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Density functional theory and correlated ab initio quantum mechanical methods were used to locate and analyze alkene hydroboration transition structures for 10-R-9-borabicyclo[3.3.2]decane reagents. Transition-state ensembles quantitatively modeled enantioselectivity for hydroboration of cis-, trans-, and gem-disubstituted alkenes in excellent agreement with experiment. The 10-R group and borabicyclo[3.3.2]decane ring conformation effects were analyzed to understand the origin of asymmetric selectivity.
Brown and co-workers’ use of diisopinocamphenylborane [(Ipc)2BH] (1a, Chart 1) for alkene hydroboration-hydroxylation is a classic example of reagent-controlled asymmetric synthesis.1 Although (Ipc)2BH induces over 99% enantiomeric excess (ee) upon reaction with cis-disubstituted alkenes, it gives quite poor ee for other types of substituted alkenes.1,2 Masamune’s reagent (1b) is highly effective for cis-, trans-, and tri-substituted alkenes, but not gem-disubstituted alkenes. However, it is not widely used due to the difficulty of its synthesis.3 In 2008, Soderquist and co-workers showed that 10-substituted-9-borabicyclo[3.3.2]decanes (2a and 2b, Chart 1) react with a variety of substituted alkenes with good to high enantioselectivity (Chart 2).4 For example, the reaction of 2a or 2b with trans-2-butene (3) results in alcohol products with greater than 95% ee. However, for cis-2-butene (4), only 2a with a 10-trimethylsilyl (TMS) group results in high enantioselectivity (84% ee). Most novel about reagent 2a is the induction of 52% ee for the hydroboration reaction of 1,1-disubstituted alkene 5 and 56% ee with alkene 6. Although the 10-Ph reagent 2b gives poor hydroboration enantioselectivity with alkenes 4 and 5, it does induce 92% ee for reaction with alkene 6. Soderquist and co-workers have also used the 10-substitution borabicylo[3.3.2]decane unit successfully for a variety of other asymmetric reactions, most notably asymmetric allyl- and crotylboration of aldehydes.5
Several theoretical studies have established that the alkene hydroboration transition structure consists of a four-centered structure with simultaneous boron-carbon and hydrogen-carbon σ-bond formation (Scheme 1).6 Because of the involvement of the unoccupied boron p-orbital, both π- and σ-interactions mix into this transition state, avoiding a high-energy four-centered four-electron addition process. This results in a transition structure with significant π-complex character.7 For BH3 addition to ethylene in the gas phase, there is also a weak pre-transition state π-complex. Although the transition states for BH3 addition to alkenes have been extensively explored, there are surprisingly few calculations of transition structures involving complex hydroboration reagents.8 The most notable hydroboration transition structure was reported by Houk and co-workers over two decades ago using parameterized molecular mechanics for (Ipc)2BH addition to ethylene.9
Oyola and Singleton have recently shown that transition state theory overestimates anti-Markovnikov/Markovnikov regioselectivity for BH3 addition to alkenes.10 A classical trajectory study using direct dynamics starting with structures prior to the π-complex matched very well with the experimental regioselectivity. The necessity of dynamics calculations to predict regioselectivity is the result of a barrierless and exothermic π-complex that does not thermally equilibrate before the transition state for B-H bond addition.10 In contrast, the dialkyl borne reactions explored in this study have B-H bond addition barriers significantly higher than separated reactants. Therefore, normal thermal population and activation should dominate and traditional transition state theory is expected to sufficiently model selectivity.
The purpose of this contribution is to quantitatively model transition states and enantioselectivity for the hydroboration of disubstituted alkenes by the Soderquist boranes 2a and 2b with the goal of understanding the origin of asymmetric induction. Paramount to understanding enantioselectivity is deciphering the role of the 10-R group (TMS and Ph) versus the borabicyclo ring conformation. Soderquist and co-workers have postulated that the borabicyclo[3.3.2]decane ring conformation is critical in determining enantioselectivity. Their molecular mechanics optimizations suggested that differences in selectivity between reagents 2a and 2b is the result of opposite boat/chair borabicyclo[3.3.2]decane ring conformations (Chart 3); the long C-SiMe3 bond in 2a favors conformation 2 (CF2) with the boat side (7-position methylene) of the borabicyclo ring syn to the TMS group while the shorter C-Ph bond favors conformation 1 (CF1) with the chair side (3-position methylene) syn to the 10-Ph group. Consequently, the 10-TMS group in 2a is responsible for the major directing interactions while in 2b the 3-position methylene exerts a so-called “α-directive effect” that enhances π-facial selectivity for reactions with trans substituted alkenes but decreases and reverses π-facial selectivity for reaction with cis alkenes.
All density functional calculations were performed in Jaguar 7.0/7.511 and all ab initio and composite method calculations were performed in Gaussian 03.12 All reactant and transition structures were optimized using B3LYP/6-31G(d,p) hybrid-density functional theory.13 Energies of these structures were also evaluated using the spin-component scaled-MP2 (SCS-MP2)/6-31G(d,p)14 method. This model of chemistry was chosen because it successfully models short-range (opposite spin) and static (same spin) correlation effects and several studies have shown it to give comparable energies to CCSD(T) theory. In addition, SCS-MP2 also gives the dimethylborane-ethylene hydroboration activation barrier in close agreement with multi-component methods such as CBS-QB3,15 G3,16 and G3B317 whereas B3LYP predicts slightly too high of barriers (see Supporting Information). Enthalpy and free energy corrections were applied at 298 K using the B3LYP/6-31G(d,p) values. Diethyl ether (ε = 4.335, radius probe = 2.74) implicit free energy of solvation corrections were applied using the Poisson-Boltzmann solvation model. All geometrical data was obtained using Molden.18 All transition structure figures were generated using pymol.19
As discussed later, there are multiple competitive transition structures due to several borabicyclo ring conformations for hydroboration of alkenes by 2a and 2b leading to both the favored and unfavored product enantiomers. Therefore, the predicted enantiomeric excess was calculated based on an approximate transition state ensemble. Friesner and co-workers have recently used a similar analysis for alkene epoxidation reactions.20 Asymmetric selectivity is the result of different rates of formation for each enantiomer. The observed enantiomeric excess (ee) is the difference between the rate of formation of the favored and unfavored enantiomer relative to the total rate (equation 1). Application of traditional transition state theory (Eyring equation) with the assumptions of equivalent pre-exponential factors gives equation 2 and equation 3.
A transition state ensemble for both favored and unfavored enantiomeric pathways was used to compute the free energy difference (ΔΔG‡) between pathways. Electronic energy or enthalpy may also be used in place of ΔΔG‡ under the assumptions of equivalent enthalpy and/or −TΔS corrections. The ensemble was approximated as the Boltzmann-weighted partition function (Λ, equation 4) over all unique transition states that lead to the favored and unfavored enantiomers. Most ensembles were limited to three unique transition states (n = 3). The difference between these ensembles, equation 5, can then be inserted into equation 3 to give the predicted ee.
To begin, Figure 1 shows the possible ground state conformations of the 10-R-9-borabicyclo[3.3.2]decane ring for 2a and 2b.21 Although ground state conformations are not important for asymmetric selectivity, each of these conformations exists as a unique starting point for transition structures for addition to alkenes. Table 1 gives the relative energies for the four possible ring conformations. For 2a and 2b all methods predict structure CF1 to be lowest in energy. In this conformation the 3-position methylene group is directed up toward the 9,10-borabicylo bridge while the 7-position methylene group is directed down to avoid interaction with the 10-R group. Conformation CF2 with the 7-position methylene oriented towards the 10-R group is also low in energy and on average only ~1 kcal/mol higher than CF1. The closest SiMe3 to 7-position methylene group contact distance in 2a-CF2 is 2.249 Å, which is only a slightly larger contact distance than the 10-Ph group to 7-position methylene group contact distance in 2a-CF2 of 2.239 Å (Figure 1). If both the 3- and 7-position methylene groups are oriented down (CF3) the relative energy increases by ~2 kcal/mol due to transannular repulsion. Conformation CF4 with both methylene groups up raises the energy by more than 4 kcal/mol. For reagent 2b there is also the possibility for rotation of the 10-phenyl group by ~85° to give 2b-CF4, which is ~1 kcal/mol higher than 2b-CF1. The alternative boat/chair conformations of 2b-CF4 are 1–4 kcal/mol higher in energy. Although this phenyl group conformation is accessible in the ground state no transition structures were located with this phenyl group conformation.
Each of these bicyclo boranes can potentially form dimeric structures. For 2a the lowest energy borane dimer corresponds to [2a-CF2]2 (see Supporting Information for structure). Significant intermolecular TMS group repulsions with the CH bridgehead and 2-position methylene group of the second borane leads to a weak binding energy (ΔE = −0.2 kcal/mol) and a highly endergonic dimeric structure (ΔG = 19.1 kcal/mol). In contrast, the flexibility of the 10-phenyl group to rotate in 2b allows the borane dimers to have a much stronger dimeric interaction. “Cis” and “trans” dimers [2b-CF1]2 have ΔE values of −16.2 and −16.3 kcal/mol. These large and nearly equal binding energies are consistent with the experimental observation of nearly equal amounts of dimeric “cis” and “trans” dimers from 2b and no dimer formation from 2a.
In addition to the four borabicyclo[3.3.2]decane ring conformations, ethylene can approach from the same or opposite side of the 10-R substituent, resulting in eight possible hydroboration transition structures. Figure 2 shows these transition structures for the reaction of 2a with ethylene. Approach from the side opposite to the TMS group (2a-TS1 through 2a-TS4) is preferred by approximately a constant 4 kcal/mol over approach from the same side as the TMS group (2a-TS5 through 2a-TS8), indicating that the 10-TMS group rather than the borabicyclo[3.3.2]decane ring conformation dictates approach of ethylene (Table 2).
The lowest energy transition structure, 2a-TS1, derives from the lowest energy ground state conformation of 2a. The B3LYP activation energy for 2a-TS1 is 12.5 kcal/mol above free reactants (ΔH‡ = 13.9, ΔG‡ = 26.2 kcal/mol; Table 2). The SCS-MP2 method predicts a moderately lower barrier of 8.0 kcal/mol. Transition structures 2a-TS2 (13.3 kcal/mol) and 2a-TS3 (13.8 kcal/mol) have energies within ~1 kcal/mol of 2a-TS1. Transition structures 2a-TS4 through 2a-TS8 are 3–8 kcal/mol above 2a-TS1 and were not considered further for substituted alkenes. Implicit diethyl ether free energy solvation corrections alter the barriers by less than 0.2 kcal/mol (see Table 2).
Geometrically, these hydroboration 4-centered addition transition structures are early along the reaction coordinate and have significant π-complexation character but do connect to the hydroboration addition adducts by IRC calculations. The B-H bond is stretched by an average of 0.02 Å compared to the ground state bond length of 1.204 Å while the C1-C2 ethylene bond is also slightly stretched to ~1.360 Å from the ground state 1.331 Å. One geometrical probe of the degree of π character is the B-C1-C2 angle, which is 72° in 2a-TS1.
Experimentally, the reaction of 2a with trans-2-butene (3) results in 95% ee.4 Figure 3 show the six most competitive transition structures for 2a addition to 3. In terms of reactivity, B3LYP predicts the hydroboration of alkene 3 with borane 2a to have ~5 kcal/mol higher barriers compared to ethylene while SCS-MP2 predicts 1–3 kcal/mol higher barriers (Table 3). The higher activation barriers are the result of later transition structure reaction coordinate positions, due to the steric congestion of the 10-TMS group. The forming B-C1 bonds are ~0.1 Å shorter and the forming H-C2 bonds are ~0.2 Å shorter in comparison to the ethylene transition structures (compare Figure 2 and Figure 3).
The favored hydroboration pathway is for BH addition to the pro-S face of 3, which places the closest alkene methyl group away from the 10-TMS group. The lowest energy transition structure is 2a-3-TS2 with an activation energy of 17.5 kcal/mol. Here SCS-MP2 predicts a significantly lower barrier of 9.1 kcal/mol. This transition structure has the same borabicyclo ring conformation that Soderquist and co-workers predicted and importantly does not correspond to the lowest energy ground state conformation (2a-CF1).4 Structure 2a-3-TS2 is slightly lower in energy than 2a-3-TS1 (ΔE‡B3LYP = 17.8 kcal/mol; ΔE‡SCS-MP2 = 9.3 kcal/mol) due to the close contact between the alkene methyl group and the 3-position bicyclo methylene group (2.101 Å) in 2a-3-TS1. This interaction is more sterically crowded than the interaction between the TMS group and the 7-position methylene group (2.329 Å) in 2a-3-TS2. The other important steric interaction in 2a-3-TS1 and 2a-3-TS2 is between the distal alkene methyl group and the 10-TMS group, which have similar distances of 2.442 Å and 2.418 Å, respectively. It is also important to note that on the free energy surface 2a-3-TS1 and 2a-3-TS2 have identical barriers with and without diethyl ether solvation correction.
For pro-R face hydroboration by 2a, the lowest energy transition strucutre 2a-3-TS4 does have the same borabicyclo ring conformation as the lowest energy ground state (2a-CF1). This transition structure is 3.8 kcal/mol above 2a-3-TS2 due to the close contacts of the alkene methyl group with the 10-TMS group (2.078 and 2.434 Å). Transition structures 2a-3-TS5 and 2a-3-TS6 are ~2 kcal/mol higher than 2a-3-TS4. 2a-3-TS4 is lower in energy than 2a-3-TS5 because now the alkene methyl group is farther away from the 3-position borabicyclo methylene group (2.323 Å). The largest geometrical difference between the favored pro-S face addition and unfavored pro-R face addition is the H-B-C1-C2 dihedral angle. In 2a-3-TS1 through 2a-3-TS3 the dihedral angles range from −3° to −6° while in 2a-3-TS4 through 2a-3-TS6 alkene 3 twists to ~+15° to avoid interaction with the TMS group. This twisting alleviates some of the steric compression and is possible because the alkene vinyl hydrogen-10-TMS interaction remains at a distance of 2.340 Å.
The B3LYP energy difference between 2a-3-TS2 and 2a-3-TS4 is 3.8 kcal/mol. SCS-MP2 predicts a slightly larger energy difference of 4.5 kcal/mol. Transition structure 2a-3-TS1 is also highly competitive and has nearly the same activation energy as 2a-3-TS2. Because the energies of these transition structures are very close, the enantioselectivity was calculated by a transition-state ensemble based on a Boltzmann-weighted average over 2a-3-TS1 through 2a-3-TS3 for the favored enantiomeric pathway and 2a-3-TS4 through 2a-3-TS6 for the disfavored enantiomeric pathway. B3LYP and SCS-MP2 both predict 99% ee, an overestimate of the 95% ee reported experimentally (see Table 8 later).22
For the reaction of 2a with cis-2-butene (4) the barrier heights are very similar to that with trans-2-butene. The lowest energy transition structure for pro-S face hydroboration, 2a-4-TS1, has a B3LYP activation energy of 17.0 kcal/mol (ΔE‡SCS-MP2 = 8.7 kcal/mol), see Figure 4 and Table 4. In this transition structure, and 2a-4-TS2/2a-4-TS3, both alkene methyl groups are directed away from the 10-TMS group. Different from the reaction with alkene 3, the lowest energy transition structure has the same borabicyclo[3.3.2]decane ring conformation as the lowest energy in the ground state (2a-CF1, Figure 1) ring conformation. This indicates that there is no severe repulsion between the 3-position methylene group and the methyl group of alkene 4 with an intramolecular distance of 2.510 Å. This is also the opposite borabicyclo[3.3.2]decane ring conformation proposed by Soderquist and co-workers indicating that an α-directive effect is not a major directing force in the reaction of 2a with alkene 4.2a-4-TS1 is lower in energy than 2a-4-TS2 because ring flip of the borabicyclo boat/chair conformation in 2a-4-TS1 decreases the distance between the 2-position methylene hydrogen and the methyl group to 2.114 Å in 2a-4-TS2 compared to a distance of 2.369 Å in 2a-4-TS1.
The lowest energy transition structure for pro-R face hydroboration of 4 is 2a-4-TS4 with a barrier of 19.2 kcal/mol. Despite both methyl groups being oriented towards the bulky 10-TMS side of the bicyclo bridge, the energy difference between 2a-4-TS1 and 2a-4-TS4 is only 2.2 kcal/mol. This is a 2.3 kcal/mol lower ΔΔE‡ value compared with the same transition structures for addition to alkene 3 where only one methyl group is direct towards the 10-TMS group. SCS-MP2 predicts a smaller ΔΔE‡ value of 1.8 kcal/mol. Again, using a transition state ensemble made up of the three most competitive transition structures for both the favored (2a-4-TS1 through 2a-4-TS3) and unfavored (2a-4-TS4 through 2a-4-TS6) enantiomeric reaction pathways, based on electronic energies, B3LYP overestimates the enantioselectivity with a predicted value of 94% ee compared to the experimental value of 84% ee. B3LYP ΔG‡ values predict an 85% ee. SCS-MP2 ΔE‡ values predict enantioselectivity induction at 89% ee.23
Why is there a lower selectivity for hydroboration of alkene 4 than 3? In order to separate the selectivity based on each methyl group of alkenes 3 and 4, the energy difference between 2a-3-TS2/2a-3-TS4 and 2a-4-TS1/2a-4-TS4 was compared with the re-optimized transition states after a single methyl group was deleted and replaced with hydrogen. These new transition structures correspond to the regioisomeric transition states for 2a hydroboration of propene (Figure 5).
For the trans alkene 3, Figure 5a shows that the methyl group closest to the TMS group induces 2.4 kcal/mol of selectivity between 2a-3-TS2/2a-3-TS4 while the methyl group near the borabicyclo 3-position methylene group induces 0.8 kcal/mol of selectivity. Importantly, the distal methyl group prefers to be close to the 10-TMS group rather than directed away from it. Therefore both interactions work in conjunction to give large π-face selectivity. The same analysis was also performed on transition structures 2a-4-TS1 and 2a-4-TS4 (Figure 5b). Here, the methyl group interacting on the side closest to the TMS group induces a slightly larger energy difference of 2.8 kcal/mol. Again, the distal cis methyl group of alkene 4 is more stable by −0.9 kcal/mol when oriented toward the 10-TMS group rather than directed away from it. However, for this cis alkene these methyl group preferences work in opposition to each other and reduce the overall π facial selectivity.
The origin of the preference for the distal methyl group to orient towards the 10-TMS group is that the long C-SiMe3 bond length (~1.91 Å) provides a hydrophobic cavity/pocket where the methyl groups experiences less repulsion than when it is oriented away from the 10-TMS group where it encounters repulsion with the 2-position and 3-position methylene groups. In 2a-4-TS1, the distance between the distal methyl group and the 2-position-methylene group is 2.369 Å while in 2a-3-TS4 this distance is 2.494 Å. Importantly, although the distal methyl prefers to be oriented towards the 10-TMS side, the distance between this methyl group and the 3-position methylene group is shorter in 2a-4-TS4 (2.304 Å) than in 2a-4-TS1 (2.510 Å). This highlights the importance of an open cavity space by the TMS group and because of this 10-TMS binding pocket there is less alkene twisting in the transition structures with alkene 4 resulting in a H-B-C1-C2 dihedral angles of ~6°.
To further explore the possibility of a 10-R group-alkene binding cavity, activation energies for hydroboration of alkenes 3 and 4 by hypothetical reagents 2c (R = 10-tert-butyl) and 2d (10-SnMe3) were computed (Chart 4). These 10-R groups have different steric congestion and with C-CMe3 and C-SnMe3 bond lengths of ~1.58 Å and ~2.19 Å they provide very different spaces for a methyl group to fit into. Figure 6 shows the two lowest energy enantiomeric transition structures for the hydroboration of alkenes 3 and 4 with 2c and 2d. Table 5 reports the B3LYP activation parameters for all of the borabicyclo ring conformation transition structures. Based on all of these transition structures, the predicted ee values for 2c hydroboration of alkene 3 is greater than 99%. The smallest energy difference between favored and unfavored enantiomeric pathways is 3.3 kcal/mol. For the reaction of 2c with 4, smallest ΔΔE‡ value is 3.6 kcal/mol. In accord with this value, the predicted ee is also greater than 99%. The higher predicted selectivity for 2c versus 2a for hydroboration of alkene 4 is the result of the tert-butyl group not providing a sufficient cavity space for the distal alkene methyl group to fit into.24
In contrast, reagent 2d with a 10-SnMe3 group is predicted to give high ee (> 99%) with alkene 3 and very poor ee with alkene 4 (22%). The smallest ΔΔE‡ between favored and unfavored enantiomeric pathways are 3.4 and 0.6 kcal/mol for 2c and 2d, respectively. Here the very long C-SnMe3 bond provides too large of a cavity and the alkene methyl group experiences little repulsion. Figure 7 shows space filling models of optimized 2a, 2c, and 2d. It is evident from these space filling models that there is essentially no cavity in 2c, a small cavity in 2a, and a large cavity in 2d. This nicely explains the decreasing order of enantioselectivity for the hydroboration of cis alkene 4.
Reagent 2a is highly novel because it also induces a moderate 52% ee for reaction with alkene 5. Typically, reagents that induce high ee with either cis or trans alkenes result in very poor or no ee with gem disubstituted alkenes. Figure 8 shows the computed transition structures for hydroboration of 5 with 2a. The overall lowest energy transition structure is for pro-R face BH addition, 2a-5-TS2, with an activation energy of 19.0 kcal/mol (ΔE‡SCS-MP2 = 11.3 kcal/mol), see Table 6. In this favored enantiomeric transition state, the bulkier isopropyl group is directed away from the 10-TMS group while the methyl group is directed towards the 10-TMS group. However, this is not general. For the same borabicyclo ring conformation only 2a-5-TS2 is lower than 2a-5-TS5. 2a-5-TS4 is lower in energy than 2a-5-TS1 (ΔΔE‡ = 0.7 kcal/mol) and 2a-5-TS6 is lower in energy than 2a-5-TS3 (ΔΔE‡ = 1.3 kcal/mol). This results in a decrease of the π-facial selectivity.
For pro-S face hydroboration, 2a-5-TS4 is lowest in energy and only 0.5 kcal/mol above 2a-5-TS2. There is also a large regioselective preference of ~6 kcal/mol (see Supporting Information). Although there is a consensus by both DFT and ab initio methods that 2a-5-TS2 is lowest overall in energy, for the unfavored pro-S face transition states, B3LYP predicts 2a-5-TS4 to be lower than 2a-5-TS5 and 2a-5-TS6 whereas SCS-MP2 predicts 2a-5-TS6 to be lower than 2a-5-TS4 and 2a-5-TS5, see Table 6. Based on transition state ensembles of activation energies, B3LYP and SCS-MP2 underestimate enantioselectivity with predicted values of 26% and 24% compared to the experimental 52%. Using B3LYP free energies gives a more accurate predicted enantioselectivity of 45% (see Table 8 later).
For alkenes 3–5, the 10-phenyl reagent 2b induces ee comparable to that from 2a for only trans alkene 3. Hydroboration of alkenes 4 and 5 with 2b results in much lower ee values than with 2a. Figure 9 shows only the lowest energy transition structures for each enantiomeric pathway for 2b addition to alkenes 3–5. Table 7 gives the computed activation energies for all transition structures.
In accord with the selectivity model proposed by Soderquist and co-workers, the lowest energy transition structures all have the 3-position methylene directed up toward the alkene and the 7-position methylene group directed away from the alkene and correspond to the ground state conformation 2b-CF1. The opposite chair/boat transition structure conformations are 1–3 kcal/mol higher in energy (see Table 7 for energies and Supporting Information for structures).
Transition-state calculations for the hydroboration of propene by 2b reveals that the alkene methyl group closest to the 10-Ph group induces 0.7 kcal/mol of selectivity. In 2b-3-TS1 this methyl group is directed away from the phenyl π-face and the vinyl hydrogen interacts with the phenyl π-face at a distance of 2.956 Å to the CA phenyl carbon. In 2b-3-TS4 the methyl group-CA phenyl carbon distance is 2.773 Å. Estimated by the propene transition structures, the distal methyl group induces 0.9 kcal/mol of selectivity. Again, this methyl group prefers to be on the same side as the 10-Ph group because the phenyl ring is able to rotate and provide a space for the methyl group which allows relief of repulsive interactions with the 2- and 3-position methylene groups.
For the hydroboration of cis alkene 4 these methyl group selectivity effects cancel and lead to poor enantioselectivity. For example, in 2b-4-TS1 the distance between the distal methyl group and the 2-position methylene hydrogen is 2.380 Å and the 3-position hydrogen is 2.582 Å. The 2-position interaction is alleviated in 2b-4-TS4 but now the other cis methyl group interacts directly with the 10-Ph group at a distance of 2.869 Å. Also, in 2b-4-TS4, the distance between the methyl group and 3-position methyl group decreases to 2.339 Å, rather than increases. B3LYP predicts equivalent activation energies for 2b-4-TS1 and 2b-4-TS4 while SCS-MP2 predicts a 0.7 kcal/mol energy difference. However, SCS-MP2 predicts 2b-4-TS1 to be lower in energy than 2b-4-TS4. This prediction is in opposition to the experimentally observed alcohol product enantiomeric excess. Although 2b-4-TS1 is favored over 2b-4-TS4 using electronic energy and enthalpy differences, the selectivity is correctly predicted when free energies are used (see Table 7). The ΔΔG‡ between 2b-4-TS1 and 2b-4-TS4 is −0.4 kcal/mol. This is also true for the two other borabicyclo ring conformations. The ΔΔG‡ between 2b-4-TS2/2b-4-TS5 and 2b-4-TS3/2b-4-TS6 are −0.2 and −0.9 kcal/mol, respectively. These free energies (as well as activation energies) show that largest selectivity occurs when the 7-position and 3-position methylene groups are directed away from the alkene, indicating that the 3-position may be less important than the 2-position methylene group. Based on the transition state free energies, B3LYP predicts a 33% ee value for the reaction of 2b with cis alkene 4. This is remarkably close to the experimental 32% measured experimentally. For reactions of 2b with alkenes 3 and 5, 97% and 44%, were predicted.
In general, B3LYP and SCS-MP2 methods predict enantiomeric excess in close agreement with experiment. Table 8 compares the predicted and experimental ee values. It is clear that the use of B3LYP ΔG‡ values gives the closest agreement with experiment. For hydroboration reactions with reagent 2a, all methods over estimate selectivity with trans alkene 3 but do correctly predict the drop in selectivity with cis alkene 4. For the reaction of 2a with alkene 5, the use of electronic energies provides too low of an estimate of ee and only B3LYP free energies gives a reasonable predicted ee value.
For reactions with reagent 2b, all methods closely model the 96% ee observed for hydroboration of alkene 3. The hydroboration of alkene 4 by 2b was the most difficult to model. Activation energies predict the incorrect favored transition state and only the use of B3LYP free energies gives a value in accord with experiment. For the reaction of 2a with alkene 5, only the SCS-MP2 method predicts a value significantly different than experiment.
DFT and ab initio methods were used to analyze alkene hydroboration transition structures for 10-R-9-borabicyclo[3.3.2]decane reagents. Transition-state ensembles quantitatively modeled enantioselectivity in excellent agreement with experiment, especially using B3LYP free energies. The 10-R group and its conformation is more important than the exact borabicyclo chair/boat ring conformation. This was supported by calculations that compared 10-tert-butyl, 10-TMS, and 10-SnMe3 groups, which show that a 10-R binding cavity allows relief of steric repulsion between alkene methyl group with the bridgehead CH bond and the 2- and 3-position methylene groups.
This work was supported by the NIH (GM038436 and GM026782) and a postdoctoral fellowship to J.K. from the Ministère des Affaires Etrangères et Europèennes (France).
Supporting Information Available. Cartesian coordinates and absolute energies are available free on the World Wide Web at http://pubs.acs.org.