Computational modelling of the enantioselectivity in the asymmetric 1,4-addition of phenylboronic acid to a bulky, doubly pro-chiral maleimide catalyzed by a Rh/chiral diene complex

Hua-Li Qin*a, Zhen-Peng Shanga, Kaicheng Zhua, You-Gui Lib and Eric Assen B. Kantchev*bc
aSchool of Chemistry, Chemical Engineering and Biological Science, Wuhan University of Technology, 205 Luoshi Road, Wuhan, 430070, China. E-mail:;;; Fax: +86-27-8774-9300; Tel: +86-27-8774-9300
bSchool of Chemistry and Chemical Engineering, Hefei University of Technology, 193 Tunxi Road, Hefei 230009, China
cSchool of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798

Received 1st July 2015 , Accepted 26th August 2015

First published on 28th August 2015

Computational chemistry is a powerful tool for understanding chemical reactions used for the synthesis of chiral compounds. Here we present a DFT (IEFPCM/PBE0/DGDZVP level of theory) modelling of the stereoselectivity in the Rh-catalyzed 1,4-addition of phenylboronic acid to a bulky maleimide with a chiral diene (Phbod) as the ligand. The substrate is doubly prochiral due to the C[double bond, length as m-dash]C bond and the N-(2-tert-butylphenyl) giving rise to a centre and axial chirality, respectively, upon 1,4-arylation. The predicted absolute configuration was in agreement with the experiment for both diastereomer pairs. Quantitative prediction of the % ee for the major diastereomer was achieved with the M06 functional instead of PBE0 and taking into account all ligand conformations. However, the % ee for the minor diastereomer was always strongly overestimated, implying a possibility for a different, unknown reaction pathway. Applying Boltzmann distribution over all transition state conformers did not improve the accuracy.


The Rh-catalyzed 1,4-addition of arylboronic acids is one of the most important methods for asymmetric C–C bond creation.1 For the most typical substrate, 2-cyclohexenone (1; Fig. 1a) high yield and enantioselectivity are obtained with the chiral diene Phbod (I, 2,5-diphenylbicycloocta[2.2.2]-2,5-diene) as the ligand.2 With the bulky N-arylmaleimide derivative 3, a more complex case of the simultaneous creation of one chiral centre and one chiral axis has also been achieved in excellent yield and enantioselectivity.3 (R)-Phbod gives (R)-2 (97% ee) and (3R) in both diastereomers of 4, albeit in much lower enantioselectivity (37% ee) in the minor (3R,Ra)-4 than in the major (99% ee) (3R,Sa)-4. Hayashi et al. proposed a pictorial model explaining the observed enantioselectivity by the avoidance of the steric clash of the ketone substituent and the large group (e.g., Ph in I) on the ligand (Fig. 1b).2 The model accounts well for the sense of asymmetric induction, and has been extended to other ligands/substrates,4 including the axially-chiral maleimide 3. Density functional theory (DFT) calculations can not only predict the stereochemical course of the addition, but also the enantiomeric excess (vide infra) as well as reveal important details about the accurate structure and electronic distribution during the reaction. As a continuation of our program on computational modelling of the stereoselectivity of asymmetric Rh-catalyzed arylation reactions,5,6 herein we present DFT calculations on the double stereoselection in the 1,4-arylation of the axially chiral maleimide 3 catalyzed by Rh(I)-complexes of (S)-I.
image file: c5ra12792k-f1.tif
Fig. 1 (a) Previously published asymmetric Rh/(R)-Phbod-catalyzed 1,4-addition reaction of phenylboronic acid with 2-cyclohexenone (1)2 and N-(2-tert-butylphenyl)maleimide (3).3 Conditions: (a) 3.3 mol% I, 3 mol% Rh as [RhCl(C2H4)2]2, 50 mol% KOH, 2.5 equiv. PhB(OH)2, dioxane/H2O = 10[thin space (1/6-em)]:[thin space (1/6-em)]1, 30 °C, 1 h; (b) 5.5 mol% I, 5 mol% Rh as [RhCl(C2H4)2]2, 30 mol% KOH, 3.0 equiv. PhB(OH)2, dioxane/H2O = 10[thin space (1/6-em)]:[thin space (1/6-em)]1, 60 °C, 5 h. (b) Pictorial models rationalizing the formation of the major enantiomer by avoiding steric repulsion with the forward-facing diene Ph group. In the case of 3, the major diastereomer configuration is similarly explained by avoidance of the steric clash of the t-Bu substituent and the ligand.

Results and discussion

Computational approach

The accepted catalytic cycle of the maleimide 1,4-arylation consists of transmetalation (TM) of PhB(OH)2 activated by the monomeric [(ligand)Rh(OH)] considered to be the active catalyst, followed by maleimide binding (MB) to the tricoordinated [(ligand)RhPh] followed by carborhodation (CR), where the enantiodiscrimination takes place and, finally, Rh-enolate hydrolysis (EH) where the product is liberated and the active catalyst recovered (Scheme 1).7 The key stationary structures (intermediates and transition states, TS) for the enantiodiscriminating, C–C bond-forming MB + CR steps of the cycle8 were calculated for both I and the parent ligand bod (II, bicyclo[2.2.2]octa-3,6-diene). All structures were optimized at the IEFPCM9/PBE0 (ref. 10)/DGDZVP11 method in implicit dioxane and the frequency calculations were performed at 60 °C (333.15 K) to obtain the vibrational partition function hence ΔS and ΔG values at the reaction temperature and to verify the nature of the stationary points by the number of the imaginary (negative) frequencies being 0 and 1 for intermediates (potential energy surface or PES minima) and TSs (1st order saddle points). As it will be explained further, for quantitative modelling of enantioselectivity, the TS structures were reoptimized with the more modern M06 DFT functional,12 which accounts for important noncovalent interactions. This method was paired with both the standard IEFPCM implicit solvation method and its more modern SMD variant,13 which includes an improved set of atomic radii and a correction for dispersion-interactions.
image file: c5ra12792k-s1.tif
Scheme 1 The accepted catalytic cycle for the 1,4-aryltaion reaction of 3 with Rh(I) complexes of diene ligands I (chiral), and II (achiral).

Substrate 3 is conformationally rigid due to the o-tert-butyl substituted N-phenyl being perpendicular to the flat maleimide ring as confirmed by relaxed PES scan around the N–C1(aryl) bond. The key [(ligand)Rh–Ph] intermediates approach the maleimide prochiral C[double bond, length as m-dash]C bond either syn- or anti- to the N-(2-t-BuPh) group (Fig. 2). Each of these pathways splits additionally into two associated with Ph addition to either si-face or re-face of the C[double bond, length as m-dash]C bond. Therefore, complete characterization of the enantiodiscrimination process requires calculation of 4 diastereomeric pathways. However, for the achiral ligand II each facial approach leads to enantiomeric structures with equal energies. Herein we arbitrarily chose the approach that gives (3S)-configuration. Moreover, the mutual orientation of the Rh–Ph and C[double bond, length as m-dash]C bonds during the MB stage gives rise to multiple conformers. The productive conformers have approximately parallel orientation, as shown in Hayashi's pictorial models. Additionally, there are two perpendicular conformers characterized by the Rh–Ph group positioned on the same (close) or opposite (far) side as the N-aryl substituent. The total number of MB structures to be considered thus becomes 12 for I and 6 for II.

image file: c5ra12792k-f2.tif
Fig. 2 Possible reaction pathways (left) and MB conformations within each pathway (right).

Reaction profile

The calculated profile for ligands I (Fig. 3a; 5–17) and II (Fig. 3b; 18–34) with substrate 3, are similar to those for 1,6 reflecting the similarities of both substrates. All possible MB conformers were found. The MB step was found to be TS-less. The energies of the MB complexes spread along a wider range than the corresponding enone binding (EB) complexes for 1. Predictably, all MB intermediates for syn-approach (6–8, 19–21) are higher in energy than those for anti-(12–14, 29–31). However, the preferred conformation differs than the one predicted by Hayashi's model. Only for the minor (syn) pathway in the parent ligand II is the “parallel” MB conformer the lowest in energy (8; ΔG = −4.4 kcal mol−1 vs. −2.9 kcal mol−1 for the “far” (7) and −0.2 kcal mol−1 for the “close” (6)). For the major diastereomer, the 3 conformers (12–14) are rather close in energy, with the “far” (13; ΔG = −6.9 kcal mol−1) being slightly more stable than “parallel” (14; ΔG = −6.6 kcal mol−1).
image file: c5ra12792k-f3.tif
Fig. 3 The reaction profile for the MB + CR stages of the catalytic cycle (Scheme 1) for ligands (a) II and (b) I calculated at IEFPCM (dioxane, 333.15 K)/PBE0/DGDZVP level of theory.

Because of the larger steric demands of the chiral ligand I, the energetic separation of the various MB conformers is more pronounced. In the syn-pathway, the “far” (20; ΔG = −6.9 kcal mol−1) is the most stable. From it, enantiodivergence commences by the Ph group rotating towards either carbon of the maleimide C[double bond, length as m-dash]C double bond producing the corresponding “parallel” intermediates 21 ((3R); ΔG = 3.2 kcal mol−1) and 25 ((3S); ΔG = −0.9 kcal mol−1). In the anti-pathway, the “far” (30; ΔG = −6.3 kcal mol−1) and “close” (20; ΔG = −6.9 kcal mol−1) structures are very close in energy as a consequence of the lack of steric hindrance from the tert-Bu group. Similarly, enantiodivergence commences from either of these structures producing the “parallel” intermediates 31 ((3R); ΔG = 1.6 kcal mol−1) and 35 ((3S); ΔG = −4.9 kcal mol−1), respectively. The “parallel” MB structures give rise to 4 key CR-TSs having Gibbs energies of 5.9 (36), 7.8 (26), 10.3 (32), and 12.4 kcal mol−1 (22), in increasing order. Compared to the smaller achiral parent II, the larger chiral ligand (I) causes a minimal energy increase of the most favourable CR-TSs from 4.2 (15) to 5.9 (36) kcal mol−1, indicating maleimides are highly active in the Rh-mediated arylation. The most stable of these, 36, is the one predicted by the Hayashi's pictorial model for (S)-Phbod, leading to (3R,Sa)-4 as the major product. It is noteworthy that the Hayashi's pictorial model is much more similar to the CR-TSs (Fig. 4a) rather than calculated most-stable MB structures (Fig. 4b), which all are characterized by a perpendicular arrangement of the Ph–Rh and maleimide C[double bond, length as m-dash]C bond. The CR-TSs collapse to the primary products of the reaction, α-Rhsuccinimides (10 and 16 for II, 23, 27, 33, and 37 for I; ΔG ∼ −26 to −27 kcal mol−1). The products of the preferred pathway are only slightly more stable, confirming the 1,4-arylation is kinetically controlled. Unlike in the profile for 1, the rearrangement to Rh-oxa-π-allyl complexes is only slightly favourable, and that in only 2 cases (2324 and 3334). In all other cases, the Rh-oxa-π-allyl complexes (11, 17, 28 and 38) were significantly less stable, in contrast of the enone cases. This is presumably due to two effects: (1) the rearrangement brings the ligand closer to the N-aryl group, increasing steric repulsion; and, (2) the flat 5-membered ring restricts rotation around the C2–C3 bond, hence precludes a significant energetic gain from torsional strain relief.

image file: c5ra12792k-f4.tif
Fig. 4 Structural plots for: (a) all MB intermediates in the lowest energy pathway; (b) all CR-TSs (Fig. 3). The hydrogen atoms are omitted for clarity.

Computational modelling of enantioselectivity

Transition state theory applied to enantioselective reactions14,15 permits calculation of the enantiomeric excess from the difference of the Gibbs energies of two competing, diastereomeric CR-TSs (ΔΔG = ΔGCR-TS(major) − ΔGCR-TS(minor)):
image file: c5ra12792k-t1.tif(1)
where R is the universal gas constant and T is the absolute temperature of the reaction/calculation (333.15 K in this case). The above equation can be applied to both the major ((S,Ra) is the major and (R,Sa) is the minor enantiomer) and minor diastereomer pairs ((S,Sa) is the major and (R,Ra) is the minor enantiomer) of 4.16 Using the Gibbs energies for the 4 CR-TSs from the profile, the calculated % ee are 99.99% (ΔΔG = −6.5 kcal mol−1) and 96% (ΔΔG = −2.5 kcal mol−1) for the major and minor diastereomer pair, respectively. Both values are much higher than the experimental values (99% and 37%, respectively). In order to improve the quantitative description of the enantioselectivity,17 we refined the model by (1) performing an exhaustive conformational search for each CR-TS; (2) reoptimizing all conformer structures at IEFPCM or SMD/M06/DGDZVP level of theory.

Due to the conformational rigidity of the substrate, we explored the dihedral angles associated with the rotation of the ligand Ph groups. The Ph groups are slightly tilted with respect to the diene plane, and can easily change the degree of tilting to accommodate the substrate. In all structures shown in the profile, the two Ph rings are tilted in a way that produces the lowest energy.6 This tilt can be described by the two dihedral angles D1 and D2 (Fig. 5) having positive (+) values, therefore this conformation can be designated as “pp”. Accordingly, 3 additional conformations, “mp”, “pm” and “mm” are possible. For all 4 CR-TSs (“pp” conformers: 22, 26, 32, and 36), the “pm” conformers were found (22a, 26a, 32a, and 36a), in addition to an “mp” conformer only for the (S,Sa)-CR-TS (26b). Comparison of the values for key dihedral angles (D1–D4; Fig. 5) for each of the nine CR-TS structures at the 3 levels of theory (Table 1) suggests that the structures change slightly, yet significantly, during the reoptimization process. The change is, unsurprisingly, much more significant with change of the DFT method than the implicit solvation method. D1 and D2 change only slightly with the method, always maintaining an absolute value around 20 to 25°. D3, which is formed by the reacting atoms shows significant deviation from the ideal value, 0°, particularly for the lowest energy CR-TS 36. This is slightly more pronounced with the PBE0 functional. Finally, D4, describing the rotation of the N-aryl group shows the most variations, even though it maintains absolute values in the neighbourhood of 90 to 100° for most of the structures. This implies that even though the N-aryl group is roughly perpendicular to the maleimide ring as in the X-ray structure, it can easily be turned to accommodate the ligand's steric bulk (Table 1).

image file: c5ra12792k-f5.tif
Fig. 5 Key dihedral angles (D1–D4) in the CR-TS structures.
Table 1 Values for the 4 key dihedral angles (D1–D4; Fig. 5) at the 3 different structural optimization DFT and implicit solvation methods with DGDZVP basis set
Structures D1, ° D2, ° D3, ° D4, °
PBE0 M06 M06 PBE0 M06 M06 PBE0 M06 M06 PBE0 M06 M06
22 25 20 19 19 23 24 24 11 11 −96 −104 −104
22a 28 25 24 −17 −22 −22 24 6 6 −93 −106 −105
26 23 22 20 23 23 19 10 8 9 106 104 104
26a 21 23 22 −17 −20 −20 8 7 9 106 109 109
26b −11 −19 −19 19 19 19 12 13 12 102 98 99
32 24 22 21 26 22 21 23 −10 −11 98 117 116
32a 26 28 28 −34 −30 −31 26 21 25 99 85 86
36 23 30 25 22 22 22 15 27 27 −107 −98 −98
36a 26 29 27 −22 −21 −26 13 26 26 −110 −76 −76

Table 2 Gibbs energies for all CR-TSs and enantioselectivity modelling at different DFT and implicit solvation methods (with DGDZVP basis set)
Method Major diastereomer pair Minor diastereomer pair
ΔG (3S,Ra)a ΔG (3R,Sa)a Enantioselectivityb,c ΔG (3S,Sa)a ΔG (3R,Ra) Enantioselectivityb,d
36 36a 22 22a Expt. Theor. 26 26a 26b 32 32a Expt. Theor.
a In kcal mol−1, calculated relative to ΔG (18) + ΔG (3). The values used for enantioselectivity calculations are shown in italics.b Given in ΔΔG, kcal mol−1 (% ee). The interconversion between the two values is done according to eqn (1).c ΔΔG = ΔG (36) − ΔG (22).d ΔΔG = ΔG (26) − ΔG (32).
IEFPCM/PBE0 5.9 6.2 12.4 12.0 −3.5 (99%) −6.1 (99.98%) 7.8 8.6 8.9 10.3 11.0 −0.5 (37%) −2.5 (96%)
IEFPCM/M06 −1.6 −0.2 4.8 1.9 −3.5 (99%) −0.2 1.4 −0.8 3.1 3.5 −3.9 (99.4%)
SMD/M06 2.2 2.9 7.7 4.8 −2.6 (96%) 2.0 2.6 2.7 6.6 5.5 −3.5 (99%)

As briefly mentioned above, the theoretical enantioselectivities (Table 2) for both diastereomeric pairs with PBE0 (calculated for “pp” conformers”) are overestimated to significant degree. Significantly, in the major diastereomer pair, the “pm” conformer (22a) of the minor enantiomer is lower in energy than the “pp” conformer (22), at all levels of theory. In combination with IEFPCM, the theoretical enantioselectivity calculated from the lowest energy conformers matches exactly the experiment (ΔΔG = −3.5 kcal mol−1 corresponding to 99% ee by eq. (1)), but is underestimated by 0.9 kcal mol−1 with the SMD variant. Considering CR-TS 22 is the least favourable CR-TS of the four, it is conceivable that the strong steric clash between the ligand and the substrate is partially alleviated by rotating the ligand Ph group on the maleimide side (D2). The minor diastereomer pair, the major enantiomer has 3 stable conformers, which are rather close in energy. The situation is similar for the minor, which only has 2 conformers. In all cases, the theoretical % ee is much higher than the experimental. However, it is possible that the minor enantiomer is formed by a yet unknown, distinct pathway. The very significant differences in the enantiomeric composition for the minor diastereomer observed for different ligands used by Hayashi et al. is consistent with such a possibility.

Eqn (1) is applicable to transition states – a macroscopic, statistical-thermodynamic concept. DFT calculations produce transition structures and their energies. When there are no other transitions structures close in energy, the only one having lowest energy represents the transition state. However, for a system reacting via multiple channels such as the one considered here, ΔG of the transition state can be approximated by a Boltzmann distribution of the ΔG of individual CR-TSs:14

image file: c5ra12792k-t2.tif(2)
where n = 2 for 22, 32, and 36 and n = 3 for 26. Table 3 presents a comparison of the theoretical enantioselectivities calculated from ΔG or DFT electronic energies (ΔEel) taken for the lowest energy conformers only, or by calculating the Boltzmann distribution of all conformers, at all 3 levels of theory. As it was briefly mentioned above, calculation of ΔG requires performing a frequency calculation (under quadratic approximation, which is much closer for minima than saddle points like TSs) and subsequent calculation of the vibrational partition function by a Boltzmann distribution of the vibrational levels. In addition, there are significant inaccuracies of estimation of translational and vibrational entropies, as well as such associated with the use of the ideal gas law for calculating the ΔPV (P = pressure, V = volume) term of ΔG.18 Many of these terms are almost the same for the structurally very similar diastereomeric CR-TS, and could cancel out, leaving the electronic energies as the only significant term. In a similar vein, often electronic energies are corrected at high level of theory in gas phase while using the frequency calculations in solution at lower level of theory (we performed proper structure reoptimization/frequency calculation when changing the level of theory). Applying the Boltzmann distribution had relatively small effect (usually 0.2 to 0.3 kcal mol−1). For the system under consideration here, it did not improve the quantitative description of the enantioselectivity. On the other hand, using the electronic energies led to decreasing of ΔΔEel for the major pair, but increasing it for the minor pair. However, inspecting the actual barrier heights (data not shown) revealed that the diastereoselectivity was adversely affected, with the major diastereomer predicted as the minor product at SMD/M06 method.

Table 3 Gibbs energies for all CR-TSs and enantioselectivity modelling at different DFT and implicit solvation methods (with DGDZVP basis set)
Method ΔΔE, major diastereomera,b ΔΔG, minor diastereomera,c
ΔGd ΔGBe ΔEeld ΔEel-Be ΔGd ΔGBe ΔEeld ΔEel-Be
a In kcal mol−1, calculated relative to ΔE(18) + ΔE(3).b ΔΔE = ΔE(36) − ΔE(22).c ΔΔE = ΔE(26) − ΔE(32).d Using ΔE (E = G or Eel) of the lowest CR-TS conformer.e Using ΔE (X = G or Eel) calculated by Boltzmann distribution of all CR-TS conformers (eqn (2)).f From the experimental % ee according to eqn (1).
IEFPCM/PBE0 −6.1 −6.2 −5.0 −5.0 −2.5 −2.6 −3.1 −3.3
IEFPCM/M06 −3.5 −3.6 −3.1 −3.0 −3.9 −3.9 −3.9 −4.5
SMD/M06 −2.6 −2.7 −3.0 −2.8 −3.5 −3.7 −4.0 −4.7
Expt.f −3.5 −0.5


The stereodifferentiation step in the 1,4-addition of phenylboronic acid to a doubly-prochiral bulky N-arylmaleimide catalyzed by Rh/Phod was modelled at PCM/PBE0/DGDZVP level of theory. The predicted absolute configuration agreed with the experiment. Excellent match of the theoretical and experimental enantioselectivity for the major diastereomer was achieved by using the modern, noncovalent interaction-corrected M06 DFT functional after a thorough conformational analysis of the ligand. However, for the minor diastereomer, the theory overestimated the experimental enantioselectivity value by a large degree in all cases. Even though the actual reasons are unknown, this may be due to erosion of enantiopurity by a yet unknown pathway. Using Boltzmann distribution to account for the effect of multiple reaction channels each associated with a separate transition state conformers did not have a major effect on the predicted enantioselectivity.


This work was supported by Wuhan University of Technology, Hefei University of Technology, and The Natural Sciences Foundation of Anhui Province (grant 11040606M35), China. The authors thank A*STAR Computational Resources Centre (Singapore) for the generous gift of computational time on the Axle, Fuji, Cirrus and Aurora HPC clusters.

Notes and references

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  16. Eqn. (1) can be applied also to diastereomers as in the case with ligand II. In this case, ΔΔG = −1.7 kcal mol−1, which corresponds to % de = 86% (the experimental value for ligand I is 92%). There is no equivalent equation applicable to 4 diastereomeric TSs as in the case for ligand I. Neglecting the contributions of the minor enantiomer within each pair (a rather crude approximation considering % ee in the minor pair is only 37%) gives ΔΔG = −1.9 kcal mol−1 corresponding to % de = 89%.
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Electronic supplementary information (ESI) available: Cartesian coordinates, energies and first 3 frequencies for all stationary points. See DOI: 10.1039/c5ra12792k

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