Mechanism Insight into the Cyanide-Catalyzed Benzoin Condensation

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Mechanism Insight into the Cyanide-Catalyzed Benzoin Condensation: A Density Functional Theory Study Yunqing He†,‡ and Ying Xue*,†,§ College of Chemistry, Key Lab of Green Chemistry and Technology in Ministry of Education and State Key Laboratory of Biotherapy, Sichuan UniVersity, Chengdu 610064, People’s Republic of China, and Department of Chemistry and Engineering, Sichuan UniVersity of Arts and Science, Dazhou 635000, People’s Republic of China ReceiVed: April 4, 2010; ReVised Manuscript ReceiVed: July 25, 2010

The reaction mechanism of the cyanide-catalyzed benzoin condensation without protonic solvent assistance has been studied computationally for the first time employing the density functional theory (B3LYP) method in conjunction with 6-31+G(d,p) basis set. Four possible pathways have been investigated. A new proposed pathway on the basis of the Lapworth mechanism is determined to be the dominant pathway in aprotic solvent, in which the formation of the Lapworth’s cyanohydrin intermediate is a sequence including three steps assisted by benzaldehyde, clearly manifesting that the reaction can take place in aprotic solvents such as DMSO. In this favorable pathway with six possible transition states located along the potential energy surface, the reaction of the cyanide/benzaldehyde complex with another benzaldehyde to afford an R-hydroxy ether is the ratedetermining dynamically with the activation free energy barrier of 26.9 kcal/mol, and the step to form cyanohydrin intermediate from R-hydroxy ether is partially rate-determining for its relatively significant barrier 20.0 kcal/mol. 1. Introduction The benzoin condensation plays an important role in convenient carbon-carbon bond formation by affording an important synthon R-hydroxycarbonyl group, which has attracted much attention for decades and has been intensively investigated.1-17 The first report was the discovery of the cyanide-catalyzed benzoin condensation (Scheme 1) by Wo¨hler and Liebig in 1832.1 Lapworth2,3 proposed the mechanism involving cyanohydrin intermediate for the cyanide-catalyzed benzoin condensation, an addition/proton-transfer/condensation sequence, in which the condensation step to produce benzoin is taken as rate determining and previous steps to produce the cyanohydrin are rapid and reversible, using his own demonstration and the kinetic evidence of Breig and Stern.4,5 In 1971, Schowen’s group performed an experimental investigation for the kinetics of benzoin condensation in methanol and affirmed the correctness of the Lapworth mechanism through examining its components step by step. They found that the only difference from Lapworth mechanism is that both the proton-transfer to form cyanohydrin and the condensation steps are rate-determining with similar free energy barries (21.31 ( 0.02 and 22.5 ( 0.1 kcal/mol at 298.15 K).6 Some calculations7-10 to the carbene-catalyzed reaction showed that the direct 1,2 proton-shift to provide an enamine intermediate (similar to step 2 of Path A, Scheme 2) has high free energy barrier. For this step in benzoin condensation, Schowen et al.6 postulated a methanol-assisted proton transfer to produce “active-aldehyde” carbanion (shown in Scheme 3), which can probably lower the free energy barrier. The only computational job of the cyanide-catalyzed benzoin condensation was carried out by Yamabe et al.,11 in which * To whom correspondence should be addressed. E-mail: [email protected], Phone: +86 28 85418330. † Key Lab of Green Chemistry and Technology in Ministry of Education, Sichuan University. ‡ Sichuan University of Arts and Science. § State Key Laboratory of Biotherapy, Sichuan University.

SCHEME 1: The Cyanide-Catalyzed Benzoin Condensation

they focused on the water-assisted benzoin condensation mechanism at RB3LYP/6-31+G(d) level adopting the reaction models (benzaldehyde)2 + CN- + (H2O)n (n ) 8 or 14). They also followed the Lapworth mechanism and concluded that the C-C bond forming is the rate-determining step, and the formation of carbanion (i.e., cyanohydrin intermediate) and the release of CN- are also of large activation free energies. Until now, the Lapworth mechanism has been accepted as definitive.12 Wiberg13 observed some apparent inconsistencies with the Lapworth mechanism in his pioneering investigations of kinetic isotope effects, where the rates of the condensation reaction and isotope exchange of C6H5CDO with protonic solvent were approximately equal in 66% ethanol-water containing 52% deuterium in exchangeable positions. Another study using a more highly deuterated solvent reinforced this view.14 Breslow and co-workers15-17 performed the investigations about salt effects in the hydrophobic acceleration and anti-hydrophobic effects of the benzoin condensation and postulated a compact condensation transition state with partially overlapping faceto-face phenyl groups. And they manifested that the reaction rate in dimethylsulfoxide (DMSO) is ∼50 times of that in water with no additives and ∼10 000 times of that in ethanol, as well as increasing of the dissolvability of benzaldehyde in water decreases the reaction rate. Methanol, ethanol, and water are the conventional protonic solvents used in benzoin condensation, but DMSO is an important aprotic solvent that can not assist the proton transfer to get cyanohydrin. Hereby, we suppose that there is another probable mechanism for the cyanide-catalyzed benzoin condensation in aprotic solvent DMSO where no

10.1021/jp103031q  2010 American Chemical Society Published on Web 08/12/2010

Cyanide-Catalyzed Benzoin Condensation

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SCHEME 2: Possible Pathways of the Title Reaction

SCHEME 3: Methanol-Catalyzed Proton-Transfer to Get “Active-Aldehyde” Carbanion

protonic solvent-assisted step appears in the process. In addition, the real structure of the transition states in the reaction still needs to be probed. In this work, we present a theoretical study on the mechanism of the cyanide-catalyzed benzoin condensation using the density functional theory (DFT) method. Four reaction pathways without protonic solvent assistance are reported (see Scheme 2). Path A is proposed on the basis of the Lapworth mechanism, in which a direct 1,2 proton-shift generates the cyanohydrin intermediate, similar to some calculations7-10 to the carbene-catalyzed reaction. Paths B and C are both newly proposed without cyanohydrin intermediate, and Path D is proposed on the basis of the

Lapworth mechanism too, in which the cyanohydrin intermediate is formed through a stepwise sequence. The effects of bulk solvents such as methanol, ethanol, water, and DMSO are examined with the self-consistent reaction field (SCRF) method. In addition, we also perform a confirmatory calculation of methanol-assisted proton transfer to produce cyanohydrin intermediate in order to affirm the barrier decreases via protonic solvent assistance. 2. Computational Details The geometry optimizations for all stationary points, including reactant complex (RC), product complex (PC), transition state (TS), and intermediate (IM), were performed in the gas-phase using the density functional theory with the Beck’s threeparameter exchange function and the gradient-corrected function of Lee, Yang, and Parr (B3LYP).18,19 The standard 6-31+G(d,p) basis set containing diffuse and polarization functions was applied in all calculations, thanks to the successful application of similar methods in analogous systems.9,11,20 For an accurate estimation of the energies, the first step in Lapworth mechanism

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TABLE 1: Activation Free Energy Barriers of All the Pathways in Different Solvents Using the CPCM Method (unit: kcal/mol, at 307.15K) steps

∆GDMSO ‡

∆Gwater ‡

∆Gethanol ‡

∆Gmethanol ‡

14.2

14.2

Common First Step 14.2

RC f TS1

14.2

IM1fA-TS2 AD-IM2+R f AD-TS3 AD-IM4 f AD-TS4

44.7 8.9 1.6

Path A 44.8 8.7 1.5

44.6 8.8 1.8

44.7 8.7 1.6

IM1 f B-TS2 B-IM2+R f B-TS3

35.1 33.1

Path B 35.2 33.0

35.1 32.8

35.1 32.7

IM1 f C-TS2 C-IM2 f C-TS3 C-IM4 f C-TS4 C-IM5 f C-TS5

41.8 3.0 35.8 13.6

Path C 41.9 3.0 36.2 13.4

41.7 3.0 35.4 13.8

41.8 3.0 35.8 13.8

IM1+R f D-TS2 D-IM2 f D-TS3 D-IM3 f D-TS4

26.9 0.6 20.0

Path D 27.1 0.8 20.2

26.5 0.8 19.8

26.7 0.8 19.6

TABLE 2: Crucial NPA Charges (unit: e) R RC TS1 IM1 A-TS2 AD-IM2 AD-IM3 AD-TS3 AD-IM4 AD-TS4 AD-PC B-TS2 B-IM2 B-IM3 B-TS3 B-PC D-IM1 D-TS2 D-IM2 D-TS3 D-IM3 D-TS4 D-IM4 E-IM5 E-TS5 E-IM6

C1

C2

0.390 0.240 0.030 -0.216 -0.036 0.100 0.123 0.160 0.498 0.573 0.343 0.476 0.450 0.360 0.569 -0.026 -0.148 0.080 -0.043 -0.043 0.245 0.032 0.015 -0.146 -0.114

-0.231 0.054 0.282 0.285 0.240 0.314 0.316 0.308 -0.050 0.171 0.052 -0.137 -0.102 -0.007 -0.197 0.306 0.297 0.235 0.240 0.242 0.235 0.241 0.294 0.299 0.245

C4 0.394

0.124 0.099 0.060 0.010 -0.008

0.393 0.253 0.008 0.360 0.366 0.373 0.384 0.383 0.138 0.357

O1

O2

O3

H1

-0.855 -0.899 -0.819

0.197 0.170 0.173 0.473 0.485 0.525 0.520 0.527 0.516 0.471 -0.017 0.102 0.118 0.255 0.485 0.274 0.431 0.519 0.501 0.506 0.528 0.521 0.206 0.404 0.992

H3

N

0.537 0.525 0.503

-0.714 -0.596 -0.472 -0.473 -0.519 -0.413 -0.418 -0.430 -0.621 -0.628 -0.537 -0.668 -0.640 -0.461 -0.632 -0.428 -0.451 -0.493 -0.493 -0.493 -0.415 -0.484 -0.444 -0.441 -0.502

-0.543 -0.588 -0.733 -0.875 -0.844 -0.765 -0.799 -0.821 -0.858 -0.680 -0.577 -0.685 -0.636 -0.660 -0.617 -0.596 -0.729 -0.609 -0.578 -0.586 -0.582 -0.644 -0.777 -0.884 -0.789 -0.772

was tested at the B3LYP/6-31+G (d,p) level of theory. The calculated Gibbs free energy barrier in methanol at 307.15 K and 101 325 Pa is 14.21 kcal/mol, coinciding with the experimental result (i.e., ∼12 kcal/mol)6 very well. Therefore, it can be concluded that the B3LYP/6-31+G(d, p) level is suitable to study the title reaction with a good compromise between accuracy and computational cost. Each stationary point was confirmed by the harmonic frequency analysis at the same calculational level as a true minimum with no imaginary frequency or a transition state with only one imaginary frequency. The frequency calculations without scaling also provided the thermodynamic quantities such as the zero-point vibrational energy, thermal correction, enthalpies, Gibbs free energies, and entropies at temperature of 307.15 K and pressure of 101 325 Pa. Transition state structures were verified with intrinsic reaction coordinate (IRC)21-23 calculations

-0.854 -0.844 -0.817 -0.782 -0.818 -0.587 -0.674 -0.809 -0.728 -0.813 -0.799 -0.783 -0.787 -0.778 -0.593

at the same level of theory. Actually, the reaction takes place in solvents, so solvation effect was considered here. Directly using the geometries optimized in gas-phase, the solvent effect is evaluate at the B3LYP/6-31+G(d,p) level using the conductor-like polarizable continuum model (CPCM),24,25 which has prevailed in the scientific community due to its accuracy and simplicity of the solvent reaction field definition. Thermal correction to Gibbs free energies was done at 307.15 K to evaluate the free energies for comparing with experimental data. Each activation free energy barrier results from the free energy difference between the transition state and its former species. Molecular orbital analysis, natural population analysis (NPA),26,27 and bond order analysis were performed at B3LYP/6-31+G(d,p) level. All calculations were carried out using the Gaussian 03 program.28



Figure 1. Structures and geometrical parameters of the stationary points in the common first step (bond length in Å).

Figure 2. Free energy profiles of Paths A-D in DMSO (unit: kcal/ mol, energies relative to RC + R).

3. Results and Discussions As depicted in Scheme 2, the four pathways without protonic solvent assistance were investigated. To affirm the barrier decreases via protonic solvent assistance, we perform a calculation of methanol-assisted proton-transfer step (Scheme 3) to get Lapworth’s “active-aldehyde” carbanion. The main structural and energetic features were presented in this section. The prefixes A-E were used to identify the stationary structures that pertain to Paths A-D and the methanol-catalyzed protontransfer step, respectively, while the prefix AD represents the stationary structures shared in Paths A and D. For example, A-TS2 is the second transition state in Path A, whereas ADTS4 is a transition state shared in Paths A and D. A structure shared in four paths has no prefix. For convenience, we use the free energies in DMSO in the following discussion unless

otherwise noted. The numbering of the atoms involved in the following discussions is given in the corresponding figures displaying the optimized structures. The relative free energies of all the species are given in Table S1 of Supporting Information. Table 1 presents the free energy barriers of all reaction steps in several solvents, and the crucial NPA charges are exhibited in Table 2. The free energy profiles of the four pathways are all presented in Figure 2. 3.1. The Common First Step of the Four Pathways (Paths A-D). As shown in Scheme 2 and Figure 2, four pathways (Paths A-D) share a common first step, that is, the nucleophile cyanide ion attacks the carbon atom of carbonyl in benzaldehyde, leading to an intermediate (IM1) of tetrahedral carbon (C1). The potential energy surface for this nuclephilic addition step in the gas phase reveals a possible transition state (TS1). The optimized geometries and important bond lengths for the stationary points in this step are shown in Figure 1. The imaginary vibrational frequency of TS1 is 201.421i cm-1, and its vibrational mode mainly corresponds to the C1-C2 bond formation. The distances of the C1-C2 bond in RC and IM1 are 4.042 and 1.546 Å, respectively, indicating the C1-C2 bond has formed in IM1. At the same time, the C1-O1 bond elongates from 1.226 to 1.321 Å. In the intermediate IM1, the hybridization of the carbonyl C1 atom is converted to sp3 from sp2 in RC. Owing to the addition to the C1 of the rich negative charge of CN-, the positive charge at C1 decreases evidently (0.030 e in IM1 and 0.390 e in RC) and the negative charge at O1 simultaneously increases (-0.875 e in IM1 and -0.558 e in RC). As exhibited in Table 1, the free energy barrier of the common first step is 14.2 kcal/mol. We presume from this low

Figure 3. Structures and geometrical parameters of the stationary points in Path A (bond length in Å).

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Figure 4. Structures and geometrical parameters of the stationary points in Path B (bond length in Å).

value that the first addition step to get the reaction complex (IM1) is rapid. In the following discussions, we describe Paths A-D beginning with IM1 and another benzaldehyde molecule. 3.2. Path A. This path is proposed on the basis of the Lapworth mechanism. Figure 3 exhibits the optimized geometries and important bond lengths for the stationary points in this pathway. Initially, a direct 1,2-proton transfer of the hydrogen atom (H1) from C1 to O1 affords only Lapworth’s cyanohydrin intermediate AD-IM2 via a three-membered ring transition state (A-TS2). In A-TS2, the distances of C1-O1, C1-H1, and O1-H1 are 1.488, 1.204, and 1.280 Å, respectively. It apparently reveals that the O1-H1 bond is forming and the C1-H1 bond is breaking. The imaginary vibrational frequency of A-TS2 is 1668.96i cm-1, and its mode mainly corresponds to the shift of H1 from C1 to O1. In the intermediate AD-IM2, the distances of C1-H1 and O1-H1 are 1.955 and 0.968 Å, respectively, suggesting that the C1-H1 bond is broken and the O1-H1 bond is formed completely. And the hybridization of C1 atom changes from sp3 in IM1 to sp2 in AD-IM2. With the H1 shift to O1, the C-O bond length is elongated to form a complete C-O single bond (1.321 Å in IM1 vs 1.426 Å in AD-IM2), and a nearly planar structure of C2-C1-C3-O1 is formed with the dihedral angle of 175.3° in AD-IM2. It is noteworthy that the relative free energy of AD-IM2 is 14.8 kcal/mol (presented in Table S1 of the Supporting Information), which is a relatively low value just more than that of AD-PC by 3.4 kcal/mol. So AD-IM2 is located in a deep valley bottom along with the reaction energy surface, this finding is consistent with previous theoretical studies.7-9 To further investigate its properties, we get the highest occupied molecular orbital (HOMO) of AD-IM2 (see Figure S1 in Supporting Information), in which a large delocalization π bond covers the benzene ring and C1, C2, N atoms with only the hydroxyl baring. The delocalization naturally decreases the energy of the cyanohydrin. After the formation of the Lapworth cyanohydrin, due to the positive charge of C4 (0.394 e) in another reactant benzaldehyde and the slightly negative charge of C1 (-0.036 e) in AD-IM2, C1 approaches to C4 resulting in the reaction complex ADIM3. In AD-IM3, the NPA charges of C4 and C1 are 0.124

and 0.100 e, respectively. These two positive charges result in the “looseness” structure of AD-IM3 with a large C1-C4 distance (1.742 Å), which is in agreement with the results of Schowen6 and Yamabe;11 and the situation of C1 is over C4, then favorable for the following C1-C4 bond formation. And then, the hydrogen on O1 shifts to O2 atom and the C1 atom further approachs to C4 via a five-membered ring transition state AD-TS3. As shown in Figure 3, AD-TS3 is compact with partially overlapping face-to-face phenyl groups, in nice agreement with the presumption of Breslow and co-workers.15-17 In AD-TS3, the distances of C1-C4, C4-O2, O2-H1, H1-O1, and O1-C1 are 1.727, 1.356, 1.254, 1.179, and 1.374 Å, respectively. The imaginary vibrational frequency of AD-TS3 is 780.765i cm-1, and its vector mainly corresponds to the shift of H1 from O1 to O2. AD-TS3 is in fact an addition-like transition state from the structure. IRC verifies that the incomplete covalent C1-C4 bond (1.667 Å) formation and the transfer of H1 perform simultaneously. In the intermediate ADIM4, the distances of O2-H1 is 1.011 Å, suggesting that the O2-H1 bond is formed completely; the C2-O2 bond length is 1.401 Å, longer than that of AD-IM3 (1.333 Å), and the C1-O1 bond length is 1.343 Å, shorter than that in AD-IM3 (1.396 Å). In the last step, the cyanide ion is eliminated from AD-IM4 and the bond C1-C4 is formed completely via the corresponding transition state (AD-TS4). The distances of C1-C2 and C1-C4 are 2.279 and 1.568 Å, respectively, apparently suggesting that the C1-C4 bond is partly formed and the cyanide ion is dropped out almost completely in this transition state. The imaginary vibrational frequency of AD-TS4 is 123.883i cm-1, and its vector mainly corresponds to the elimination of the cyanide ion. After overcoming this AD-TS4, consequently, the product AD-PC is obtained. As illustrated in Table 1, the direct 1,2-proton transfer to form the Lapworth cyanohydrin performs with a very high free energy barrier (e.g., 44.7 kcal/mol in DMSO), so the direct 1,2-proton transfer is unexpected from thermodynamics and for orbital symmetry forbidden.10 One can get the free energy barrier of 8.9 kcal/mol in the step of H1 transfer from O1 to O2 from the free energy difference between AD-TS3 and AD-IM2+R, for



Figure 5. Structures and geometrical parameters of the stationary points in Path C (bond length in Å).

the verified complex (AD-IM3) by IRC is not stable with its higher free energy than AD-IM2+R (25.8 kcal/mol of AD-IM3 vs 14.8 kcal/mol of AD-IM2+R). This is a very low barrier process, maybe because of the baring hydroxyl in HOMO of AD-IM2 and the more negative charge on O2 than that on O1. Also, the free energy barrier of the elimination of the cyanide ion is only 1.6 kcal/mol. So the direct 1,2-proton transfer to produce cyanohydrin is the rate-determining step of Path A. The free energy barrier of the rate-determining step is too high to carry on. When the reaction takes place in protonic solvent, a solvent-catalyzed proton-transfer to get Lapworth “activealdehyde” carbanion may perform with relatively low activation free energy barrier. Kuebrich Schowen6 postulated a methanolcatalyzed proton shift (Scheme 3). We do a confirmatory calculation of methanol-assisted proton transfer (presented in Section 3.6., vide infra), which confirms that the free energy barrier can be decreased apparently for methanol-assistance, but no protonic solvent molecule can take part in the 1,2-proton transfer when the reaction occurs in aprotic solvent (e.g., DMSO), so this step with too high activation free energy barrier is difficult to carry out. This is in contrast with experimental fact of a very large rate in DMSO.15 Therefore, we turn our attention to seek for a pathway with relatively low free energy barrier without protonic solvent molecule participation. 3.3. Path B. This pathway remains two steps: first, the hydrogen atom (H1) transfers from C1 to C2 of IM1, which is

different from the 1,2-proton transfer in Path A, affording the intermediate B-IM2. Then, via a concerted transition state (BTS3), H1 shifts from C2 to oxygen atom (O2) of another benzaldehyde molecule, the C1-C4 bond forms, and the cyanide ion drops out, simultaneously. All the involved structures are presented in Figure 4. The transfer of H1 to C2 performs via a three-membered ring transition state (B-TS2), in which the distances of C1-C2, C1-H1, and C2-H1 are 1.461, 1.698, and 1.458 Å, respectively. The imaginary vibrational frequency of B-TS2 is 866.002i cm-1 and its vector mainly corresponds to the H1 transfer from C1 to C2 atom. In the intermediate B-IM2, the C1dO1 double bond is restored, and the CtN triple bond is elongated to become a CdN double bond, with the proton transfer from C1 to C2. The hybridizations of the carbonyl C1 and C2 are all sp2 in B-IM2. In the final step, the potential energy surface in the gas phase reveals a possible concerted transition state (B-TS3), and IRC verifies that the leaving of cyanide ion, H1 transfer from C2 to O2, and the forming of the C1-C4 bond take place simultaneously. The transition state (B-TS3) is a fivenumbered ring, its only imaginary vibrational frequency is 337.01i cm-1 and mainly corresponds to the shift of H1 from C2 to O2 atom, the breaking of the C1-C2 bond, and the formation of the C1-C4 bond. In B-TS3, the distances of C1-C2, C2-H1, H1-O2, O2-C4, and C4-C1 are 2.029, 1.107, 1.783, 1.255, and 2.499 Å, respectively. It evidently shows that the C1-C2 bond has already broken in B-TS3, and

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Figure 6. Structures and geometrical parameters of the stationary points in Path D (bond length in Å).

the O2-H1 bond is generating. We deem B-TS3 is actually an addition-like transition state from the structure. After the barrier of B-TS3 is overcome, benzoin is obtained. No cyanohydrin intermediate is generated in this pathway. As shown in Table S1 of Supporting Information, the complex B-IM3 is not stable due to its higher free energy than that of B-IM2+R (41.0 kcal/mol of B-IM3 vs 28.2 kcal/mol of B-IM2+R), so we deem that the free energy barrier of the concerted step related to B-TS3 is the free energy difference between B-TS3 and B-IM2+R. Noted that the free energy barrier of B-TS2 is lower than that of the direct proton transfer to produce the Lapworth enol by 9.6 kcal/mol. This may be because of the orbital symmetrical permission, and the HOMO (Figure S2 of Supporting Information) of B-TS2 indicates that there is a large tendency of the leaving of H1 for C2; and Wiberg bond order of C2-H1 (0.849) in B-IM2 is stronger than that of O1-H1 (0.743), suggesting the C1-H1 bond (Path B) forms easily than O1-H1 bond (Path A). As illustrated in Table 1 and Figure 2, there are two maxima (B-TS2 and B-TS3) along the potential free energy surface, the free energy barriers of B-TS2 and B-TS3 are 35.1 and 33.1 kcal/mol, respectively. Regretfully, the two high-barrier steps related to B-TS2 and B-TS3 make Path B not a good pathway. 3.4. Path C. In 2007, Gronert10 proposed a possible epoxide intermediate in his computational work to explore the nucleophilic species derived from the fluoride activation of O-silylated

thiazolium carbinols. Considering that the thiazolium salt can catalyze the benzoin condensation too, we postulated a channel in which a similar epoxy transition state included. All the geometrical parameters of the complexes in this pathway are presented in Figure 5. There are four transition states along with the reaction coordinate except for TS1. The imaginary vibrational frequency of C-TS2 is 350.975i cm-1, its vibrational mode is mainly associated with the C1-C2 bond broken and C2-O1 bond formation. To favor the C1-C4 bond formation, C-IM2 slightly adjusts its geometry via a transition state (C-TS3) related to the C1-O1 bond rotation. The vibrational mode of C-TS4 is associated with the shift of H1 from C1 to O2, and the only imaginary frequency is 1698.17i cm-1. The final transition state (C-TS5) relates to the release of CN- and C2dO1 double bond formation; its imaginary vibrational frequency is 662.461i cm-1. From the energy profile and the activation free energy barriers in Table 1, the step involving epoxy transition state (C-TS2) is rate-determining, with the corresponding free energy barrier of 41.8 kcal/mol. In this mechanism, no cyanohydrin is formed too. Obviously, Path C is not the dominate mechanism. Evidently, the above three pathways are all with high barriers, so we continue our job to seek for other possible pathway with relative low barriers. We noted that there is only one high barrier step in Path A, that is, the formation of the Lapworth’s cyanohydrin intermediate AD-IM2, so we concentrate our



Figure 7. Structures and geometrical parameters of the stationary points in methanol-catalyzed proton transfer to form cyanohydrin (bond length in Å).

Figure 8. Energy profile of the methanol-assisted proton transfer to form cyanohydrin (unit: kcal/mol. The values in parentheses are the relative free energies (∆G)).

attention to seek for other possible mechanism to form cyanohydrin with lower barriers. 3.5. Path D. After our exhaustive study (see Scheme S1 of Supporting Information), and enlightened by the highlighted mechanism study of asymmetric Stetter reaction by Hawkes and Yates29 in 2008, a possible sequence of intermolecular proton transfer was found, which decreases the free energy barrier of the cyanohydrin formation in Path A. As presented in Scheme 2, Path D is proposed on the basis of the Lapworth mechanism, too, and its only difference from Path A is the process of the affording of Lapworth’s cyanohydrin intermediate, in which the stepwise proton transfers between the CN--benzaldehyde complex (IM1) and another benzaldehyde are involved. The optimized geometries and important bond lengths for the stationary points in this process are exhibited in Figure 6. First, an addition-like transition state (D-TS2) is located, due to the negative charges on O1 (-0.875 e) and O2 (-0.543 e), and the positive charges are on C4 (0.394 e) and H1 (0.173 e) in IM1 and benzaldehyde. In the five-membered ring transition state D-TS2, the distances of C1-O1, O1-C4, C4-O2, O2-H1, and C1-H1 are 1.412, 1.532, 1.347, 1.225, and 1.385 Å, respectively. It apparently reveals that the O2-H1 and O1-C4 bonds are forming and that the C1-H1 bond is breaking. The imaginary vibrational frequency of D-TS2 is 1160.51i cm-1, and its mode mainly corresponds to the shift of H1 from C1 to O2 and the O1-C4 bond forming. The intermediate D-IM2 is a R-hydroxy ether in which the distances of O1-C4 and O2-H1 are 1.417 and 0.975 Å, respectively, suggesting that the O1-C4 and O2-H1 bonds are formed completely. With the formation of the O1-C4 and O2-H1 bonds, the C1-C3 bond length is shortened (1.564 Å in IM1 vs 1.430 Å in D-IM2), and the hybridization of C1 atom changes from sp3 in IM1 to sp2 in D-IM2, whereas that of C4 atom changes from sp2 in benzaldehyde to sp3 in D-IM2. Second, there is a rotational transition state (D-TS3), the imaginary vibrational frequency of D-TS3 is 15.4585i cm-1, and its mode mainly corresponds to the rotation of the benzene ring related to C5. IRC verifies the next related intermediate

(D-IM3). The dihedral angles of C1-O1-C4-O2 are 59.9° and 151.4° in D-IM2 and D-IM3, indicating that the hydroxyl have adjusted its situation ready to the next transferring of the hydrogen atom (H1) from O2 to O1. Finally, via a fourmembened ring transition state (D-TS4), the hydrogen atom (H1) transfers from O2 to O1 with simultaneous broken of the O1-C4 bond, affording cyanohydrin intermediate. The distance of C4-O1 is 2.379 Å in D-TS4, revealing the C4-O1 bond has been broken in the transition state. The tendency of the shorten of the O2-C4 bond indicating by the distances of O2-C4 in D-IM3 and D-TS4 (1.415 Å in D-IM3 to 1.365 Å in D-TS4), and the hydrogen bond of O1-H1-O2 in D-TS4 results in the final transferring of H1 from O2 to O1. The imaginary vibrational frequency of D-TS4 is 16.6496i cm-1, and its vector mainly corresponds to the approaching of O1 and H1 and the breaking of the O2-C4 bond. IRC verifies the formation of Lapworth’s cyanohydrin intermediate and the regeneration of benzaldehyde in D-IM4. As depicted in Table S1, the free energy of D-IM4 is higher than the sum of that of AD-IM2 and benzaldehyde, so the process from D-IM4 to ADIM2 and benzaldehyde is spontaneously. The sequent steps of this pathway are the same as those of Path A. As presented in Table S1 in the Supporting Information, the free energy of D-IM1 is much higher than the sum of that of IM1 and benzaldehyde, so one can get the free energy barrier related to D-TS2 from the difference of the free energies of D-TS2 and IM1+R in Table S1. Thus, the free energy barrier related to D-TS2 is 26.9 kcal/mol. The free energy barrier of the rotation transition (D-TS3) is only 0.6 kcal/mol. As given in Table 1, the free barrier of the final step to afford cyanohydrin is 20.0 kcal/mol. Obviously, these three barriers related D-TS2, D-TS3, and D-TS4 are all much lower than that of the direct 1,2-proton transfer to produce cyanohydrin in Path A. For overall Path D, six transition states (TS1, D-TS2, D-TS3, D-TS4, ADTS3, and AD-TS4) were located, and the related free energy barriers are 14.2, 26.9, 0.6, 20.0, 8.9, and 1.6 kcal/mol, respectively. So Path D is the dominant pathway, clearly manifesting that the reaction can carry out in aprotic solvents such as DMSO. In this mechanism, the intermolecular proton (H1) transfer from cyanide/benzaldehyde IM1 to oxygen (O2) of another benzaldehyde with simultaneous C4-O1 bond formation to afford a R-hydroxy ether is the rate-determining theoretically, while the step to form cyanohydrin intermediate from R-hydroxy ether is partially rate-determining for its relatively significant barrier. 3.6. A Solvent-Catalyzed Proton-Transfer to Get Lapworth “Active-Aldehyde” Carbanion in Protonic Solvents. Methanol, ethanol, and water are the conventional protonic solvents used in benzoin condensation. Considering that protonic

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solvents can participate in proton-transfer, taking methanol as a example, a solvent-catalyzed proton shift to form the Lapworth cyanohydrin is calculated (see Scheme 3).6 The potential energy surface for the methanol-catalyzed proton shift to form cyanohydrin reveals a possible transition state (E-TS5), which is a five-membered ring structure. The distances of C1-H1, H1-O3, O3-H3, H3-O1, and O1-C1 are 1.279, 1.362, 1.974, 0.982, and 1.435 Å, respectively. It is evident that the hydrogen (H3) of methanol has already transferred to O1, and H1 is transferring to O3 of methanol in this transition state. The only imaginary vibrational frequency is 814.786i cm-1, and its vector mainly corresponds to the H1 transfer from C1 to O3 of methanol and the O1-H3 bond formation. The relevant geometrical parameters of the complexes and the energy profile are shown in Figures 7 and 8, respectively. As shown in Figure 8, the free energy barrier of this step is 19.9 kcal/mol in methanol, which is lower than that of direct proton shift by 24.8 kcal/mol. As shown in Table 1, solvation effects in protonic solvents do not result in a decrease of the free energy barriers, so we presume that the step to produce the just cyanohydrin intermediate may perform via the solvent-assisted proton shift transition state E-TS5 in methanol, and we think the similar process is existing in other protonic solvents (such as ethanol and water). 4. Conclusions This article studies four pathways for the cyanide-catalyzed benzoin condensation by the density functional theory. From the results, one can see that when the title reaction is performed in protonic solvents, the mechanism involving cyanohydrin formation step catalyzed by solvent is the dominant pathway thermodynamically. However, benzaldehyde is insoluble or sparingly soluble in protonic solvents, and the dissoluble rate inevitably restraints the reaction rate of the solvent-catalyzed path to quantitative disadvantage. So we still believe Path D without protonic solvent assistance is competitive. When the cyanide-catalyzed benzoin condensation is performed in aprotic solvents such as DMSO, Path D is the dominant pathway with an overall free energy barrier of 26.9 kcal/mol, in which the formation of the cyanohydrin intermediate proceeds through the stepwise intermolecular proton transfers assisted by the reactant benzaldehyde. AD-TS3 is compact with partially overlapping face-to-face phenyl groups, in good agreement with the results of Breslow and co-workers.15-17 Acknowledgment. This project has been supported by the National Natural Science Foundation of China (Grants 20773089 and 20835003) and the Scientific Research Foundation of the Education Department of Sichuan Province (Grant 09ZC065).

He and Xue Supporting Information Available: The optimized Cartesian coordinates and geometrical structures of all stationary points along the potential energy profiles. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Wo¨hler, F.; Liebig, J. Ann. Pharm. 1832, 3, 249. (2) Lapworth, A. J. Chem. Soc. 1903, 83, 995. (3) Lapworth, A. J. Chem. Soc. 1904, 85, 1206. (4) Bredig, H. G.; E. Stern, Z. Elektrochem. 1904, 10, 582. (5) Stern, E. Z. Phys, Chem. 1905, 50, 513. (6) Kuebrich, J. P.; Schowen, R. L.; Wang, M.-S.; et al. J. Am. Chem. Soc. 1971, 93 (5), 1214. (7) Castells, J.; Lo´pez-Calahorra, F.; Domingo, L. J. Org. Chem. 1988, 53, 4433. (8) Sakaki, S.; Musashi, Y.; Ohkubo, K. J. Am. Soc. 1993, 115, 1515. (9) Marto´, J.; Lo´pez-Calahorra, F.; Bofill, J. M. J. Mol. Struct. (Theochem) 1995, 339, 179. (10) Gronert, S. Org. Lett. 2007, 9 (16), 3065. (11) Yamabe, S.; Yamazaki, S. Org. Biomol. Chem. 2009, 7, 951. (12) Linghu, X.; Bausch, C. C.; Jeffrey, S. H. J. Am. Chem. Soc. 2005, 127, 1833. (13) Wiberg, K. B. J. Am. Chem. Soc. 1954, 76, 5371. (14) Wiberg, K. B. J. Am. Chem. Soc. 1955, 77, 5988. (15) Kool, E. T.; Breslow, R. J. Am. Chem. Soc. 1988, 110, 1596. (16) Breslow, R. Acc. Chem. Res. 1991, 24, 159. (17) Breslow, R.; Connors, R. V. J. Am. Chem. Soc. 1995, 117, 6601. (18) Beck, A. D. J. Chem. Phys. 1993, 98, 5648. (19) Parr, R. G.; Yang, W. Density Functional Theory of Atoms and Molecules; Oxford University Press: Oxford, 1989. (20) Wei, D.; Tang, M. J. Phys. Chem. A. 2009, 113, 11035. (21) Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154. (22) Gonzalez, C.; Schlegel, H. B. J. Phys. Chem. 1990, 94, 5523. (23) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J. Chem. Phys. 1972, 56, 2257. (24) Barone, V.; Cossi, M. J. Phys. Chem. A. 1998, 102, 1995. (25) Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. J. Comput. Chem. 2003, 24, 669. (26) Reed, A. E.; Weinstock, R. B.; Weinhold, F. J. Chem. Phys. 1985, 83, 735. (27) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. ReV. 1988, 88, 899. (28) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A.; Jr., T.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniel, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi,r.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y. ; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head.Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 03, ReVision D.01; Gaussian, Inc.: Pittsburgh PA, 2005. (29) Hawkes, K. J.; Yates, B. F. Eur. J. Org. Chem. 2008, 5563.

JP103031Q

Mechanism Insight into the Cyanide-Catalyzed Benzoin Condensation

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