur on the side of the unsubstituted six-membered ring. Observing that a difference in ring size influences enamine conformation led us to hypothesize that enamine 4*, lacking the biasing element of the gem-dimethyl group, should also undergo stereoselective alkylation (compared with enamine 1*, the lack of an endomethyl group in enamine 4* does not result in axial exo-H being any less close to the C that undergoes alkylation: the H···C distances being 2.85 Å in 1* and 2.86 Å in 4*). The level of asymmetric induction with this system would be intriguing as, aside from the bridgehead methyl necessary to confer chirality and restrict the enamine to one rotamer, facial bias on alkylation would simply be dependent on the influence of different ring sizes (5 versus 6) in the otherwise unsubstituted N-bridged bicyclic system 4*. The global minimum energy conformation of this enamine illustrates this design element, the N atom being pyramidalized and the CC bond siting closer to the six-membered ring. Moreover, models of enamine 5* showed that the incorporation of the gem-dimethyl group in the six-membered ring should, in combination with the conformational bias already described, effectively shield approach to the enamine from the side of the six-membered ring (modeling was performed for the same enantiomeric series as 4*, although in subsequent experimental work the "opposite" enantiomer was synthesized). The introduction of this additional biasing element results in two ground state conformations of similar stability. We turned to computations of the competing TSs to predict the sense and levels of stereoinduction resulting from the proposed structural changes.
Alkylation of 4* was predicted to occur preferentially on the same side as the five-membered ring ( Figure 2). This reflects the ground-state conformational bias of the enamine (Figure  The Journal of Organic Chemistry Article 1). Nonbonding contacts between the axial H atoms and the electrophile are visible in the noncovalent interaction (NCI) isosurface of the disfavored pathway ( Figure 2). We also noticed a favorable N---HC interaction in the most favored TS, which requires orientation of the electrophile Me group toward nitrogen. Such a conformation is sterically more challenging for the other enamine face (see Figure S2). The sense of stereoinduction was predicted to be the same as computed and observed for enamine 1, but showing higher levels of selectivity. The selectivity predictions were obtained from the Boltzmann population over six conformations; a further six TSs were also evaluated for alkylation of the minor (syn) rotamer, however, these did not contribute appreciably to the observed selectivity.
Calculated levels of selectivity for 5* were noticeably higher (B3LYP predicted 98:2, Figure 3) than for any of those enamines studied previously. The most stable TS conformer was the same as for 4*, with the electrophile CH interacting with the enamine N atom. Nonbonding interactions between the axial methyl group and electrophile are visible from the NCI isosurface, giving greater levels of stereoinduction than 4*.
Throughout this work the B3LYP functional performed well in describing, and importantly predicting, levels of enantioselectivity and trends between the four synthesized enamines. Relatively small energetic differences between competing TSs can be influenced by noncovalent interactions, notably dispersion forces, and the performance of B3LYP, which lacks long-range correlation effects (as do all semilocal functionals), is perhaps surprisingly good. In this respect, intermolecular basis-set superposition error can mimic the effects of dispersion, albeit in an unphysical way, and equally, dispersion corrections in combination with small basis sets should be approached carefully. 29 We repeated our computational analysis with different density functionals, optimizing all competing TSs for each enamine with the implicit (M06-2X) and explicit (B3LYP-D3, wB97XD) inclusion of dispersion effects (Figure 4). 30 The increase in enantioselectivity progressing from enamines 1, 2, 4, and 5 obtained experimentally is captured by all four functionals tested (using 1*, 2*, 4*, and 5*). Dispersion is evidently not a decisive element of stereocontrol for these reactions. The experimentally and computationally observed differences in facial selectivity between enamines 1(*) and 4(*) indicate that the presence of the 6-exo Me in 1(*) does slightly work against the inherent bias for alkylation on the side of the five-membered ring. These computational studies suggest a contributory factor to this: the favored transition state for 4* with a favorable N−H interaction is not seen analogously for 1*, as this would result in nonbonded steric interactions between the 6-exo Me and the electrophile. While B3LYP-D3, M06-2X, and wB97XD gave quantitative values of enantioselectivity closer to experiment for 2, B3LYP predictions were actually closer to the final experimental selectivities of 4 and 5.
For each diastereomeric pair of TSs, differences in forming and breaking bond distances vary only slightly across different levels of theory (ca. 0.01−0.03 Å). Energy differences between major and minor pathways are therefore relatively insensitive, leading  The Journal of Organic Chemistry Article to a broad consensus in the levels of selectivity. Tighter transition structures were found with the dispersion-corrected methods vs B3LYP, in some cases with forming/breaking distances shorter by more than 0.1 Å. More pronounced nonbonding interactions arise, and consequently, higher computed levels of selectivity.

■ CONCLUSION
The first tropane-type derived enamines computationally predicted to show high levels of asymmetric induction on alkylation have been synthesized, and the experimentally observed ers are in good agreement with the DFT studies. The monomethyltropane derived enamine 4 illustrates the use of differing ring size (piperidine versus pyrrolidine in the Nbridged bicycle) as an unusual design element to bias π-facial selectivity with an electrophile. While undesired N-alkylation became competitive with this system, the presence of an additional exo-methyl group in the six-membered ring (enamine 5) was sufficient to restore a synthetically useful yield (63%) and provide the highest level of asymmetric induction for ethylation observed so far (95:5 er). This chemistry demonstrates the potential of the tropane scaffold as a useful chiral auxiliary for the synthesis of α-alkylated aldehydes by nucleophilic substitution. Predictions of trends in enantioselectivity, which can be used synthetically to optimize levels of stereoinduction, are in this case relatively insensitive to the level of theory chosen. However, accurate predictions of the precise magnitude of enantioselectivity remain a continuing challenge.

■ EXPERIMENTAL SECTION
General Details. Where anhydrous conditions were required, reactions were performed using flame-dried glassware under an atmosphere of nitrogen. C 6 H 6 , CH 2 Cl 2 , Et 2 O, MeOH, EtOH, pentane, and THF were dried over 4 Å molecular sieves, then degassed and dried over activated alumina under nitrogen. CD 3 CN was purchased in glass ampules (0.75 mL), and C 6 D 6 was purchased as a bottled reagent (1 g); both were opened under an atmosphere of nitrogen and distilled over CaH 2 immediately prior to use. EtI was passed through basic alumina immediately prior to use. All other reagents were used as received. Reactions were monitored by TLC using silica gel-coated aluminum-backed plates (Kieselgel 60 F 254 ). The plates were visualized using UV light and developed in basic potassium permanganate, phosphomolybdic acid, or ninhydrin solutions. Column chromatography was performed using the solvent systems indicated. The stationary phase used was silica gel (0.04−0.06 mm particle size, Kieselgel 60). Where silica gel is indicated as deactivated, this was carried out by stirring the silica gel overnight in 20% Et 3 N in petroleum ether. Petroleum ether refers to the fraction of light petrol boiling between 30 and 40°C. HPLC was performed using Daicel chiral columns and HPLC grade solvents. Melting points are uncorrected. Specific rotations [α] λ T were measured using a cell of path length 10 cm, at T = 25°C, with λ = 589 nm (sodium D line), in the stated solvent, at a concentration (c) given in g/100 mL, and are recorded in 10 −1 deg cm 2 g −1 . IR spectra were recorded as either neat samples or thin films in CH 2 Cl 2 /CHCl 3 . The intensity of the peaks are recorded as strong (s), medium (m), or weak (w) and prefixed with broad (br) where appropriate. 1 H, 13 C and 77 Se NMR spectra were recorded in CDCl 3 (unless stated otherwise) at ambient temperature using either 400 or 500 MHz spectrometers. Data are expressed as chemical shifts in parts per million (ppm) relative to residual chloroform and CDCl 3 ( 1 H δ 7.27, 13 C δ 77.0 respectively), residual DMSO and DMSO-d 6 ( 1 H δ 2.50, 13 C δ 40.0, respectively) or residual benzene and C 6 D 6 ( 1 H δ 7.16, 13 C δ 128.4, respectively) as the internal standard on the δ scale. The multiplicity of each signal is designated using the following abbreviations; s, singlet; br s, broad singlet; d, doublet; dd, doublet of doublets; ddd, doublet of doublet of doublets; dt, doublet of triplets; t, triplet; td, triplet of doublets; m, multiplet. Where diastereoselectivity is quoted, this was determined from isolated, corresponding, signals of each diastereomer in the crude 1 H NMR. 1 H and 13 C NMR peak assignments were made using COSY, DEPT, and HSQC experiments. High-resolution mass spectra were obtained by ESI (MicroTOF); values are quoted as ratio of mass to charge (m/z) in Daltons, and relative intensities of assignable peaks observed are quoted as a percentage value.
Computational Methodology. Density functional theory (DFT) calculations were performed using the Gaussian 09 package. 31 Optimizations of the enamine ground state structures and of transition state structures for alkylation were performed using the default (fine) grid density for numerical integration with the B3LYP, wB97XD, and M06-2X functionals. 32 Optimizations were also performed with an atom-pairwise density independent Becke-Johnson damped D3dispersion correction (s 6 = 1.0; a 1 = 0.3981; s 8 = 1.9889; a 2 4.4211). 33 Harmonic vibrational frequencies were computed for all optimized structures to verify that they were either minima or transition states, possessing zero imaginary frequencies and one imaginary frequency, respectively. The Pople 6-31G(d) basis set was used for all elements except I, which was described with the LANL2DZ effective core potential and associated valence basis of Hay and Wadt. 34 Effects of solvation due to acetonitrile (ε = 35.688) were implicitly included in all geometry optimizations and in the evaluation of energies using a conductor-like polarizable continuum model (CPCM). 35 Gibbs energies were evaluated at the reaction temperature of 65°C. A quasi-rigid rotor harmonic oscillator approximation was applied, switching to a free rotor description of vibrational entropy below 100 cm −1 . This mitigates spuriously large entropic terms from low frequencies, reducing the sensitivity of the computed selectivities to the choice of numerical convergence criteria or grid size. 36 Conformers of the diastereomeric transition structures arising from rotation about the incipient C−C bond were systematically generated and optimized for each enamine: in each case there are three TS geometries for attack from either enamine diastereoface. Stereoselectivities were computed from a summation of competing Boltzmann populations. 37 Noncovalent interaction (NCI) isosurfaces were generated from the B3LYP densities using NCIplot using default density (0.2) and reduced density gradient (1.0) cutoffs. 38 Molecular graphics were produced by Pymol, including Bondi Atomic van der Waals radii where appropriate. 39 ■ ASSOCIATED CONTENT

* S Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.joc.7b01954. 1 H and 13 C NMR spectra, 77 Se NMR spectra for determination of er, and HPLC traces of formamides showing enantiopurity (PDF) Determination of absolute configuration, Cartesian coordinates, imaginary frequencies, and computed energies (ZIP) X-ray crystallographic data for compound (S,1S,1R,5S)-11·THF (CIF)