Theoretical Insight into Stereoselective Reaction Mechanisms of 2, 4

Article pubs.acs.org/JPCA

Theoretical Insight into Stereoselective Reaction Mechanisms of 2,4Pentanediol-Tethered Ketene-Olefin [2 + 2] Cycloaddition Katsumasa Kamiya,†,* Toru Matsui,‡,§ Takashi Sugimura,∥ and Yasuteru Shigeta‡ †

Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8571, Japan Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan § Department of Chemistry, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan ∥ Graduate School of Material Science, University of Hyogo, 3-2-1, Kohto, Kamigori, Hyogo 678-1297, Japan ‡

S Supporting Information *

ABSTRACT: We report ab initio molecular dynamics calculations based on density functional theory performed on an intramolecular [2 + 2] cycloaddition between ketene and olefin linked with a 2,4-pentanediol (PD) tether. We find that the encounter of the ketene and olefin moieties could be prearranged in the thermal equilibrated state before the cycloaddition. The reaction mechanism is found to be stepwise, similar to that of intermolecular ketene [2 + 2] cycloadditions with ordinary alkenes. A distinct feature of the reaction pathway for a major diastereoisomer is a differential activation free energy of about 1.5 kcal/mol, including 2.8 kcal/mol as the differential activation entropy, with a transition state consisting of a flexible nine-membered ring in the olefin-PD-ketene moiety. This theoretical study provides a reasonable explanation for the strict stereocontrollability of the PD-tethered ketene-olefin cycloaddition, irrespective of reaction types or conditions.

1. INTRODUCTION A unique propensity in ketene chemistry is to give facile [2 + 2] cycloaddition reactions with compounds such as alkenes, dienes, and imines.1−3 These cycloadditions usually proceed quickly with a high degree of stereoselectivity, which have attracted a great deal of attention as useful tools in organic synthesis. Stereoselectivity can be enhanced by using an intramolecular reaction in a way not possible in intermolecular reactions.4−9 Actually, the intramolecular version of ketenealkene cycloaddition has been used in the preparation of bicyclic cyclobutanones with good overall yield.10,11 In this case, the efficiency and selectivity of the intramolecular reaction is highly dependent on the length and flexibility of the linking part.10 An outstanding example of intramolecular ketene-olefin [2 + 2] cycloadditions is provided by using a 2,4-pentanediol (PD) tether. It is a widely available chiral compound, connecting a prochiral reactant and a reagent as a chiral tether. The PD tether has been shown to control many different reactions. Indeed, twelve different types of reactions have been conducted with the PD tether in 97−99% diastereomeric excess and in good yields.11−26 Most notably, the diastereoselectivity of the PD-tethered [2 + 2] cycloaddition of ketene and olefin has been shown to be unchanged mostly in a wide range of temperature (from −78 °C in solution to 300 °C in vapor), suggesting strongly that the stereoselectivity for PD-tethered © 2012 American Chemical Society

ketene-olefin [2 + 2] reaction is formally driven by differential activation entropy.24−26 However, the stereocontrollability for the PD-tethered reaction irrespective of reaction types or conditions is still far from being fully understood. On the theoretical side, ketene [2 + 2] cycloadditions have been studied using ab initio calculations.27−41 The PD-tether ketene-olefin system is, however, expected to be a fluxional system due to high flexibility of the PD-tether. The intramolecular reaction is thus supposed to be coupled with this stereochemical-nonrigid structural change. To investigate the reaction mechanism of this complex chemical system, ab initio molecular dynamics (AIMD) simulations are particularly suitable as a theoretical tool because it includes thermal fluctuations and electronic structural changes a priori in the theoretical description. Specifically, density functional theory (DFT),42,43 combined with methods suitable to sample reaction paths, represents a computationally efficient approach. More recently, the metadynamics approach,44,45 combined with Car−Parrinello molecular dynamics (CPMD),46 has been shown to be a versatile tool to explore the free-energy surface of a given set of reaction coordinates and allows for Received: November 30, 2011 Revised: January 5, 2012 Published: January 5, 2012 1168

dx.doi.org/10.1021/jp211542m | J. Phys. Chem. A 2012, 116, 1168−1175

The Journal of Physical Chemistry A

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core electron interactions are described by Troullier-Martins norm-conserving pseudopotentials.53 Valence electrons are represented in a plane wave basis set with an energy cutoff of 70 Ry. The ionic temperature is controlled by velocity rescaling and kept at 298 ± 40 K. An integration time step of 0.097 fs and a fictitious electron mass of 300 au ensure a good control of the conserved quantities and preserve the Born−Oppenheimer adiabaticity. The system is placed in a large cubic supercell with a = 20.00 and 16.40 Å for the equilibrium CPMD calculations of ketene intermediate state and the metadynamics simulations of intramolecular cycloaddition, respectively. Such a size guarantees that our model system is separated from its periodic image by a minimum distance of 6.7 Å, avoiding artificial interactions among images of the molecule. The reaction paths were sampled by the metadynamics approach. In this method, the collective variables sα(t) (α = 1, 2, ...), selected as representative of the reaction coordinates, are treated as new dynamical variables and added to the Car− Parrinello (CP) Lagrangian LCP along with a history-dependent Gaussian potential V(sα, t), i.e.,

microscopic insight into reaction pathways within affordable simulation times.46−51 The purpose of this work is to provide theoretical insight into the stereocontrol mechanism of PD-tethered ketene-olefin [2 + 2] cycloadditions using AIMD simulations in the framework of DFT. Here we consider the ketene-olefin cycloaddition reaction in vacuum well studied experimentally (Scheme 1).24 In this reaction, the ketene was generated by the Scheme 1. PD-Tethered Ketene-Olefin [2 + 2] Cycloaddition Studied in This Work

photolysis of a diazo carbonyl compound 1 through the Wolff rearrangement; the majority of the adduct of the (1R,6R)isomer 2 was obtained via the ketene intermediate state, and only a trace amout of the diastereomer 3 was detected in the reaction. Our calculations showed that the diastereoselectivity of the PD-tethered ketene-olefin [2 + 2] cycloaddition is ascribed to two factors: (1) the broad Γ-space around transition state (TS) in the case of 2 that could lead to the gain of differential activation entropy, and (2) the prearranged conformation for the encounter of ketene and olefin moieties in the ketene intermediate state.

1 1 L = LCP + ∑ M αsα̇2 − ∑ k α[sα(q) − sα]2 2 α 2 α + V (sα , t )

(1)

where sα(q) can be any function of an arbitrary set of ionic coordinates, q = {Rion}, and describes the process that we want to simulate. Mα and kα are fictitious effective masses and harmonic coupling constants, which were used for adiabatic decoupling between fast and slow degrees of freedom. In our specific case, we selected sα as two C−C distances in diastereomers: C1−C12 (s1) and C6−C13 (s2) (Scheme 1). These variables represent all of the slowly varying degrees of freedom and account for the formation and cleavage of each C−C bond occurring during cycloaddition. For both collective variables, M = 12.0 au and k = 0.24 were adopted. A new

2. THEORETICAL CALCULATIONS AIMD simulations were performed in the framework of a DFTbased CPMD scheme with generalized gradient approximation (GGA) on the exchange and correlation functional named after Hamprecht, Cohen, Tozer, and Handy (HCTH).52 Valence-

Figure 1. Scatterplot of the C1−C12 and C6−C13 distances obtained from a set of AIMD simulations for the cases of two diastereoisomers, (a) 2 and (b) 3. The equilibrium CPMD results for the sampling of the ketene-intermediate region are shown in red in both panels. In each panel, the results of the metadynamics simulations for the sampling of the diastereoisomer region are shown in green in each panel; blue crosses represent the positions of transition state (TS). 1169



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Figure 2. (a) Histogram of the C7−C8−C9−C10 and C8−C9−C10−C11 torsion angles, (b) scatterplot of the C7−C11 and C6−C13 distances, (c) scatterplot of the C6−C13 distance and C8−O−C1−C6 torsion angle, and (d) scatterplot of the C6−C13 distance and C10−O−C12−C13 torsion angle, obtained in AIMD simulations for the ketene intermediate state.

Table 1. Representative Bond Lengths (Å) for the Ketene Intermediate State, 2, And 3 in Thermal Equilibrium ketene intermediate 2 3

C1−C12

C6−C13

O−C1

C1−C6

O−C12

C12−C13

C13−O

5.57 (±0.82) 1.60 (±0.04) 1.59 (±0.04)

6.64 (±1.18) 1.54 (±0.04) 1.54 (±0.03)

1.38 (±0.02) 1.43 (±0.03) 1.43 (±0.03)

1.35 (±0.02) 1.58 (±0.04) 1.57 (±0.03)

1.39 (±0.03) 1.40 (±0.03) 1.40 (±0.03)

1.33 (±0.02) 1.55 (±0.04) 1.56 (±0.03)

1.18 (±0.01) 1.21 (±0.02) 1.21 (±0.02)

bonds with only two methyl substituents, the ketene intermediate state is expected to be conformationally more flexible than the cycloadducts. For an effective sampling in the reaction-coordinate space, we thus performed two independent simulations: the CPMD calculations and the metadynamics method to sample the ketene-intermediate and diastereoisomer regions, respectively. 3.1. Characteristics of Ketene Intermediate State Determined by Equilibrium CPMD. Figure 1 shows the scatterplot of the C1−C12 and C6−C13 distances of the system in the ketene intermediate state during 95 ps equilibrium CPMD simulations. The system in this state was observed to be in broad Γ-space, ranging from 2.97 to 7.62 Å and from 3.21 to 9.27 Å for the C1−C12 and C6−C13 distances, respectively. This indicates clearly that the ketene intermediate has a flexible chain-like structure. To characterize further the ketene intermediate state, we analyzed the conformation of the PD tether part. Figure 2a shows the histogram of the backbone torsion angles in the PD tether, C7−C8−C9−C10 and C8−C9−C10−C11. It was found that the PD tether takes several staggered structures, but a linear trans-trans conformer was found to be dominant. This feature

Gaussian penalty potential was added every 38.8 fs with a width and height of 0.04 Å and 0.25 kcal/mol, respectively. For the metadynamics simulations, it is not guaranteed that the obtained trajectory passes to the exact TS geometry. To determine the exact TS structure, we thus performed static DFT calculations, i.e., vibrational analyses, with a Gaussian basis set (HCTH/6-31G(d,p)), starting with the initial configurations suggested from the metadynamics simulations. The dynamical and static calculations were performed using the CPMD 3.13.254 and GAUSSIAN 03 program packages,55 respectively.

3. RESULTS AND DISCUSSION The inspection of the reaction pathway leading to each diastereoisomer from conformers of the ketene intermediate state was performed via a set of AIMD simulations making use of CPMD and the metadynamics approach. As mentioned previously, the reaction coordinates were chosen to be two C− C distances, i.e., C1−C12 and C6−C13 (Scheme 1). These reaction coordinates account for the formation and breaking of a four-membered ring (C1−C12−C13−C6) in the diastereoisomers. Because the PD tether part contains single C−C 1170



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Figure 3. The evolution of the collective variables during metadynamics for diastereoisomers of (upper) 2 and (lower) 3.

is similar to that in the case for a free n-pentane molecule.56 This linear conformation appears when the olefin and ketene moieties are close each other, as indicated by the scatterplot of the C7−C11 distance in the PD tether and C6−C13 distance shown in Figure 2b; the C7−C11 distance is large when C6− C13 distance is smaller than 4 Å. These results suggest that the system takes a flexible structure when C6−C13 distance is large, but it is likely to take a linear conformation when the olefin and ketene moieties become close. Table 1 lists representative bond lengths for the ketene intermediate state in thermal equilibrium. Double bonds that are expected formally from its chemical structure were confirmed by their bond lengths of C1−C6, C12−C13, and C13−O. However, the O−C1 and O−C12 bonds, connecting the PD tether to olefin and ketene, respectively, were found to be partially double-bonded. Their results suggested that the conformation of the olefin and/or ketene moieties with respect to the PD tether could be restricted to a certain extent through the O−C partial double bonds as compared with the case of rotation about a single bond. Indeed, a detailed analysis of the trajectory indicated the restricted conformation for the olefin in the ketene intermediate state. Figure 2c,d shows scatter plots of the C6−C13 distance against C8−O−C1−C6 and C10−O−C12− C13 torsion angles that characterize the conformations of the olefin and ketene moieties with respect to the PD tether, respectively. Although the two angles fluctuate largely when the C6−C13 distance is greater than 4 Å, they take some definite values when the C6−C13 distance is much closer. In particular, the C8−O−C1−C6 torsion angle was found to fluctuate around 0°, indicating that the C8−O−C1−C6 moiety has a tendency to take an eclipsed cis-like conformation. As a result of these conformational features, the ketene moiety can approach from one side of the olefin face. In other words, the encounter of the ketene and olefin moieties could be prearranged in the thermally equilibrated state before the PDtethered [2 + 2] cycloaddition. Details about the relationship of this cis-conformation to the reaction will be discussed in subsection 3.3. 3.2. Reaction Pathways for the Intramolecular Cycloaddition Determined by Metadynamics. As shown in the previous subsection, the system in the ketene intermediate state exhibits very high flexibility, which can be represented as a large area in the reaction-coordinate space (Figure 1). To find the

reaction path for the subsequent [2 + 2] cycloadditions, sufficient sampling of this region is thus difficult and computationally demanding. To overcome this difficulty, we started sampling from the diastereoisomer region using the metadynamics approach. In this method, a history-dependent Gaussian potential iteratively compensates the underlying free energy, and thus a system evolved with metadynamics tends to escape from a free energy minimum for the diastereomers via the lowest free energy saddle point. The metadynamics simulation was followed until the system turned out to be the ketene intermediate state. Before starting the metadynamics simulations, we performed 5.8 ps equilibrium CPMD-simulations on the two diastereomers to obtain not only the thermally equilibrated configurations and velocities for the initial state, but also the inspection of choosing next metadynamics parameters: the width of the history-dependent Gaussian potential. Table 1 lists the main bond lengths for 2 and 3 in a thermal equilibrium state. As compared with the ketene intermediate state, the formation of the C1−C12 and C6−C13 bonds in 2 and 3 leads to a conversion of the C1−C6 and C12−C13 double bonds and the O−C1 and O−C12 partial double bonds to a single bond. The four-membered ring, C1−C12−C13−C6, is distorted with two different edge (bond) lengths for both of the diastereomers, characterized by the longer C1−C12 and C1−C6 bond lengths than the C6−C13 and C12−C13 ones (Table 1). A similar distorted four-membered ring is also seen in cyclobutanones obtained from intermolecular ketene-ethylene cycloaddition,39 where the edge lengths of the ring are 1.56 Å and 1.53 Å. Taking these characteristics of the diastereoisomers into account, we selected the C1−C12 and C6−C13 distances as the collective variables, s1 and s2, respectively. In particular, the width of the history-dependent Gaussian potential was set to be the same amount of thermal fluctuation for s1 (C1−C12 distance), 0.04 Å (Table 1), and the width of the Gaussians for s2 (C6−C13 distance) was scaled by a factor 0.9 to obtain homogeneous dynamics for all collective variables. The metadynamics results are summarized as a scatterplot of the collective variables in Figure 1. The reaction of the C1− C12 and C6−C13 bond breaking occurs in a stepwise fashion for both 2 and 3; the breaking of the C1−C12 bond is followed by that of the C6−C13 bond along the pathway to the ketene intermediate state. This mechanism is similar to that of 1171



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Figure 4. Reconstructed free-energy surface (FES) in the space defined by the collective variables obtained from the metadynamics simulations for (a) 2 and (b) 3; in each panel, the FES are drawn from different angles.

Figure 5. Trajectories obtained from the equilibrium CPMD simulations with random velocities at room temperature, starting from the (a) 2-TS2 and (b) 3-TS configurations. The cross points indicate a starting point for each simulation.

(upper panel), the system escaped from the free energy minimum at ∼11 000th metastep, while 5500 more metasteps were needed to fill the local minimum completely in the 3 case (lower panel). Figure 4 shows the reconstructed free energy surface (FES) obtained from the metadynamics simulation. This clearly indicates that the exit free-energy barrier is lower for 2 than that for 3 by ∼5 kcal/mol. Using this energy difference, the differential activation free energy from the ketene intermediate, ΔΔF = F2 − F3, is estimated to be −1.5 kcal/mol.57 This value is consistent with experimental observations that the differential activation energy is −2.6 kcal/mol.58

intermolecular ketene [2 + 2] cycloadditions with ordinary alkenes, where the forming bond from the alkene to the ketene carbonyl carbon is short while the second bond to the alkene carbon atom is long.1,30 These results clearly indicated that PDtethered ketene-olefin [2 + 2] cycloaddition in a gas phase is a stepwise reaction. 3.3. Diasteroselective Mechanisms of the PD-Tethered Ketene-Olefin [2 + 2] Cycloaddition. Closer inspection of the evolution of the collective variables during metadynamics uncovered the diastereoselectivity of the PDtethered ketene-olefin [2 + 2] cycloaddition. These data are shown in Figure 3 for the diastereomer cases. In the case of 2 1172



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Figure 6. Geometries of (a) 2-TS1, (b) 2-TS2, and (c) 3-TS. The color code for the atoms is yellow for C, red for O, and white for H. The arrows indicate atomic displacements corresponding to the imaginary frequency in each case.

Table 2. Representative Bond Lengths (Å) for The TS and Metastable (MS) Configurations 2-TS1 2-MS 2-TS2 3-TS

C1−C12

C6−C13

O−C1

C1−C6

O−C12

C12−C13

C13−O

2.55 3.03 3.21 3.07

1.57 1.69 1.96 1.95

1.34 1.33 1.33 1.34

1.48 1.44 1.40 1.40

1.38 1.39 1.38 1.38

1.41 1.38 1.36 1.36

1.24 1.24 1.22 1.22

These results suggest that curvature of the FES is different between the two reaction pathways and some broad Γ-space exists nearby. As an additional check, we conducted equilibrium CPMD simulations 74 times independently with 2000 CPMD steps with random velocities at room temperature, starting from the 2-TS2 and 3-TS configurations. The results are shown in Figure 5. The existence of two 2-TSs and one 3-TS on each reaction pathway are also observed in this calculation. Notably, there are large amounts of configurations that can be accessed at room temperature around 2-TSs. This may lead by the increase of flatness on the potential energy surface around 2TSs, contributing to the gain of configurational entropy in this reaction. The broad Γ-space around TSs for the majority of diastereoisomer 2 could result from the formation of a flexible nine-membered ring in the olefin-PD-ketene moiety in its TS geometry. Figure 6 and Table 2 show the exact geometry and main distances for TS and metastable state, respectively. The major difference in TS geometries between two diastereoisomers is observed in the C6−C13 distance, where the corresponding C−C bond is formed only in the case of 2: the respective length of 1.57 Å for 2-TS1. In contrast, 3-TS has the C6−C13 distance of 1.95 Å as similar to that for 2-TS2, but the C1−C12 distance is 3.07 Å, which is longer than that for 2TS2. Analyses of the Mulliken charges and frontier orbitals of the TSs indicated a zwitterionic character for all of the TSs, through which the cycloaddition of ketenes and olefins occurs by a two-step ring-closure reaction, as indicated in intermolecular ketene [2 + 2] cycloadditions with olefins.1,26,30,32,35,39,41,59 However, in the PD-tethered intramolecular reaction, the ring-closure step is different for the two diastereomers; in the case of 2, the four-membered ring is closed after the formation of a single bond from ketene carbonyl carbon to the olefin carbon atom, whereas the ring is closed without forming such a bond in the case of 3. As a result of the single bond formation in 2-TS, a nine-membered ring of the C1, C6, C13, C12, O, C10, C9, C8, and O atoms appears. In particular, the C6−C13 bond length in 2-TS1 is 1.57 Å, which is much shorter compared with that for intermolecular ketene [2 + 2] cycloadditions with ethylene, ∼1.7 Å.39 Due to

To obtain further insight into the diastereoselection mechanism in the reaction, we determined the exact geometry of TS. Although the trajectory obtained from the metadynamics is expected to pass close to TS, another method is needed in principle to determine the exact geometry. For this reason, we performed static DFT calculations with a Gaussian basis set (HCTH/6-31G(d,p)) using the GAUSSIAN 03 program package,55 starting with the TS-like configurations obtained from the metadynamics trajectories for the diastereoisomers. The static DFT calculations showed that the exact TS geometries are similar to the initial configurations, assuring that the trajectory determined by the metadynamics passes very close to the exact TS. Interestingly, we found that two different TSs in between exist along the reaction pathway leading to the major diastereoisomer 2, while only one TS is determined for the 3 case. The position for these TSs in the reaction-coordinate space is presented in Figure 1. Regarding the energetics of these states, the static calculations showed that 2-TS1 is higher in potential energy than 2-TS2 only by 0.9 kcal/mol. In contrast, 3-TS is higher in potential energy by 4.3 kcal/mol than 2-TS1. As mentioned in the previous subsection, the differential activation free energy ΔΔF is estimated to be 1.5 kcal/mol. Taking the potential energy difference of 4.3 kcal/mol into account, differential activation entropy TΔΔS is evaluated to be 2.8 kcal/mol. Hence, the metadynamics simulations indicated a large entropy contribution to stereocontrol in the PD-tethered ketene-olefin [2 + 2] cycloaddition, as suggested in our experimental works.24,58 However, the static DFT calculations showed that differential activation entropy is 1.2 kcal/mol. This discrepancy between the two methods may originate from unharmonic dynamical effects, because the metadynamics approach evaluates the free energy difference at a finite temperature and the geometry optimization predicts the free energy difference with zero point correction within a harmonic approximation. The large amount of differential activation entropy may be ascribed to the broad Γ-space around 2-TS. Actually, the calculated imaginary frequencies are 162.1i cm−1, 212.2i cm−1, and 233.9i cm−1 for 2-TS1, 2-TS2, and 3-TS, respectively. 1173



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this strong bond formation, the C1−C6, C12−C13, and C13− O bonds are elongated (Table 2), making the nine-membered ring flexible. This flexibility may be reflected in the smallest imaginary frequency of 2-TS1 compared with the other TSs. Therefore, the existence of such a nine-membered ring around 2-TS could be one of the key factors in the increase of configurational entropy in the PD-tethered ketene-olefin [2 + 2] cycloaddition. Another important feature of the diastereoselectivity of the PD-tethered ketene-olefin [2 + 2] reaction was observed in the C8−O−C1−C6 torsion angle in the TS geometry. This angle reflects the diastereomer difference, where it takes about +60 and −180° in a product of 2 and 3, respectively. However, in the TS, this torsion angle is significantly changed for 2; it decreases from 60 to −16° in 2-TS2, while it increases from −180 to −140° in 3-TS. This means that the C8−O−C1−C6 moiety takes a cis-like conformation for 2-TS2. Such a cis-like configuration is considered to be preferred when the [2 + 2] reaction occurs, because the O−C1 bond has a partial double bond character for all TSs (Table 2). Moreover, as mentioned in the subsection 3.1, the ketene intermediate state takes similar cis-like conformation preferentially in thermal equilibrium. These results suggest that another important factor in the diastereoselectivity of the PD-tethered [2 + 2] reaction is the existence of a prearranged cis-like conformation in the ketene intermediate state.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].

ACKNOWLEDGMENTS Computations were performed on the computer facilities at the Institute for Solid-State Physics, University of Tokyo, and at the Research Center for Computational Science, Okazaki Research Facilities, National Institutes of Natural Sciences. This research is supported by a Grant-in-Aid for Young Scientists (B) (Nos. 20750004 and 22740259) from the Japan Society for the Promotion of Science (JSPS), by a Grant-in-Aid for Young Scientists (A) (No. 22685003) from JSPS, and the CREST program “Multi-scale and Multiphysics integrated simulation” from Japanese Science and Technology (JST). T.M. is thankful to the research fellowship for young scientists from JSPS.

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REFERENCES

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4. CONCLUSIONS We have investigated the reaction pathway and diastereoselectivity diastereocontrol mechanism of PD-tethered keteneolefin [2 + 2] cycloadditions using AIMD simulations based on DFT. Our calculations showed that the ketene intermediate state has a flexible chain-like structure in thermal equilibrium. However, when the ketene and olefin get close to each other, we found that the olefin takes an eclipsed cis-like conformation, and the ketene can approach from one side of the olefin face. The reaction mechanism was found to be stepwise, similar to that of intermolecular ketene [2 + 2] cycloadditions with ordinary alkenes. A distinct feature of the reaction pathway for the major diastereoisomer is a differential activation free energy of about 1.5 kcal/mol, including a differential activation entropy of 2.8 kcal/mol. The pathway involves two TSs, one of which has a flexible nine-membered ring in the olefin-PD-ketene moiety. In contrast, there is only one TS for the pathway leading to the formation of minor diastereoisomer. The diastereoselectivity of the present reaction is thus ascribed to two factors: (1) the broad Γ-space around the TS that could lead to the gain of differential activation entropy, and (2) the prearranged cis-like conformation of the encounter between the ketene and olefin moieties in the ketene intermediate state. This theoretical study clarified the distinct features of the PDtethered ketene-olefin [2 + 2] cycloadditions and provided new insight into the behavior of intramolecular reaction via a flexible tether. Furthermore, because such a reaction has similarity to enzymatic reactions, the present calculations can give some useful hints to understand a fundamental aspect of enzymatic reactions that are also largely controlled by the entropy factor.

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ASSOCIATED CONTENT

S Supporting Information *

Cartesian coordinates of TS geometries for diastereoselective reaction pathways. This material is available free of charge via the Internet at http://pubs.acs.org. 1174



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Theoretical Insight into Stereoselective Reaction Mechanisms of 2, 4

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